Observation of dressed odd-order multi-wave mixing in five-level atomic medium

doi:10.1364/OE.20.001912

Observation of dressed odd-order multi-wave mixing in five-level atomic medium

Ning Li, Zhengyang Zhao, Haixia Chen, Peiying Li, Yueheng Li, Yan Zhao, Guozhen Zhou, Shuqiao Jia, and Yanpeng Zhang »View Author Affiliations

Optics Express, Vol. 20, Issue 3, pp. 1912-1929 (2012)
http://dx.doi.org/10.1364/OE.20.001912

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▸ Article Outline
– Abstract
1. Introduction
2. Basic theory and experimental scheme
3. Dressed odd-order multi-wave mixing
4. Conclusion
– References and links

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Abstract

By selectively blocking specific laser beams, we investigate coexisting seven distinguishable dressed odd-order multi-wave mixing (MWM) signals in a K-type five-level atomic system. We demonstrate that the enhancement and suppression of dressed four-wave mixing (FWM) signal can be directly detected by scanning the dressing field instead of the probe field. We also study the temporal and spatial interference between two FWM signals. Surprisingly, the pure-suppression of six-wave mixing signal has been shifted far away from resonance by atomic velocity component. Moreover, the interactions among six MWM signals have been studied.

1. Introduction

Recently a lot of attention has been concentrated on the four-wave mixing (FWM) [1

P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. 20(9), 982–984 (1995). [CrossRef] [PubMed]

–5

H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70(6), 061804 (2004). [CrossRef]

] and six-wave-mixing (SWM) [6

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006). [CrossRef] [PubMed]

-8

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys. 108(10), 3897–3902 (1998). [CrossRef]

] under atomic coherence. And electromagnetically induced transparency (EIT) [9

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]

, 10

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]

] is an beneficial tool to investigate these multi-wave mixing (MWM) processes since the weak generated signals can be allowed to transmit through the resonant atomic medium with little absorption. It also plays an important role in lasing without inversion [11

A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14(24), 1344–1346 (1989). [CrossRef] [PubMed]

], quantum communications [12

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001). [CrossRef] [PubMed]

], slow light [13

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999). [CrossRef]

], photon controlling and information storage [14

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001). [CrossRef] [PubMed]

–16

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001). [CrossRef] [PubMed]

]. Furthermore, the enhancement and suppression of FWM also attracted the attention of many researchers, which has been experimentally studied and the generated FWM signals can be selectively enhanced and suppressed [17

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009). [CrossRef]

]. Besides, the doubly-dressed states in cold atoms were observed, in which triple-photon absorption spectrum exhibits a constructive interference between transition paths of two closely spaced, doubly-dressed-states [18

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001). [CrossRef]

, 19

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999). [CrossRef]

]. In addition, the generated FWM and SWM signals can be made to coexist and interfere with each other not only in the frequency domain but also spatially, using phase control [20

B. Anderson, Y. P. Zhang, U. Khadka, and M. Xiao, “Spatial interference between four- and six-wave mixing signals,” Opt. Lett. 33(18), 2029–2031 (2008). [CrossRef] [PubMed]

In this paper, we show seven coexisting distinguishable multi-wave mixing signals (including three FWM and four SWM signals) by selectively blocking different laser beams in a K-type five-level atomic system. Also by blocking several certain laser beams respectively, the interactions among six MWM signals have been studied. In addition, when scanning the frequency detuning of external-dressing, self-dressing and probe fields respectively in the dressed FWM process, we first analyze the corresponding relationship and differentia between the experimental results of different scanning methods, and demonstrate that scanning the dressing field can be used as a technique to directly observe the dressing effects of FWM process. Also, we first observe the enhancement and suppression of SWM signal at large detuning, due to the atomic velocity component and optical pumping effect. Moreover, we demonstrate the temporal and spatial interferences between two FWM signals.

2. Basic theory and experimental scheme

The experiments are performed in a five-level atomic system as shown in Fig. 1(a) where the five energy levels are

5 S_{1 / 2} (F = 3) (| 0 〉)

5 P_{3 / 2} (| 1 〉)

5 D_{5 / 2} (| 2 〉)

5 S_{1 / 2} (F = 2) (| 3 〉)

and

5 D_{3 / 2} (| 4 〉)

in ⁸⁵Rb. The resonant frequencies are

Ω_{1}

Ω_{2}

Ω_{3}

and

Ω_{4}

for transitions

| 0 〉

| 1 〉

| 1 〉

| 2 〉

| 1 〉

| 3 〉

and

| 1 〉

| 4 〉

respectively. The lower transition

| 0 〉

| 1 〉

is driven and probed by a weak laser beam

E_{1}

, and the two strong coupling beams

E_{2}

and

{E^{'}}_{2}

connect with the transition

| 1 〉

| 2 〉

. Two pumping beams

E_{3}

and

{E^{'}}_{3}

are applied to drive the transition

| 1 〉

| 3 〉

and two additional strong coupling beams

E_{4}

and

{E^{'}}_{4}

drive the transition

| 1 〉

| 4 〉

. In the experimental setup, the two coupling beams

E_{2}

(frequency

ω_{2}

, wave vector

k_{2}

, Rabi frequency

G_{2}

and frequency detuning

Δ_{2}

, where

Δ_{i} = Ω_{i} - ω_{i}

) and

{E^{'}}_{2}

(

ω_{2}

{k^{'}}_{2}

{G^{'}}_{2}

and

Δ_{2}

) with vertical polarization (wavelength 775.978nm) are from the same external cavity diode laser (ECDL) . The other two vertically polarized coupling beams

E_{4}

(

ω_{4}

k_{4}

G_{4}

and

Δ_{4}

) and

{E^{'}}_{4}

(

ω_{4}

{k^{'}}_{4}

{G^{'}}_{4}

and

Δ_{4}

) are from a tapered-amplifier diode laser with the same wavelength 776.157nm. Two pumping beams

E_{3}

(

ω_{3}

k_{3}

G_{3}

and

Δ_{3}

) and

{E^{'}}_{3}

(

ω_{3}

{k^{'}}_{3}

{G^{'}}_{3}

and

Δ_{3}

) with equal power are split from a LD beam and have polarizations vertical with each other via a polarization beam splitter. The probe beam

E_{1}

(

ω_{1}

k_{1}

G_{1}

and

Δ_{1}

) is generated by a ECDL (Toptica DL100L) with horizontally polarization. These laser beams are spatially designed in a square-box pattern as shown in Fig. 1(b), in which the laser beams

E_{2}

{E^{'}}_{2}

E_{3}

{E^{'}}_{3}

E_{4}

and

{E^{'}}_{4}

propagate through the Rubidium vapor cell (50mm long) with a temperature of 60 °C in the same direction with small angles (about 0.3°) between one another, and the probe beam

E_{1}

propagates in the opposite direction with a small angle from the other beams.

Fig. 1 (a) The diagram of the K-type five-level atomic system. (b) Spatial beam geometry used in the experiment. (c) The diagram of the ladder-type three-level atomic subsystem when the fields

E_{3}

{E^{'}}_{3}

E_{4}

and

{E^{'}}_{4}

are blocked and

E_{1}

E_{2}

and

{E^{'}}_{2}

are turned on. (d) The diagram of the Y-type four-level atomic subsystem when the fields

E_{3}

and

{E^{'}}_{3}

are blocked and other beams are turned on. (e) The diagram of the K-type five-level atomic system when the fields

{E^{'}}_{2}

and

{E^{'}}_{4}

are blocked only.

In such beam geometric configuration, the two-photon Doppler-free conditions will be satisfied for the two ladder-type subsystems both

| 0 〉 \to | 1 〉 \to | 2 〉

and

| 0 〉 \to | 1 〉 \to | 4 〉

, thus two EIT windows appear. When all the seven laser beams (

E_{1}

E_{2}

{E^{'}}_{2}

E_{3}

{E^{'}}_{3}

E_{4}

{E^{'}}_{4}

) are turned on, three FWM processes

E_{F 2}^{}

(satisfying the phase-matching condition

k_{F 2} = k_{1} + k_{2} - {k^{'}}_{2}

E_{F 4}^{}

(satisfying

k_{F 4} = k_{1} + k_{4} - {k^{'}}_{4}

) and

E_{F 3}^{}

(satisfying

k_{F 3} = k_{1} - {k^{'}}_{3} + k_{3}

), and four SWM processes

E_{S 2}^{}

(satisfying

k_{S 2} = k_{1} - {k^{'}}_{3} + k_{3} + k_{2} - k_{2}

{E^{'}}_{S 2}

(satisfying

{k^{'}}_{S 2} = k_{1} - {k^{'}}_{3} + k_{3} + {k^{'}}_{2} - {k^{'}}_{2}

E_{S 4}^{}

(satisfying

k_{S 4} = k_{1} - {k^{'}}_{3} + k_{3} + k_{4} - k_{4}

) and

{E^{'}}_{S 4}

(satisfying

{k^{'}}_{S 4} = k_{1} - {k^{'}}_{3} + k_{3} + {k^{'}}_{4} - {k^{'}}_{4}

) can occur simultaneously. The propagation direction of all the generated signals with horizontal polarization is determined by the phase-matching conditions, so all the signals propagate along the same direction deviated from probe beam at an angle θ, as shown in Fig. 1(a). The wave-mixing signals are detected by an avalanche photodiode detector, and the probe beam transmission is simultaneously detected by a silicon photodiode.

Generally, the expression of the density-matrix element related to the MWM signals can be obtained by solving the density-matrix equations. For the simple FWM process of

E_{F 2}^{}

, via the perturbation chain

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{10}^{(1)} \overset{ω_{2}}{\to} ρ_{20}^{(2)} \overset{- ω_{2}}{\to} ρ_{10}^{(3)}

we can obtain the third-order density element

ρ_{F 2}^{(3)} = G_{F 2} / (d_{1}^{2} d_{2})

, the amplitude of which determines the intensity of the simple FWM process, where

G_{F 2} = - i G_{1} G_{2} {({G^{'}}_{2})}^{*} \exp (i k_{F 2} \cdot r)

d_{1} = Γ_{10} + i Δ_{1}

d_{2} = Γ_{20} + i (Δ_{1} + Δ_{2})

, and

Γ_{i j}

is the transverse relaxation rate between states

| i 〉

and

| j 〉

. Similarly, for the simple FWM process of

E_{F 4}^{}

, we can obtain

ρ_{F 4}^{(3)} = G_{F 4} / (d_{1}^{2} d_{4})

via

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{10}^{(1)} \overset{ω_{4}}{\to} ρ_{40}^{(2)} \overset{- ω_{4}}{\to} ρ_{10}^{(3)}

, where

G_{F 4} = - i G_{1} G_{4} {({G^{'}}_{4})}^{*} \exp (i k_{F 4} \cdot r)

d_{4} = Γ_{40} + i (Δ_{1} + Δ_{4})

. And for the simple FWM process of

E_{F 3}^{}

, we can obtain

ρ_{F 3}^{(3)} = G_{F 3} / (d_{1}^{2} d_{4})

via

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{10}^{(1)} \overset{- ω_{3}}{\to} ρ_{30}^{(2)} \overset{ω_{3}}{\to} ρ_{10}^{(3)}

, where

G_{F 3} = - i G_{1} G_{3} {({G^{'}}_{3})}^{*} \exp (i k_{F 3} \cdot r)

d_{3} = Γ_{30} + i (Δ_{1} - Δ_{3})

. Additionally, via perturbation chain

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{10}^{(1)} \overset{- ω_{3}}{\to} ρ_{30}^{(2)} \overset{ω_{3}}{\to} ρ_{10}^{(3)} \overset{ω_{2}}{\to} ρ_{20}^{(4)} \overset{- ω_{2}}{\to} ρ_{10}^{(5)}

we can obtain

ρ_{S 2}^{(5)} = G_{S 2} / (d_{1}^{3} d_{2} d_{3})

for the simple SWM process of

E_{S 2}

, where

G_{S 2} = i G_{1} G_{2} G_{2}^{*} {G^{'}}_{3}^{*} G_{3} \exp (i k_{S 2} \cdot r)

(or

{ρ^{'}}_{S 2}^{(5)} = {G^{'}}_{S 2} / (d_{1}^{3} d_{2} d_{3})

for

{E^{'}}_{S 2}

, where

{G^{'}}_{S 2} = i G_{1} {G^{'}}_{2} {G^{'}}_{2}^{*} {G^{'}}_{3}^{*} G_{3} \exp (i {k^{'}}_{S 2} \cdot r)

). And via

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{10}^{(1)} \overset{- ω_{3}}{\to} ρ_{30}^{(2)} \overset{ω_{3}}{\to} ρ_{10}^{(3)} \overset{ω_{4}}{\to} ρ_{40}^{(4)} \overset{- ω_{4}}{\to} ρ_{10}^{(5)}

we obtain

ρ_{S 4}^{(5)} = G_{S 4} / (d_{1}^{3} d_{4} d_{3})

for the simple SWM process of

E_{S 4}

, where

G_{S 4} = i G_{1} G_{4} G_{4}^{*} {G^{'}}_{3}^{*} G_{3} \exp (i k_{S 4} \cdot r)

(or

{ρ^{'}}_{S 4}^{(5)} = {G^{'}}_{S 4} / (d_{1}^{3} d_{4} d_{3})

for

{E^{'}}_{S 4}

, where

{G^{'}}_{S 4} = i G_{1} {G^{'}}_{4} {G^{'}}_{4}^{*} {G^{'}}_{3}^{*} G_{3} \exp (i {k^{'}}_{S 4} \cdot r)

). Further, the dressing effect on these MWM signals and the interaction among them will be researched in the following section.

In the experiments, these multi-wave mixing signals are researched by selectively blocking different laser beams. When the beams

E_{3}

{E^{'}}_{3}

E_{4}

and

{E^{'}}_{4}

are blocked and

E_{1}

E_{2}

and

{E^{'}}_{2}

are turned on (as shown in Fig. 1(c)), only the

E_{F 2}^{}

signal with self-dressing effect could be generated in the ladder-type three-level subsystem

| 0 〉 \to | 1 〉 \to | 2 〉

. When the beams

E_{3}

and

{E^{'}}_{3}

are blocked and other beams on (Fig. 1(d)), two FWM signals

E_{F 2}^{}

and

E_{F 4}^{}

will coexist in the Y-type four-level subsystem, both of them would be perturbed by self-dressing effect and external-dressing effect, and spatiotemporal coherent interference and interaction between them could be observed. When the beams

{E^{'}}_{2}

and

{E^{'}}_{4}^{}

are blocked only (Fig. 1(e)), two SWM signals

E_{S 2}^{}

and

E_{S 4}

will coexist and interact with each other.

3. Dressed odd-order multi-wave mixing

By individually adjusting the frequency detunings

Δ_{2}

and

Δ_{4}

, these generated wave-mixing signals can be separated in spectra for the identification, or be overlapped for investigating the interplay among them. Firstly, by detuning the frequency of the participating laser beams and blocking one or two participating laser beams, we can successfully separate two EIT windows and these MWM signals can be identified. Figures 2(a) -2(e) present the measured signals versus the probe detuning

Δ_{1}

with different laser beams blocked, in which the lower curves are the measured MWM signals while the corresponding probe transmission signals versus

Δ_{1}

are shown in the upper curves. Figure 2(a) depicts the case when all the participating laser beams are turned on, and Figs. 2(b), 2(c), 2(d) and 2(e) show the measured signals when the laser beams or beam combinations

{E^{'}}_{2}

E_{2}

E_{4} & {E^{'}}_{4}

and

E_{3} & {E^{'}}_{3}

are blocked, respectively. In the upper curves, the left EIT window is created by

E_{4}

(

{E^{'}}_{4}

) at

Δ_{1} = - 140MHz

satisfying

Δ_{1} + Δ_{4} = 0

and the right one is created by

E_{2}

(

{E^{'}}_{2}

) at

Δ_{1} =150MHz

satisfying

Δ_{1} + Δ_{2} = 0

. The generated FWM and SWM signals except for

E_{F 3}^{}

all fall into these two separate EIT windows, so the linear absorptions of the generated signals are greatly suppressed. Specifically, the MWM signals related to

E_{4}

(

{E^{'}}_{4}

) (i.e.

E_{F 4}^{}

E_{S 4}^{}

and

{E^{'}}_{S 4}

) fall into the

| 0 〉 \to | 1 〉 \to | 4 〉

EIT window while the MWM signals related to

E_{2}

(

{E^{'}}_{2}

) (i.e.

E_{F 2}^{}

E_{S 2}^{}

and

{E^{'}}_{S 2}

) fall into the

| 0 〉 \to | 1 〉 \to | 2 〉

EIT window. The FWM signal

E_{F 3}^{}

can be obtained in Figs. 2(a)-(d), and it appears as a Doppler broadened background signal because the Doppler-free condition cannot be satisfied in the FWM process generating

E_{F 3}^{}

with opposite propagation direction between

E_{1}^{}

and

E_{3}^{}

(

{E^{'}}_{3}^{}

). By comparing Fig. 2(a) with Fig. 2(d), we find the interaction between MWM signals related to

E_{4}

(

{E^{'}}_{4}

) and those related to

E_{2}

(

{E^{'}}_{2}

) does not exist when the two EIT widows are separated from each other, since the intensity of the MWM signals related to

E_{2}

(

{E^{'}}_{2}

) behaves identical in both curves.

Fig. 2 The probe transmission (the upper curves) and measured MWM signals (the bottom curves) with different ways of blocking laser beams. The left peaks show the EIT window and MWM signals related to

E_{4}

(

{E^{'}}_{4}

) and the right peaks are related to

E_{2}

(

{E^{'}}_{2}

). (a) Measured total MWM signals with all beams turned on. (b) Measured MWM signals related to

E_{4}

(

{E^{'}}_{4}

) and SWM signal

E_{S 2}

, with

{E^{'}}_{2}

blocked. (c) Measured MWM signals related to

E_{4}

(

{E^{'}}_{4}

) and SWM signal

{E^{'}}_{S 2}

, with

E_{2}

blocked. (d) Measured MWM signals related to

E_{2}

(

{E^{'}}_{2}

) with

E_{4}

and

{E^{'}}_{4}

blocked. (e) Measured FWM signal

E_{F 2}^{}

and

E_{F 4}^{}

with

E_{3}

and

{E^{'}}_{3}

blocked. The experimental parameters are

Δ_{2} = - 150MHz

Δ_{4} =140MHz

Δ_{3} =0MHz

, and the powers of all laser beams are 5.3mW (

E_{1}

), 40.9mW (

E_{2}

), 5mW (

{E^{'}}_{2}

), 44mW (

E_{3}

and

{E^{'}}_{3}

), 21mW (

E_{4}

and

{E^{'}}_{4}

Moreover, the interaction between FWM and SWM processes in the same EIT window of

E_{2}

(

{E^{'}}_{2}

) can be observed, by comparing the total MWM signal related to

E_{2}

(

{E^{'}}_{2}

) (Fig. 2(a)) with the sum of FWM signal

E_{F 2}^{}

(Fig. 2(e)), SWM signals

E_{S 2}

(Fig. 2(b)) and

{E^{'}}_{S 2}

(Fig. 2(c)) in amplitude. We can find that the MWM signal is suppressed by 40%, which shows the interaction and competition between FWM and SWM when they coexist. This phenomenon could be explained by the dressing effect of

E_{3}^{}

(

{E^{'}}_{3}^{}

) on FWM signal

E_{F 2}^{}

. The dressed FWM process can be described by

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{(G_{3} \pm) 0}^{(1)} \overset{ω_{2}}{\to} ρ_{20}^{(2)} \overset{- ω_{2}}{\to} ρ_{(G_{3} \pm) 0}^{(3)}

, we can obtain

ρ_{F 2}^{(3)} = G_{F 2} / [d_{2} {(d_{1} + {| G_{3}^{b} |}^{2} / d_{3})}^{2}]

, where

G_{3}^{b} = G_{3} + {G^{'}}_{3}

. And the density-matrix element related to the SWM processes can be obtained as

ρ_{S 2}^{(5)} = G_{S 2} / (d_{1}^{3} d_{2} d_{3})

and

{ρ^{'}}_{S 2}^{(5)} = {G^{'}}_{S 2} / (d_{1}^{3} d_{2} d_{3})

(for simplicity, the self-dressing effects on

E_{F 2}^{}

E_{S 2}

and

{E^{'}}_{S 2}

are not considered here). Since these MWM processes exist at the same time in the experiment, and the signals are copropagating in the same direction, the total detected MWM signal (Fig. 2(a)) will be proportional to the mod square of

ρ_{M}

, where

ρ_{M} = ρ_{S 2}^{(5)} + {ρ^{'}}_{S 2}^{(5)} + ρ_{F2}^{(3)}

Next, we investigate the singly-dressed FWM process in the ladder-type three-level subsystem

| 0 〉 \to | 1 〉 \to | 2 〉

(shown as Fig. 1(c)) when only the laser beams

E_{1}

E_{2}

and

{E^{'}}_{2}

are turned on. In this three-level subsystem, only the wave-mixing signal

E_{F 2}^{}

is generated, with self-dressing effect of

E_{2}

(

{E^{'}}_{2}

). According to the perturbation chain of the self-dressed FWM process

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{(G_{2} \pm) 0}^{(1)} \overset{ω_{2}}{\to} ρ_{20}^{(2)} \overset{- ω_{2}}{\to} ρ_{(G_{2} \pm) 0}^{(3)}

, we obtain

ρ_{F 2}^{(3)} = G_{F 2} / [d_{2} {(d_{1} + {| G_{2}^{b} |}^{2} / d_{2})}^{2}]

for this singly-dressed FWM process, where

G_{2}^{b} = G_{2} + {G^{'}}_{2}

The spectra of the singly-dressed FWM process are shown in Fig. 3 . Figures 3(a1) and (a2) respectively present the intensities of the probe transmission (Fig. 3(a1)) and

E_{F 2}^{}

(Fig. 3(a2)) versus

Δ_{2}

at discrete

Δ_{1}

values. Figure 3(a3) and (a4) respectively depict the intensities of probe transmission (Fig. 3(a3)) and

E_{F 2}^{}

(Fig. 3(a4)) versus

Δ_{1}

at discrete

Δ_{2}

values, and the Doppler Broadening of the probe transmission signal in Fig. 3(a3) has been subtracted. Figures 3(b1), (b3), (b4) and (b5) are the theoretical calculations corresponding to Figs. 3(a1)-(a4), and Fig. 3(b2) represents the theoretical enhancement and suppression of

E_{F 2}^{}

, which respectively depicted as the peak and dip on each baseline of the curves, by the self-dressing effect. Notice the experimentally obtained

E_{F 2}^{}

signal when scanning

Δ_{2}

(Fig. 3(a2)) includes two components: the pure FWM signal when not considering dressing effect, and the modification (enhancement and suppression) of the FWM process which is theoretically shown in Fig. 3(b2). Figure 3(c) shows the singly-dressed energy level diagrams corresponding to the curves at discrete frequency detunings in Fig. 3(a).

Fig. 3 (a) The measured intensity of (a1) the probe transmission and (a2) the singly-dressed FWM signal

E_{F 2}^{}

versus

Δ_{2}

at discrete probe detunings

Δ_{1} = - 80, - 20, 0, 20 and 80 MHz

, and the measured intensity of (a3) the probe transmission and (a4) the singly-dressed FWM signal

E_{F 2}^{}

versus

Δ_{1}

at discrete dressing detunings

Δ_{2} = 80, 20, 0, - 20 and - 80 MHz

. (b1), (b3), (b4), (b5) are theoretical calculations corresponding to (a1)-(a4). (b2) is the theoretical calculations of enhancement and suppression of singly-dressed

E_{F 2}^{}

. (c) The dressed energy level diagrams corresponding to (a). Powers of participating laser beams are 4mW (

E_{1}

), 34.5mW (

E_{2}

), 8.7mW (

{E^{'}}_{2}

).The detuning range is 200MHz when scanning

Δ_{1}

, 60MHz when scanning

Δ_{2}

When scanning

Δ_{2}

, the FWM signal shows the evolution from pure-enhancement (

Δ_{1} = - 80 MHz

), to first enhancement and next suppression (

Δ_{1} = - 20 MHz

), to pure-suppression (

Δ_{1} = 0

), to first suppression and next enhancement (

Δ_{1} = 20 MHz

), to pure-enhancement (

Δ_{1} = 80 MHz

), as shown in Fig. 3(b2). And the corresponding probe transmission shows the evolution from pure-EIA, to first EIA and next EIT, to pure-EIT, to first EIT and next EIA, finally to pure-EIA (electromagnetically induced absorption) in series as shown in Fig. 3(a1). The height of each baseline of the curves represents the probe transmission without dressing effect of

E_{2}

(

{E^{'}}_{2}

) versus probe detuning

Δ_{1}

, while the peak and dip on each baseline represent EIT and EIA respectively. We can see that every enhancement and suppression correspond to EIA and EIT respectively, and the curves show symmetric behavior.

In order to understand the phenomena mentioned above, we resort to the singly-dressed energy level diagrams in Fig. 3(c). With the self-dressing effect of

E_{2}

(

{E^{'}}_{2}

), the energy level

| 1 〉

will be split into two dressed states

| G_{2} \pm 〉

, as shown in Figs. 3(c1)-3(c5). When

Δ_{2}

is scanned at

Δ_{1} = 0

, on the one hand, EIT is obtained in Fig. 3(a1) at the point

Δ_{2} = 0

where the suppression condition

Δ_{1} + Δ_{2} = 0

is satisfied. On the other hand, a pure-suppression of

E_{F 2}^{}

is gotten in Fig. 3(b2) because the probe field

E_{1}

could not resonate with either of the two dressed energy levels

| G_{2} \pm 〉

, as shown in Fig. 3(c3). In the region with

Δ_{1} < 0

, when

Δ_{2}

is scanned, the probe transmission shows EIA firstly and EIT afterwards in Fig. 3(a1) at

Δ_{1} = - 20 MHz

. Correspondingly,

E_{F 2}^{}

is first enhanced when the EIA is gotten and next suppressed when the EIT is obtained, shown in Fig. 3(b2) at

Δ_{1} = - 20 MHz

. The reason for the first EIA and the corresponding enhancement of

E_{F 2}^{}

is that the probe field

E_{1}

resonates with the dressed state

| G_{2} + 〉

at first, thus the enhancement condition

Δ_{1} + (Δ_{2} + \sqrt{Δ_{2}^{2} + 4 {| G_{2}^{b} |}^{2}}) / 2 = 0

is satisfied. While the reason for the next EIT and the corresponding suppression of

E_{F 2}^{}

is that two-photon resonance occurs so as to satisfy the suppression condition

Δ_{1} + Δ_{2} = 0

(see Fig. 3(c2)). When

Δ_{1}

changes to be positive, the curves at

Δ_{1} =2 0 MHz

show symmetric evolution behavior with the curves at

Δ_{1} = - 20 MHz

, i.e., EIT as well as a suppression of

E_{F 2}^{}

are obtained due to the two-photon resonance which matched the suppression condition

Δ_{1} + Δ_{2} = 0

firstly; and then EIA as well as an enhancement of

E_{F 2}^{}

are obtained when

E_{1}

is in resonance with

| G_{2} - 〉

satisfying the enhancement condition

Δ_{1} + (Δ_{2} - \sqrt{Δ_{2}^{2} + 4 {| G_{2}^{b} |}^{2}}) / 2 = 0

, as depicted in Fig. 3(c4). When

Δ_{1}

is far away from resonance point (

Δ_{1} = \pm 80 MHz

), the pure-EIA as well as the pure-enhancement of

E_{F 2}^{}

are obtained because the probe field can only resonate with one of the two dressed states

| G_{2} \pm 〉

(as shown in Figs. 3(c1) and 3(c5)).

On the other hand, when

Δ_{2}

is set at discrete values orderly from positive to negative and

Δ_{1}

is scanned, the probe transmission shows an EIT window on each curve in Fig. 3(a3) satisfying

Δ_{1} + Δ_{2} = 0

. Also, the FWM signal

E_{F 2}^{}

presents double peaks (Fig. 3(a4)), due to Autler-Townes (AT) splitting. The two peaks are obtained when

E_{1}

resonates with

| G_{4} + 〉

and

| G_{4} - 〉

, respectively. The theoretical calculations (Fig. 3(b)) are in good agreement with the experimental results (Fig. 3(a)).

Moreover, when we compare the results of these two kinds of scanning method (i.e. scanning

Δ_{2}

at discrete

Δ_{1}

values, and scanning

Δ_{1}

at discrete

Δ_{2}

values), an interesting corresponding relationship between them could be discovered, as expressed with the dash lines in Fig. 3(a) and 3(b). Referring to the dressed energy level diagrams in Figs. 3(c), one can easily find out that the curves in the same column which are connected by dash lines correspond to the same dressed energy level diagram in Fig. 3(c), although these curves are obtained by scanning different fields. In other words, the positions of enhancement points and suppression points of FWM signal in the probe frequency detuning (

Δ_{1}

) domain correspond with the positions in the dressing frequency detuning (

Δ_{2}

) domain, satisfying same enhancement/suppression conditions. Take the curves obtained when scanning

Δ_{2}

Δ_{1} = - 20 MHz

in Figs. 3(b1)-3(b2), and curves obtained when scanning

Δ_{1}

Δ_{2} = 20 MHz

in Figs. 3(b4)-3(b5) for example. These four curves, although gotten by scanning different field, correspond to the same energy state depicted in Fig. 3(c2) and reveal some common features. When

E_{1}

resonates with the dressed state

| G_{2} + 〉

, a dip of probe transmission (EIA) is gotten both in Fig. 3(b1) and 3(b4), and a peak (enhancement point) of

E_{F 2}^{}

appears correspondingly both in Fig. 3(b2) and 3(b5), as the left dash line expresses; when two-photon resonance occurs at the point

Δ_{1} + Δ_{2} = 0

, a peak (EIT) is gotten both in Fig. 3(b1) and 3(b4), and a dip (suppression point) of

E_{F 2}^{}

appears correspondingly both in Fig. 3(b2) and 3(b5), as the right dash line expresses. Additionally, we notice that when scanning the probe detuning, two enhancement points (i.e. the two peaks of AT splitting) and one suppression point could be obtained, while when scanning the dressing detuning, only one enhancement point and one suppression point could be gotten at most. The reason is that the two splitting states

| G_{2} \pm 〉

could not move across the original position of

| 1 〉

and therefore only one of them can resonate with

E_{1}

when scanning the dressing detuning.

Furthermore, the spectra of the doubly-dressed FWM process of

E_{F 2}^{}

in the Y-type four-level subsystem are investigated as shown in Fig. 4 , with the laser beams

E_{3}

{E^{'}}_{3}

and

{E^{'}}_{4}

blocked and

E_{1}

E_{2}

{E^{'}}_{2}

and

E_{4}

turned on. Since

E_{4}

is turned on, the FWM signal

E_{F 2}^{}

is dressed by

E_{4}

(external-dressing effect) as well as

E_{2}

(

{E^{'}}_{2}

) (self-dressing effect). According to the perturbation chain of the doubly-dressed FWM process:

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{(G_{2} \pm G_{4} \pm) 0}^{(1)} \overset{ω_{2}}{\to} ρ_{20}^{(2)} \overset{- ω_{2}}{\to} ρ_{(G_{2} \pm G_{4} \pm) 0}^{(3)}

, we can obtain

ρ_{F 2}^{(3)} = G_{F 2} / [{(d_{1} + {| G_{2}^{b} |}^{2} / d_{2} + {| G_{4} |}^{2} / d_{4})}^{2} d_{2}]

for the doubly-dressed FWM process.

Fig. 4 (a) The measured intensity of (a1) the probe transmission and (a2) the doubly-dressed FWM signal

E_{F 2}^{}

versus

Δ_{2}

at discrete probe detunings

Δ_{1} = - 80, - 40, - 20, - 10, 0, 10, 20, 40 and 80 MHz

, and the measured intensity of (a3) the probe transmission and (a4) the doubly-dressed FWM signal

E_{F 2}^{}

versus

Δ_{1}

at discrete self-dressing detunings

Δ_{2} = 80, 40, 20, 10, 0, - 10, - 20, - 40 and - 80 MHz

(

Δ_{4}

is fixed at

Δ_{4} = 0

). (b1), (b3), (b4), (b5) are theoretical calculations corresponding to (a1)-(a4). (b2) is the theoretical calculations of enhancement and suppression of doubly-dressed

E_{F 2}^{}

. (c) The energy level diagrams corresponding to (a). (d) The measured intensity of (d1) the probe transmission and (d2) the doubly-dressed FWM signal

E_{F 2}^{}

versus

Δ_{4}

at discrete probe detunings

Δ_{1} = - 80, - 40, - 20, - 10, 0, 10, 20, 40 and 80 MHz

, and the measured intensity of (d3) the probe transmission and (d4) the doubly-dressed FWM signal

E_{F 2}^{}

versus

Δ_{1}

at discrete external-dressing detunings

Δ_{4} = 80, 40, 20, 10, 0, - 10, - 20, - 40 and - 80 MHz

(

Δ_{2}

is fixed at

Δ_{2} = 0

). (e1)-(e4) Theoretical calculations corresponding to (d1)-(d4). (f) The energy level diagrams corresponding to (d). Powers of participating laser beams are 4.6mW (

E_{1}

), 33mW (

E_{2}

), 8.4mW (

{E^{'}}_{2}

), 39mW (

E_{4}

Firstly, the probe transmission and FWM signal

E_{F 2}^{}

versus probe detuning

Δ_{1}

and self-dressing detuning

Δ_{2}

are investigated (Figs. 4(a)-4(c)). Figures 4(a1) and 4(a2) present the intensities of the probe transmission (Fig. 4(a1)) and

E_{F 2}^{}

(Fig. 4(a2)), respectively, versus

Δ_{2}

at discrete

Δ_{1}

values. Figures 4(a3) and (a4) depict the intensities of probe transmission (Fig. 4(a3)) and

E_{F 2}^{}

(Fig. 4(a4)) versus

Δ_{1}

, respectively, at discrete

Δ_{2}

values (with fixed

Δ_{4}

Δ_{4} = 0

). Notice the Doppler Broadening of the probe transmission signal in Fig. 3(a3) has been subtracted. Figures 4(b1), 4(b3), 4(b4) and 4(b5) are the theoretical calculations corresponding to Fig. 4(a1)-(a4), while Fig. 4(b2) represents the theoretical enhancement and suppression of

E_{F 2}^{}

, respectively expressed by the peak and dip on each baseline of the curves. Figure 4(c) show the doubly-dressed energy level diagrams corresponding to the curves at discrete detuning values in Fig. 4(a).

When

Δ_{1}

is set at discrete values orderly from negative to positive and

Δ_{2}

is scanned, the experimentally obtained

E_{F 2}^{}

signal is shown in Fig. 4(a2), including two components: the pure FWM signal when not considering dressing effect, and the modification (enhancement and suppression) of the FWM process which is theoretically shown in Fig. 4(b2). The profile of all the baselines in Fig. 4(b2) reveals AT splitting of

E_{4}

, and the transition of enhancement and suppression in each curve is induced by the interaction between

E_{2}

(

{E^{'}}_{2}

) and

E_{4}

, showing the evolution from pure-enhancement (

Δ_{1} = - 80 MHz

), to first enhancement and next suppression (

Δ_{1} = - 40 MHz

), to pure-suppression (

Δ_{1} = - 20 MHz

), to first suppression and next enhancement (

Δ_{1} = - 10 MHz

), to pure-suppression (

Δ_{1} = 0

), to first enhancement and next suppression (

Δ_{1} = 10 MHz

), to pure-suppression (

Δ_{1} = 20 MHz

), to first suppression and next enhancement (

Δ_{1} = 40 MHz

), finally to pure-enhancement (

Δ_{1} = 80 MHz

). Correspondingly, the probe transmission shows the evolution from pure-EIA, to first EIA and next EIT, to pure-EIT, to first EIT and next EIA, to pure-EIT, to first EIA and next EIT, to pure-EIT, to first EIT and next EIA, finally to pure-EIA in series as shown in Fig. 4(a1). The height of the baseline of each curve represents the probe transmission without dressing field

E_{2}

(

{E^{'}}_{2}

) versus probe detuning

Δ_{1}

. The profile of these baselines reveals an EIT window induced by external-dressing field

E_{4}

Δ_{1} = - Δ_{4}

. While the peak and dip on each baseline of the curves represent EIT and EIA induced by self-dressing fields

E_{2}

and

{E^{'}}_{2}

. We can see that every enhancement and suppression correspond to EIA and EIT respectively, which is similar to the singly-dressing case observed in Fig. 3.

Such variations in the probe transmission and the transition of enhancement and suppression of

E_{F 2}^{}

are caused by the interaction of the dressing fields

E_{2}

(

{E^{'}}_{2}

) and

E_{4}

. Because of the doubly-dressing effect, the energy level

| 1 〉

is totally split into three dressed states (shown in Fig. 4(c)). Firstly under the external-dressing effect of

E_{4}

, the energy level

| 1 〉

will be broken into two primarily dressed states

| G_{4} \pm 〉

. Then in the region with

Δ_{1} < 0

, when

Δ_{2}

is scanned around

| G_{4} + 〉

, two secondarily dressed states

| G_{4} + G_{2} \pm 〉

could be created from

| G_{4} + 〉

by the self-dressing effect of

E_{2}

(

{E^{'}}_{2}

), as shown in Figs. 4(c1)-4(c4). Symmetrically, in the region with

Δ_{1} > 0

, when

Δ_{2}

is scanned around

| G_{4} - 〉

, two secondarily dressed states

| G_{4} - G_{2} \pm 〉

could be created from

| G_{4} - 〉

, as shown in Figs. 4(c6)-(c9). Since the phenomena and analysis method are similar with those in the singly-dressing case, here we only give the enhancement and suppression conditions as

Δ_{1} + ({Δ^{'}}_{2} \pm \sqrt{{Δ^{'}}_{2}^{2} + 4 {| G_{2}^{b} |}^{2}}) / 2 + G_{4} = 0

and

Δ_{1} + Δ_{2} = 0

for

Δ_{1} < 0

, where

{Δ^{'}}_{2} = Δ_{2} - G_{4}

represents the detuning of

E_{2}

(

{E^{'}}_{2}

) from

| G_{4} + 〉

, and

Δ_{1} + ({Δ^{'}}_{2} \pm \sqrt{{Δ^{'}}_{2}^{2} + 4 {| G_{2}^{b} |}^{2}}) / 2 - G_{4} = 0

and

Δ_{1} + Δ_{2} = 0

for

Δ_{1} > 0

, where

{Δ^{'}}_{2} = Δ_{2} + G_{4}

represents the detuning of

E_{2}

(

{E^{'}}_{2}

) from

| G_{4} - 〉

. When the enhancement condition is satisfied, the probe field

E_{1}

resonates with one of the secondarily dressed states, leading to an EIA of probe transmission and enhancement of

E_{F 2}^{}

. When the suppression condition is satisfied, two-photon resonance occurs, leading to an EIT and suppression of

E_{F 2}^{}

. Especially, we notice the enhancement and suppression of

E_{F 2}^{}

in Fig. 4(b2) show symmetric behavior with three symmetric centers at

Δ_{1} = 0, - 20, and 20 MHz

, all of which are pure-suppression. The pure-suppression at

Δ_{1} = 0 MHz

is induced by primary dressing effect of

E_{4}

, while pure-suppressions at

Δ_{1} = \pm 20 MHz

are caused by the secondary dressing effect of

E_{2}

(

{E^{'}}_{2}

On the other hand, when

Δ_{2}

is set at discrete values orderly from positive to negative and

Δ_{1}

is scanned, the intensity of probe transmission shows double EIT windows on each curve in Fig. 4(a3), which are EIT windows

| 0 〉 \to | 1 〉 \to | 2 〉

(appearing at

Δ_{1} = - Δ_{2}

) and

| 0 〉 \to | 1 〉 \to | 4 〉

(appearing at

Δ_{1} = - Δ_{4}

), respectively. As

Δ_{4}

is fixed at

Δ_{4} = 0

and

Δ_{2}

is set at discrete values from positive to negative, the EIT window

| 0 〉 \to | 1 〉 \to | 4 〉

is fixed at

Δ_{1} = - Δ_{4} = 0

and the EIT window

| 0 〉 \to | 1 〉 \to | 2 〉

moves from negative to positive. Especially, when

Δ_{2}

is set at

Δ_{2} = 0

, the two EIT windows overlap as shown in Fig. 4(a3), and a double-peak FWM signal is obtained because both

E_{2}

(

{E^{'}}_{2}

) and

E_{4}

dress the energy level

| 1 〉

simultaneously into two dressed states

| + 〉

and

| - 〉

, as shown in Fig. 4(a4). When

Δ_{2}

is set at

Δ_{2} \neq 0

, in the process of scanning

Δ_{1}

, the FWM signal

E_{F 2}^{}

presents three peaks, corresponding to the three dressed state respectively. Firstly,

E_{4}

dresses

| 1 〉

into two primarily dressed state

| G_{4} + 〉

and

| G_{4} - 〉

, corresponding to primary AT splitting. Then when the frequency of

E_{2}^{}

and

{E^{'}}_{2}

is tuned so as to move the

| 0 〉 \to | 1 〉 \to | 2 〉

EIT window into the left FWM peak (

Δ_{2} > 0

), secondary AT splitting occurs and the left peak splits into two peaks, respectively corresponding to secondarily dressed states

| G_{4} + G_{2} + 〉

and

| G_{4} + G_{2} - 〉

. Symmetrically, in the region with

Δ_{2} < 0

, the three peaks corresponding to

| G_{4} + 〉

| G_{4} - G_{2} + 〉

and

| G_{4} - G_{2} - 〉

respectively. The theoretical calculations (Fig. 4(b)) are in good agreement with the experimental results (Fig. 4(a)).

When comparing the results of these two kinds of scanning method (i.e. scanning

Δ_{2}

at discrete

Δ_{1}

values, and scanning

Δ_{1}

at discrete

Δ_{2}

values), the corresponding relationship could also be discovered, as expressed with the dash lines in Figs. 4(a) and 4(b). By referring to the energy level diagrams in Figs. 4(c), one can easily find out that positions of enhancement points and suppression points of FWM signal in the probe frequency detuning (

Δ_{1}

) domain correspond with the positions in the self-dressing frequency detuning (

Δ_{2}

) domain, satisfying same enhancement/suppression conditions. Take the curves at

Δ_{1} = - 40 MHz

in Figs. 4(b1)-(b2) and the curves at

Δ_{2} = 40 MHz

in Figs. 4(b4)-4(b5) for example. These four curves, although gotten by scanning different fields, correspond to the same energy state depicted in Fig. 4(c2) and reveal some common features. When

E_{1}

resonates with the dressed state

| G_{4} + G_{2} + 〉

, a dip of probe transmission (EIA) is gotten both in Fig. 4(b1) and 4(b4), and a peak (enhancement point) of

E_{F 2}^{}

signal appears both in Fig. 4(b2) and 4(b5), as the left dash line expresses; when two-photon resonance (

Δ_{1} + Δ_{2} = 0

) occurs, a peak (EIT) is gotten both in Fig. 4(b1) and 4(b4), and a dip (suppression point) appears both in Fig. 4(b2) and (b5), as the right dash line expresses. Especially, the position of the pure-suppression at

Δ_{1} = 0

in Fig. 4(b2) corresponds to the center of primary AT splitting at

Δ_{2} = 0

in Fig. 4(b5); and the positions of the pure-suppression at

Δ_{1} = \pm 20 MHz

in Fig. 4(b2) correspond to the center of secondary AT splitting at

Δ_{2} = \pm 20 MHz

in Fig. 4(b5). We also notice that when

Δ_{1}

scanned, three enhancement points and two suppression points could be obtained, while when scanning

Δ_{2}

only one enhancement point and one suppression point could be gotten at most.

Next, we investigate the probe transmission and the enhancement and suppression of

E_{F 2}^{}

versus the probe detuning

Δ_{1}

and external-dressing detuning

Δ_{4}

(Figs. 4(d)-4(e)). Figures 4(d1) and 4(d2) respectively present the intensities of the probe transmission (Fig. 4(d1)) and the enhancement and suppression of

E_{F 2}^{}

(Fig. 4(d2)) versus

Δ_{4}

at discrete

Δ_{1}

values. While Fig. 4(d3) and (d4) depict the intensities of probe transmission (Fig. 4(d3)) and

E_{F 2}^{}

(Fig. 4(d4)) versus

Δ_{1}

at discrete

Δ_{4}

values (with fixed

Δ_{2}

Δ_{2} = 0

). Figures 4(e1)-4(e4) are the theoretical calculations corresponding to Figs. 4(d1)-4(d4). Figure 4(f) shows the doubly-dressed energy level diagrams corresponding to the curves at discrete detuning values in Fig. 4(d). Similar to the above discussion of Figs. 4(a)-(c), the signal

E_{F 2}^{}

is dressed by both

E_{2}

(

{E^{'}}_{2}

) and

E_{4}

. Firstly, under the self-dressing effect of

E_{2}

(

{E^{'}}_{2}

), the state

| 1 〉

will be broken into two primarily dressed states

| G_{2} \pm 〉

. Then in the region with

Δ_{1} < 0

, when

Δ_{4}

is scanned around

| G_{2} + 〉

, two secondarily dressed states

| G_{2} + G_{4} \pm 〉

could be created from

| G_{2} + 〉

by the external-dressing field

E_{4}

, as shown in Fig. 4(f1)-4(f4). Symmetrically, in the region with

Δ_{1} > 0

, when

Δ_{4}

is scanned around

| G_{2} - 〉

, two secondarily dressed states

| G_{2} - G_{4} \pm 〉

could be created from

| G_{2} - 〉

, as shown in Fig. 4(f6)-4(f9). Here we only give the enhancement and suppression conditions as

Δ_{1} + ({Δ^{'}}_{4} \pm \sqrt{{Δ^{'}}_{4}^{2} + 4 {| G_{4} |}^{2}}) / 2 + G_{2} = 0

and

Δ_{1} + Δ_{4} = 0

for

Δ_{1} < 0

, where

{Δ^{'}}_{4} = Δ_{4} - G_{2}

represents the detuning of

E_{4}

from

| G_{2} + 〉

, and

Δ_{1} + ({Δ^{'}}_{4} \pm \sqrt{{Δ^{'}}_{4}^{2} + 4 {| G_{4} |}^{2}}) / 2 - G_{2} = 0

and

Δ_{1} + Δ_{4} = 0

for

Δ_{1} > 0

, where

{Δ^{'}}_{4} = Δ_{4} + G_{2}

represents the detuning of

E_{4}

from

| G_{2} - 〉

. Unlike scanning self-dressing detuning (Fig. 4(a2)), by scanning the external-dressing detuning the enhancement and suppression of

E_{F 2}^{}

could be detected directly, excluding the pure FWM component (Fig. 4(d2)). We can see that the enhancement and suppression of

E_{F 2}^{}

in Fig. 4(d2) shows similar evolution with that in Fig. 4(b2). The profile of all the baselines, which has two peaks, reveals AT splitting of

E_{2}

(

{E^{'}}_{2}

), and the transition of enhancement and suppression in each curve is induced by the interaction between

E_{2}

(

{E^{'}}_{2}

) and

E_{4}

with three symmetric centers at

Δ_{1} = 0, - 20, and 20 MHz

, all of which are pure-suppression. The pure-suppression at

Δ_{1} = 0 MHz

is induced by primary dressing effect of

E_{2}

(

{E^{'}}_{2}

), while pure-suppressions at

Δ_{1} = \pm 20 MHz

are caused by the secondary dressing effect of

E_{4}

. On the other hand, when

Δ_{1}

is scanned, the FWM signal

E_{F 2}^{}

in Fig. 4(d4) also presents three peaks, corresponding to the three dressed state respectively. Moreover, the corresponding relationship between scanning probe detuning and scanning external-dressing detuning is similar with above, as expressed by the dash lines in Fig. 4(d) and 4(e). It is obvious that the theoretical calculations (Fig. 4(e)) are in good agreement with the experimental results (Fig. 4(d)).

Comparing with the singly-dressed FWM process in Fig. 3, we notice the doubly-dressed FWM process, although derives from the former, shows more complexities since one more dressing field is considered. When scanning probe detuning, doubly-dressed FWM signal shows three peaks resulting from two orders of AT splitting (Fig. 4(a4) and 4(d4)); whereas singly-dressed FWM signal shows only two peaks resulting from of AT splitting of self-dressing effect (Fig. 3(a4)). When scanning the dressing detuning, only one symmetric center appears in singly-dressing case (Fig. 3(b2)), whereas three symmetric centers appear in doubly-dressing case respectively at

Δ_{1} = 0, - 20, and 20 MHz

(Fig. 4(b2) and 4(e2)), all of which reveals pure-suppression. The symmetric center at

Δ_{1} = 0

is caused by the primary dressing effect, while the two symmetric centers at

Δ_{1} = \pm 20 MHz

are due to the secondary dressing effect.

Synthetically, based on the analysis above, we find the methods of scanning the probe detuning (Fig. 3(a3)-3(a4), Fig. 4(a3)-4(a4), Fig. 4(d3)-4(d4)), scanning self-dressing detuning (Fig. 3(a1)-3(a2), Fig. 4(a1)-4(a2)) and scanning external-dressing detuning (Fig. 4(d1)-4(d2)) individually show some different features and advantages on research the FWM process. When scanning the probe detuning, the obtained FWM signal includes two components: the pure FWM signal when not considering dressing effects, and the modification (revealing AT splitting) of the FWM process. When scanning self-dressing detuning, the obtained signal also includes two components: the pure FWM signal and the modification (revealing the transition between enhancement and suppression) of the FWM process. While by scanning external-dressing detuning, the enhancement and suppression could be detected directly, excluding the pure FWM component. On the other hand, by scanning the probe detuning, all enhancement points and suppression points could be observed corresponding to the peaks and dips of AT splitting. In singly-dressing case, there are two enhancement points and one suppression point (Fig. 3(a3)-3(a4)), and in doubly-dressing case, three enhancement points and two suppression points (Fig. 4(a3)-4(a4)), etc. In contrast, by scanning dressing detuning, at most one enhancement point and one suppression point could be gotten in the spectra. Furthermore, the positions of the enhancement and suppression points when scanning dressing detuning match with the positions of corresponding points when scanning probe detuning, as the dash lines express in Fig. 3 and Fig. 4.

After that, we demonstrate a new type of phase-controlled, spatiotemporal coherent interference between two FWM processes (

E_{F 2}^{}

and

E_{F 4}^{}

) in a four-level, Y-type subsystem when the laser beams

E_{3}

and

{E^{'}}_{3}

are turned off (shown as Fig. 1(d)). With a specially designed spatial configuration for the laser beams with phase matching and an appropriate optical delay introduced in one of the coupling laser beams, we can have a controllable phase difference between the two FWM processes in the subsystem. When this relative phase is varied, temporal and spatial interferences can be observed. The interference in the time domain is in the femtosecond time scale, corresponding to the optical transition frequency excited by the delayed laser beam. In the experiment, the beam

{E^{'}}_{2}

is delayed by an amount

τ

using a computer-controlled stage. The CCD and an avalanche photodiode (APD) are set on the propagation path of the two FWM signals to measure them. By changing the frequency detuning

Δ_{4}

, the

| 0 〉 - | 1 〉 - | 4 〉

EIT window can be shifted toward the

| 0 〉 - | 1 〉 - | 2 〉

EIT window. When the two EIT windows overlap with each other, temporal and spatial interferences of two FWM signal

E_{F 2}^{}

and

E_{F 4}^{}

can be observed, as shown in Fig. 5 .

Fig. 5 The spatiotemporal interferograms of

E_{F 2}^{}

and

E_{F 4}^{}

in the Y-type atomic subsystem. (a) A three-dimensional spatiotemporal interferogram of the total FWM signal intensity

I (τ, r)

versus time delay

τ

of beam

{E^{'}}_{2}

and transverse position

r

. (b) The temporal interference with a much longer time delay of beam

{E^{'}}_{2}

. (c) Measured beat signal intensity

I (τ, r)

versus time delay

τ

together with the theoretically simulated result (solid curve).

The coexisting

E_{F 1}^{}

and

E_{F 2}^{}

signals give the total detected intensity as:

I (τ, r) \propto | χ_{F 2}^{(3)} |^{2} + | χ_{F 4}^{(3)} |^{2} + 2 | χ_{F 2}^{(3)} | | χ_{F 4}^{(3)} | \cos (φ_{2} - φ_{4} + φ)

, where

χ_{F 2}^{(3)} = \frac{N μ_{1}^{2}}{ℏ ε_{0} G_{1}} ρ_{F 2}^{(3)} \times \frac{μ_{2}^{2}}{ℏ^{2} G_{2} {G^{'}}_{2}^{*}}

= - i μ_{1}^{2} μ_{2}^{2} N / {ε_{0} ℏ^{3} {(d_{1} + G_{2}^{2} / d_{2} + G_{4}^{2} / d_{4})}^{2} d_{2}} = | χ_{F 2}^{(3)} | \exp (i φ_{2})

χ_{F 4}^{(3)} = \frac{N μ_{1}^{2}}{ℏ ε_{0} G_{1}} ρ_{F 4}^{(3)} \times \frac{μ_{4}^{2}}{ℏ^{2} G_{4} {G^{'}}_{4}^{*}}

= - i μ_{1}^{2} μ_{4}^{2} N / {ε_{0} ℏ^{3} {(d_{1} + G_{2}^{2} / d_{2} + G_{4}^{2} / d_{4})}^{2} d_{4}} = | χ_{F 4}^{(3)} | \exp (i φ_{4})

, and

φ = Δ k \cdot r - ω_{2} τ

with the frequency of spatial interference

Δ k = k_{F 2} - k_{F 4} = (k_{2} - {k^{'}}_{2}) - (k_{4} - {k^{'}}_{4})

μ_{1}

μ_{2}

, and

μ_{4}

are the dipole moments of the transitions

| 0 〉 \to | 1 〉

| 1 〉 \to | 2 〉

, and

| 1 〉 \to | 4 〉

, respectively. From the expression of

I (τ, r)

, we can see that the total signal has an ultrafast time oscillation with a period of

2 π / ω_{2}

and spatial interference with a period of

2 π / Δ k

, which forms a spatiotemporal interferogram. Fig. 5(a) shows a three-dimensional interferogram pattern, and Fig. 5(b) shows the temporal interference with a much longer time delay in beam

{E^{'}}_{2}

while Fig. 5(c) shows its projections on time. Figure 5(c) depicts a typical temporal interferogram with the temporal oscillation period of

2 π / ω_{2} = 2 .6 fs

corresponding to the

| 1 〉

| 2 〉

transition frequency of

Ω_{2} = 2.4 {fs}^{- 1}

{}^{85}R b

.This gives a technique for precision measurement of atomic transition frequency in optical wavelength range. The solid curve in Fig. 5(c) is the theoretical calculation from the full density-matrix equations. It is easy to see that the theoretical results fit well with the experimentally measured results.

Now, we concentrate on the SWM process when

Δ_{3}

is at large detuning, with

{E^{'}}_{2}

and

{E^{'}}_{4}

blocked (shown as Fig. 1(e)). When take the atomic velocity component and the dressing effect of

E_{3}

(

{E^{'}}_{3}

) into consideration, the enhancement and suppression of the SWM signal would be shifted far away from resonance, as shown in Fig. 6 .

Fig. 6 (a1) The probe transmission signal and (a2) the SWM signal with the enhancement and suppression effect versus

Δ_{2}

for different

Δ_{1}

with the laser beams

{E^{'}}_{2}

and

{E^{'}}_{4}

blocked when

Δ_{3}

is at large detuning. (b) The doubly-dressed state diagram of the SWM signal. Powers of participating laser beams are 3mW (

E_{1}

), 4.6mW (

E_{2}

), 44mW (

E_{3}

and

{E^{'}}_{3}

), 65mW (

E_{4}

When considering Doppler effect the atom moving towards the probe laser beam with velocity

v

, the frequency of

E_{1}

is changed to

ω_{1} + ω_{1} v / c

, and the frequencies of

E_{2}

E_{3}

and

E_{4}

are changed to

ω_{2} - ω_{2} v / c

ω_{3} - ω_{3} v / c

ω_{4} - ω_{4} v / c

under our experimental geometry configuration, therefore their detunings are changed to

Δ_{1} - ω_{1} v / c

Δ_{2} + ω_{2} v / c

Δ_{3} + ω_{3} v / c

Δ_{4} + ω_{4} v / c

. Noticing that in such beam geometric configuration, the two-photon Doppler-free condition will not be satisfied for the

Λ

-type three-level subsystem

| 0 〉 \to | 1 〉 \to | 3 〉

, the atomic velocity component

ω_{3} v / c

will behaves dominant. The density-matrix element of SWM signal

E_{S 4}^{}

can be obtained as

ρ_{S 4}^{(5)} = G_{S 4} / [{d^{'}}_{1} {d^{'}}_{3} {d^{'}}_{4} {({d^{'}}_{1} + {| G_{4} |}^{2} / {d^{'}}_{4} + {| G_{3}^{b} |}^{2} / {d^{'}}_{3})}^{2}]

via the self-dressed perturbation chain

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{(G_{4} \pm G_{3} \pm) 0}^{(1)} \overset{- ω_{3}}{\to} ρ_{30}^{(2)} \overset{ω_{3}}{\to} ρ_{(G_{4} \pm G_{3} \pm) 0}^{(3)} \overset{ω_{4}}{\to} ρ_{40}^{(4)} \overset{- ω_{4}}{\to} ρ_{10}^{(5)}

, where

{d^{'}}_{1} = d_{1} - i ω_{1} v / c + γ_{1}

{d^{'}}_{3} = d_{3} - i ω_{3} v / c - i ω_{1} v / c + γ_{1} - γ_{3}

{d^{'}}_{4} = d_{4} + i ω_{4} v / c - i ω_{1} v / c + γ_{1} + γ_{4}

, and

γ_{1}

γ_{3}

γ_{4}

are the half linewidth of laser beams

E_{1}

E_{3}

E_{4}

respectively. When the SWM signal

E_{S 4}^{}

is externally dressed by

E_{2}

(defined as

E_{S 4}^{D}

), the solved expression is

ρ_{S 4}^{(5)} = G_{S 4} / [{d^{'}}_{3} {d^{'}}_{4} ({d^{'}}_{1} + {| G_{2} |}^{2} / {d^{'}}_{2}) {({d^{'}}_{1} + {| G_{2} |}^{2} / {d^{'}}_{2} + {| G_{4} |}^{2} / {d^{'}}_{4} + {| G_{3}^{b} |}^{2} / {d^{'}}_{3})}^{2}]

via the dressed perturbation chain:

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{(G_{4} \pm G_{3} \pm G_{2} \pm) 0}^{(1)} \overset{- ω_{3}}{\to} ρ_{30}^{(2)} \overset{ω_{3}}{\to} ρ_{(G_{4} \pm G_{3} \pm G_{2} \pm) 0}^{(3)} \overset{ω_{4}}{\to} ρ_{40}^{(4)} \overset{- ω_{4}}{\to} ρ_{(G_{2} \pm) 0}^{(5)}

, where

{d^{'}}_{2} = d_{2} + i ω_{2} v / c - i ω_{1} v / c + γ_{1} + γ_{2}

and

γ_{2}

are the half linewidth of laser beam

E_{2}

. Similarly, the density-matrix element of SWM signal

E_{S 2}^{}

can be obtained as

ρ_{S 2}^{(5)} = G_{S 2} / [{d^{'}}_{1} {d^{'}}_{2} {d^{'}}_{3} {({d^{'}}_{1} + {| G_{2} |}^{2} / {d^{'}}_{2} + {| G_{3}^{b} |}^{2} / {d^{'}}_{3})}^{2}]

via the self-dressed perturbation chain:

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{(G_{2} \pm G_{3} \pm) 0}^{(1)} \overset{- ω_{3}}{\to} ρ_{30}^{(2)} \overset{ω_{3}}{\to} ρ_{(G_{2} \pm G_{3} \pm) 0}^{(3)} \overset{ω_{2}}{\to} ρ_{20}^{(4)} \overset{- ω_{2}}{\to} ρ_{10}^{(5)}

. When the SWM signal

E_{S 2}^{}

is externally dressed by

E_{4}

(defined as

E_{S 2}^{D}

), the solved expression is

ρ_{S 2}^{(5)} = G_{S 2} / [{d^{'}}_{2} {d^{'}}_{3} ({d^{'}}_{1} + {| G_{4} |}^{2} / {d^{'}}_{4}) {({d^{'}}_{1} + {| G_{2} |}^{2} / {d^{'}}_{2} + {| G_{4} |}^{2} / {d^{'}}_{4} + {| G_{3}^{b} |}^{2} / {d^{'}}_{3})}^{2}]

via the dressed perturbation chain:

ρ_{00}^{(0)} \overset{ω_{1}}{\to} ρ_{(G_{2} \pm G_{3} \pm G_{4} \pm) 0}^{(1)} \overset{- ω_{3}}{\to} ρ_{30}^{(2)} \overset{ω_{3}}{\to} ρ_{(G_{2} \pm G_{3} \pm G_{4} \pm) 0}^{(3)} \overset{ω_{2}}{\to} ρ_{20}^{(4)} \overset{- ω_{2}}{\to} ρ_{(G_{4} \pm) 0}^{(5)}

. From the expressions of

E_{S 4}^{D}

and

E_{S 2}^{D}

signals, one can see that the two SWM processes are closely connected by mutual dressing effect.

In Fig. 6(a), we present the probe transmission (Fig. 6(a1)) and the measured SWM signal (Fig. 6(a2)) by scanning

Δ_{2}

at different designated

Δ_{1}

values, with

G_{2} < < G_{4}

. In Fig. 6(a1), The profile of each baseline represents the probe transmission without dressing field

E_{2}

versus probe detuning

Δ_{1}

, which reveals an EIT window (

- {80MHz<Δ}_{1} <80MHz

) induced by

E_{4}

, and the peak on each baseline is the EIT induced by

E_{2}

. In Fig. 6(a2), the profile of each baseline represents the intensity variation of the triple-peak SWM signal

E_{S 4}^{}

versus

Δ_{1}

. The peak and dip on each baseline include the dressed SWM signal

E_{S 2}^{D}

and the enhancement and suppression of

E_{S 4}

induced by

E_{2}

. Considering

G_{2} < < G_{4}

, we can deduce the signal of

E_{S 2}^{D}

is quite small. Therefore, the peak and dip on each baseline mainly represent the enhancement and suppression of SWM signal

E_{S 4}

induced by

E_{2}

One can see that the curves in Fig. 6(a2) shows pure-suppression at

Δ_{1} = 0 MHz

and

Δ_{1} = - 2 50MHz

. This two pure-suppressions can be explained by the triple-dressing effect of

E_{2}

E_{3}

(

{E^{'}}_{3}

) and

E_{4}

. The enhancement and suppression of the SWM is caused by the triply-dressing fields. Firstly, due to the self-dressing effect of

E_{4}

, the state

| 1 〉

would be split into two dressed states

| G_{4} \pm 〉

. Next, the dressing field

E_{3}

(

{E^{'}}_{3}

) split the state

| G_{4} + 〉

into

| G_{4} + G_{3} \pm 〉

. Finally, when

Δ_{2}

is scanned,

E_{2}

will further split

| G_{4} + G_{3} \pm 〉

into two dressed states

| G_{4} + G_{3} + G_{2} \pm 〉

| G_{4} + G_{3} - G_{2} \pm 〉

; or split

| G_{4} - 〉

into two dressed states

| G_{4} - G_{2} \pm 〉

, as shown in Fig. 6(b). When two-photon resonance occurs at the original states

| G_{4} + G_{3} + 〉

(Fig. 6(b2)),

| G_{4} + G_{3} - 〉

(Fig. 6(b3)) or

| G_{4} - 〉

(Fig. 6(b4)), the pure-suppressions of SWM can be obtained. When Doppler effect being considered, the dominant atomic velocity component

ω_{3} v / c

moving the

| G_{4} + G_{3} + 〉

state far away from the resonance, the pure-suppression on the left induced by triply-dressing effect will be shifted to large detuning. In the experiment, only two pure-suppressions can be obtained, of which the left one is caused by two-photon resonance at original

| G_{4} + G_{3} + 〉

state, and the right one is related to the original

| G_{4} + G_{3} - 〉

state. This inconsistence is because when the frequency of

E_{3}

(

{E^{'}}_{3}

) is at large detuning (

Δ_{3} > > 0

), the enhancement and suppression of SWM signal is no more symmetrical. Specifically, due to the optical pumping effect corresponding to the transition from

| 3 〉

| 1 〉

E_{3}

and

{E^{'}}_{3}

, the suppression will be intensified with

Δ_{1} < 0

(especially when

Δ_{1} + Δ_{3} = 0

) as shown in Fig. 6(b); but with

Δ_{1} > 0

, the inexistence of such effect makes the suppression caused by the two photon resonance at original

| G_{4} - 〉

state unobtainable.

In this way, we first demonstrate that the enhancement and suppression signal can be observed out of the EIT window (

{-80MHz<Δ}_{1} <+80MHz

) through the Doppler frequency shift led by atomic velocity component and optical pumping. From the figures one can see that even

Δ_{1}

is at large detuning (Fig. 6(b1) and 6(b5)), the enhancement and suppression of SWM will still exists in the region with

Δ_{1} < 0

Finally, the interaction of the six wave-mixing signals is studied. When all seven laser beams are turned on, two FWM signals (

E_{F 2}

and

E_{F 4}

) and four SWM signals (

E_{S 2}^{}

{E^{'}}_{S 2}

E_{S 4}^{}

and

{E^{'}}_{S 4}

) can be generated simultaneously and interact with each other (considering the FWM signal

E_{F 3}

is so weak that it could be negligible). When the

| 0 〉 \to | 1 〉 \to | 4 〉

EIT window and the

| 0 〉 \to | 1 〉 \to | 2 〉

EIT window are tuned separated, the interaction of MWM processes related to the same EIT window has been displayed in Fig. 2, by scanning probe detuning under different blocking conditions. Here, we overlap the two EIT windows experimentally, therefore the interaction between these two groups of wave-mixing signals (those related to

E_{2}

(

{E^{'}}_{2}

) and those related to

E_{4}

(

{E^{'}}_{4}

)) will be studied, by scanning the dressing field detuning

Δ_{2}

at discrete probe detuning

Δ_{1}

values (as shown in Fig. 7 ).

Fig. 7 (a) Measured total MWM signal versus

Δ_{2}

at discrete

Δ_{1}

when all seven laser beams on. (b) Measured FWM signals versus

Δ_{2}

at discrete

Δ_{1}

. (b1) Signal obtained with the laser beams

E_{3}

and

{E^{'}}_{3}

blocked and others on. (b2) The enhancement and suppression of the FWM signal

E_{F 4}

when the laser beams

E_{3}

{E^{'}}_{3}

and

{E^{'}}_{2}

are blocked. (b3) The FWM signal when the laser beams

E_{3}

{E^{'}}_{3}

and

{E^{'}}_{4}

are blocked. (c) Measured SWM signals versus

Δ_{2}

at discrete

Δ_{1}

. (c1) Signal obtained with laser beams

{E^{'}}_{2}

{E^{'}}_{4}

blocked and others on. (c3) Signal obtained with the laser beams

{E^{'}}_{2}

{E^{'}}_{4}

and

E_{4}

blocked. (c2) The sum of

E_{S 4}^{D} - E_{S 4}^{}

and

E_{S 2}^{D} - E_{S 2}^{}

. Powers of all laser beams are 3.7mW (

E_{1}

), 55mW (

E_{2}

), 5.3mW (

{E^{'}}_{2}

), 44mW (

E_{3}

and

{E^{'}}_{3}

), 85mW (

E_{4}

), 8.6mW (

{E^{'}}_{4}

Generally, due to the mutual dressings of the two ladder subsystems, we can obtain the density elements

ρ_{F 2}^{(3)} = G_{F 2} / [d_{2} {(d_{1} + {| G_{4}^{b} |}^{2} / d_{4})}^{2}]

(where

G_{4}^{b} = G_{4} + {G^{'}}_{4}

) for the external-dressed FWM process of

E_{F 2}

ρ_{S 2}^{(5)} = G_{S 2} / [d_{3} d_{2} {(d_{1} + {| G_{4}^{b} |}^{2} / d_{4})}^{3}]

(or

{ρ^{'}}_{S 2}^{(5)} = {G^{'}}_{S 2} / [d_{3} d_{2} {(d_{1} + {| G_{4}^{b} |}^{2} / d_{4})}^{3}]

) for the external-dressed SWM process of

E_{S 2}

(or

{E^{'}}_{S 2}

); and

ρ_{F 4}^{(3)} = G_{F 4} / [d_{4} {(d_{1} + {| G_{2}^{b} |}^{2} / d_{2})}^{2}]

for the external-dressed FWM process

E_{F 4}

ρ_{S 4}^{(5)} = G_{S 4} / [d_{3} d_{4} {(d_{1} + {| G_{2}^{b} |}^{2} / d_{2})}^{3}]

(or

{ρ^{'}}_{S 4}^{(5)} = {G^{'}}_{S 4} / [d_{3} d_{4} {(d_{1} + {| G_{2}^{b} |}^{2} / d_{2})}^{3}]

) for the external-dressed SWM process of

E_{S 4}

(or

{E^{'}}_{S 4}

), when not considering the self-dressing effects. The total detected MWM signal (Fig. 7(a)) will be proportional to the mod square of

{ρ^{'}}_{M}

, where

{ρ^{'}}_{M} = (ρ_{S 2}^{(5)} + {ρ^{'}}_{S 2}^{(5)} + ρ_{F 2}^{(3)}) + (ρ_{S 4}^{(5)} + {ρ^{'}}_{S 4}^{(5)} + ρ_{F 4}^{(3)})

The measured total MWM signal when all the laser beams are turned on is depicted in Fig. 7(a). The global profile of the baselines of each curve, which mainly includes the self-dressed

E_{F 4}

E_{S 4}

and

{E^{'}}_{S 4}

signals, exhibits AT splitting induced by

E_{4}

(

{E^{'}}_{4}

). The peak on each profile is mainly composed of the doubly-dressed

E_{F 2}

E_{S 2}

{E^{'}}_{S 2}

signals and the enhancement and suppression of

E_{F 4}

E_{S 4}

and

{E^{'}}_{S 4}

induced by

E_{2}

(

{E^{'}}_{2}

). To understand the interaction of these six generated signals deeply, we divide it into two parts: the interaction of FWM signals

E_{F 2}

and

E_{F 4}

(shown as Fig. 7(b)), and the interaction of SWM signals

E_{S 2}

{E^{'}}_{S 2}

and

E_{S 4}

{E^{'}}_{S 4}

. Since

{E^{'}}_{S 2}

and

E_{S 2}

share similar characteristics (so do

E_{S 4}

and

{E^{'}}_{S 4}

), the interaction between

{E^{'}}_{S 2}

E_{S 2}

and

E_{S 4}

{E^{'}}_{S 4}

can be studied by only investigating the interaction between

E_{S 2}

and

E_{S 4}

(shown as Fig. 7(c)) [21

Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011). [CrossRef]

]. Therefore, by blocking different laser beams and scanning

Δ_{2}

at discrete

Δ_{1}

values, the interaction of these six wave-mixing signals can be observed directly, separated into the interplay between two FWM signals, two SWM signals and the interplay between FWM and SWM signals.

First we investigate the interplay between the two FWM signals

E_{F 2}

and

E_{F 4}

in the Y-type subsystem (Fig. 1(d)) by blocking the laser beams

E_{3}

and

{E^{'}}_{3}

. The interplay between these two FWM signals will occur when we overlap the two separated EIT windows, as shown in Fig. 7(b). Figure 7(b1) shows the measured FWM signal versus

Δ_{2}

at discrete

Δ_{1}

values, which including the information of both

E_{F 2}

and

E_{F 4}

, with mutual dressings. In Fig. 7(b1), the global profile of baselines of all the curves represents the intensity variation of

E_{F 4}

at designated probe detuning values, and the peak and dip on each baseline include two components: the doubly-dressed

E_{F 2}

signal and the enhancement and suppression of

E_{F 4}

induced by

E_{2}

(

{E^{'}}_{2}

). These two components could be individually detected by additionally blocking

{E^{'}}_{2}

{E^{'}}_{4}

, as shown in Fig. 7(b2) and 7(b3) separately. When blocking

{E^{'}}_{2}

, the information related to

E_{F 4}

could be extracted since

E_{F 2}

is turned off (Fig. 7(b2)). The global profile of all the baselines in Fig. 7(b2) reveals AT splitting of

E_{F 4}

, and the peak and dip of each curve represent the enhancement and suppression of

E_{F 4}

induced by

E_{2}

, which show similar evolution to the curves in Fig. 4(d2). On the other hand, when turning on

{E^{'}}_{2}

and blocking

{E^{'}}_{4}

, the doubly-dressed

E_{F 2}

signal could be obtained in Fig. 7(b3), which is similar to Fig. 4(a2). It is quite obvious that the measured total FWM signal (Fig. 7(b1)) is approximate to the sum of the enhancement and suppression of

E_{F 4}

which mainly behaves dips (Fig. 7(b2)), and the dressed FWM signal

E_{F 2}

, which mainly behave peaks (Fig. 7(b3)).

Next we investigate the interplay between two SWM signals

E_{S 2}

and

E_{S 4}

in Fig. 7(c) [21

Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011). [CrossRef]

], with

{E^{'}}_{2}

and

{E^{'}}_{4}

blocked (shown as Fig. 1(e)). When all the five laser beams (

E_{1}

E_{2}

E_{4}

E_{3}

and

{E^{'}}_{3}

) are turned on, two external-dressed SWM signals

E_{S 2}^{D}

and

E_{S 4}^{D}

will form simultaneously, as shown in Fig. 7(c1). The global baseline variation profile shows the intensity variation of the SWM signal

E_{S 4}^{}

revealing AT splitting. The peak and dip on each baseline include the SWM signal

E_{S 2}^{D}

and

E_{S 4}^{D} - E_{S 4}^{}

which represents the enhancement and suppression of

E_{S 4}^{}

caused by

E_{2}

. When the beam

E_{4}

is also blocked, only the measured SWM signal

E_{S 2}^{}

remains, as shown in Fig. 7(c3). By subtracting the SWM signal

E_{S 2}^{}

(Fig. 7(c3)) and the height of each baseline from the total signal (Fig. 7(c1)), the sum of the signals

E_{S 4}^{D} - E_{S 4}^{}

and

E_{S 2}^{D} - E_{S 2}^{}

revealing the pure dressing effect can be obtained, as shown in Fig. 7(c2). Here,

E_{S 2}^{D} - E_{S 2}^{}

expresses the enhancement or suppression of the

E_{S 2}^{}

caused by the

E_{4}

. On the one hand, we can see from the curve (c2) that when two-photon resonance occurs at

Δ_{1} = - 20 MHz

and

Δ_{1} = 25 MHz

, the depth of the dip is approximately maximum, meaning that the suppression is most significant. On the other hand, when

E_{1}

resonates with

| G_{4} + G_{2} + 〉

and

| G_{4} - G_{2} - 〉

, the generated SWM signals are enhanced as shown by the small peaks.

When the FWM signals and SWM signals coexist in Fig. 7(a) with all seven beams on, the interaction of these generated wave-mixing signals can be obtained. Theoretically, the intensity of the measured total MWM signal in Fig. 7(a) can be described as sum of the FWM signal intensity (Fig. 7(b1)), the SWM signal intensity (Fig. 7(c1)) and the intensity of the SWM signals relate to

{E^{'}}_{S 2}

and

{E^{'}}_{S 4}

which is similar to Fig. 7(c1). From the experimental result, one can see that the generated signal with all laser beams tuned on in (a) is approximate to the sum of the FWM intensity in (b1) and the SWM intensity in (c1), but behaves FWM dominant. Because the SWM signals are too weak to be distinguished when compared with the FWM. We also notice that when the FWM signals and SWM signals coexist and interplay with each other, the enhancement and suppression effect of FWM will be weakened by the interaction of six MWM signal.

4. Conclusion

In summary, we distinguish seven coexisting multi-wave mixing signals in a K-type five-level atomic system by selectively blocking different laser beams. And the interactions among these MWM signals have been studied by investigating the interaction between two FWM signals, between two SWM signals, and the interaction between FWM and SWM signals. We also report our experimental results on the dressed FWM process by scanning the frequency detuning of the probe field, the self-dressing field and the external-dressing field respectively, proving the corresponding relationship between different scanning methods. Especially, by scanning external-dressing detuning, the enhancements and suppressions of FWM can be detected directly. In addition, we successfully demonstrate the temporal interference between two FWM signals with a femtosecond time scale. Moreover, when

Δ_{3}

is far away from resonance, we first observe the enhancement and suppression of SWM signal at large detuning, which is moved out of the EIT window through the Doppler frequency shift led by atomic velocity component.

Acknowledgments

This work was supported by 973 Program (2012CB921804), NSFC (10974151, 61078002, 61078020, 11104214, 61108017, 11104216), NCET (08-0431), RFDP (20110201110006, 20110201120005, 20100201120031).

References and links

1.	P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. 20(9), 982–984 (1995). [CrossRef] [PubMed]
2.	Y. Q. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett. 21(14), 1064–1066 (1996). [CrossRef] [PubMed]
3.	M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999). [CrossRef]
4.	D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004). [CrossRef] [PubMed]
5.	H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70(6), 061804 (2004). [CrossRef]
6.	Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006). [CrossRef] [PubMed]
7.	H. Ma and C. B. de Araujo, “Interference between third- and fifth-order polarizations in semiconductor doped glasses,” Phys. Rev. Lett. 71(22), 3649–3652 (1993). [CrossRef] [PubMed]
8.	D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys. 108(10), 3897–3902 (1998). [CrossRef]
9.	S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]
10.	M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]
11.	A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14(24), 1344–1346 (1989). [CrossRef] [PubMed]
12.	L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001). [CrossRef] [PubMed]
13.	L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999). [CrossRef]
14.	M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001). [CrossRef] [PubMed]
15.	C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001). [CrossRef] [PubMed]
16.	D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001). [CrossRef] [PubMed]
17.	C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009). [CrossRef]
18.	M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001). [CrossRef]
19.	M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999). [CrossRef]
20.	B. Anderson, Y. P. Zhang, U. Khadka, and M. Xiao, “Spatial interference between four- and six-wave mixing signals,” Opt. Lett. 33(18), 2029–2031 (2008). [CrossRef] [PubMed]
21.	Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011). [CrossRef]

OCIS Codes
(190.3270) Nonlinear optics : Kerr effect
(190.4180) Nonlinear optics : Multiphoton processes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(270.1670) Quantum optics : Coherent optical effects
(300.2570) Spectroscopy : Four-wave mixing

ToC Category:
Nonlinear Optics

History
Original Manuscript: October 31, 2011
Revised Manuscript: December 9, 2011
Manuscript Accepted: January 6, 2012
Published: January 13, 2012

Citation
Ning Li, Zhengyang Zhao, Haixia Chen, Peiying Li, Yueheng Li, Yan Zhao, Guozhen Zhou, Shuqiao Jia, and Yanpeng Zhang, "Observation of dressed odd-order multi-wave mixing in five-level atomic medium," Opt. Express 20, 1912-1929 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-1912

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References

P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett.20(9), 982–984 (1995). [CrossRef] [PubMed]
Y. Q. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett.21(14), 1064–1066 (1996). [CrossRef] [PubMed]
M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett.82(26), 5229–5232 (1999). [CrossRef]
D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett.93(18), 183601 (2004). [CrossRef] [PubMed]
H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A70(6), 061804 (2004). [CrossRef]
Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett.97(19), 193904 (2006). [CrossRef] [PubMed]
H. Ma and C. B. de Araujo, “Interference between third- and fifth-order polarizations in semiconductor doped glasses,” Phys. Rev. Lett.71(22), 3649–3652 (1993). [CrossRef] [PubMed]
D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys.108(10), 3897–3902 (1998). [CrossRef]
S. E. Harris, “Electromagnetically induced transparency,” Phys. Today50(7), 36 (1997). [CrossRef]
M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77(2), 633–673 (2005). [CrossRef]
A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett.14(24), 1344–1346 (1989). [CrossRef] [PubMed]
L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414(6862), 413–418 (2001). [CrossRef] [PubMed]
L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature397(6720), 594–598 (1999). [CrossRef]
M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature413(6853), 273–276 (2001). [CrossRef] [PubMed]
C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature409(6819), 490–493 (2001). [CrossRef] [PubMed]
D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett.86(5), 783–786 (2001). [CrossRef] [PubMed]
C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett.95(4), 041103 (2009). [CrossRef]
M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A64(1), 013412 (2001). [CrossRef]
M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A60(4), 3225–3228 (1999). [CrossRef]
B. Anderson, Y. P. Zhang, U. Khadka, and M. Xiao, “Spatial interference between four- and six-wave mixing signals,” Opt. Lett.33(18), 2029–2031 (2008). [CrossRef] [PubMed]
Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A84(1), 013804 (2011). [CrossRef]

Appl. Phys. Lett.

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett.95(4), 041103 (2009). [CrossRef]

J. Chem. Phys.

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys.108(10), 3897–3902 (1998). [CrossRef]

Nature

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414(6862), 413–418 (2001). [CrossRef] [PubMed]
L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature397(6720), 594–598 (1999). [CrossRef]
M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature413(6853), 273–276 (2001). [CrossRef] [PubMed]
C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature409(6819), 490–493 (2001). [CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A70(6), 061804 (2004). [CrossRef]
Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A84(1), 013804 (2011). [CrossRef]
M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A64(1), 013412 (2001). [CrossRef]
M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A60(4), 3225–3228 (1999). [CrossRef]

Phys. Rev. Lett.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett.86(5), 783–786 (2001). [CrossRef] [PubMed]
Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett.97(19), 193904 (2006). [CrossRef] [PubMed]
H. Ma and C. B. de Araujo, “Interference between third- and fifth-order polarizations in semiconductor doped glasses,” Phys. Rev. Lett.71(22), 3649–3652 (1993). [CrossRef] [PubMed]
M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett.82(26), 5229–5232 (1999). [CrossRef]
D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett.93(18), 183601 (2004). [CrossRef] [PubMed]

Phys. Today

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today50(7), 36 (1997). [CrossRef]

Rev. Mod. Phys.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys.77(2), 633–673 (2005). [CrossRef]

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