Observation of Autler-Townes splitting in six-wave mixing

doi:10.1364/OE.19.007769

Observation of Autler-Townes splitting in six-wave mixing

Yanpeng Zhang, Peiying Li, Huaibin Zheng, Zhiguo Wang, Haixia Chen, Changbiao Li, Ruyi Zhang, and Min Xiao »View Author Affiliations

Optics Express, Vol. 19, Issue 8, pp. 7769-7777 (2011)
http://dx.doi.org/10.1364/OE.19.007769

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▸ Article Outline
– Abstract
1. Introduction
2. Theoretical model and experimental scheme
3. Autler-Townes Splitting
4. Conclusion
– References and links

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Abstract

We report an observation of the self- and external-dressed Autler-Townes (AT) splitting in six-wave mixing (SWM) within an electromagnetically induce transparency window, which demonstrates the interaction between two coexisting SWM processes. The multi-dressed states induced by the nested interactions between many dressing fields and the five-level atomic system lead to the primary, secondary and triple AT splittings in the experiment. Such controlled multi-channel splitting of nonlinear optical signals can be used in a range of applications, e.g. the wavelength-demultiplexer in optical communication and quantum information processing.

1. Introduction

Aulter-Townes (AT) splitting was first observed on a radio-frequency transition more than sixty years ago [1

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955). [CrossRef]

]. Such effect has been clearly demonstrated in a four-wave mixing on a simple atomic system dressed with a single laser beam [2

W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994). [CrossRef] [PubMed]

]. With the cw triple-resonant spectroscopy and the ultrashort intense laser pulses, respectively, the AT splitting effect in lithium molecules [3

J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999). [CrossRef]

] and a semiconductor material [4

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002). [CrossRef] [PubMed]

] was investigated. Theoretical studies also indicate that the AT-split Rydberg population can lead to an antiblockade effect [5

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007). [CrossRef] [PubMed]

] and such phenomenon was experimentally demonstrated with two-photon excitation in a three-level atomic system [6

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010). [CrossRef] [PubMed]

]. Recently, a great deal of attention has been paid to observe and understand the phenomenon of electromagnetically induced transparency (EIT) [7

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

–10

S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A 58(3), 2500–2505 (1998). [CrossRef]

] and related effects in multi-level atomic systems interacting with two or more electromagnetic fields [11

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007). [CrossRef] [PubMed]

,12

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]

The interaction of double-dark states (nested scheme of doubly-dressing) and splitting of dark state (the secondarily-dressed state) in a four-level atomic system with EIT were studied theoretically by Lukin, et al [13

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]

]. Then doubly-dressed states in cold atoms were observed, in which triple-photon absorption spectrum exhibits a constructive interference between the excitation pathways of two closely-spaced, doubly-dressed states [14

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]

]. A similar result was obtained in the inverted-Y [15

R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009). [CrossRef]

] and double-Λ [16

G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001). [CrossRef]

] atomic systems.

In this letter, we present the first experimental observation of the self-, doubly- and triply-dressed AT splitting states of the SWM process within the EIT window in a five-level atomic system. Theoretical calculations are carried out and used to well explain the observed results, giving a full physical understanding of the interesting multiple AT splittings in the high-order nonlinear optical processes. On the basis of our previous study of the AT splitting in the four-wave mixing (FWM) process [17

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010). [CrossRef] [PubMed]

], we go further to investigate the complex AT splitting phenomena in the SWM process.

2. Theoretical model and experimental scheme

The experimental demonstration of the AT splitting of SWM within the EIT window is carried out in the atomic system of ⁸⁵Rb. The energy levels of

5 S_{1 / 2} (F = 3)

5 S_{1 / 2} (F = 2)

5 P_{3 / 2} (F = 3)

5 D_{3 / 2}

, and

5 D_{5 / 2}

form the five-level atomic system, as shown in Fig. 1(b) . The atomic vapor cell temperature is set at

60^{\circ} C

. The probe laser beam

E_{1}

(with frequency

ω_{1}

, wave vector k₁, Rabi frequency

G_{1}

, and wavelength of 780.245 nm, connecting the transition

5 S_{1 / 2} - 5 P_{3 / 2}

) is from an external cavity diode laser (Toptica DL100L), which is horizontally polarized and has a power of about

P_{1} \approx 1.3 mW

. The coupling laser beams

E_{2}

(

ω_{2}

k_{2}

G_{2}

, and wavelength 775.978 nm, connecting the transition

5 P_{3 / 2} - 5 D_{5 / 2}

) and

E_{4}

(

ω_{4}

k_{4}

G_{4}

, and wavelength 776.157 nm, connecting the transition

5 P_{3 / 2} - 5 D_{3 / 2}

) are from two external cavity diode lasers (Hawkeye Optoquantum and UQEL100), respectively. The pump laser beams

E_{3}

(

ω_{3}

k_{3}

G_{3}

) and

E_{3}^{'}

(

ω_{3}

k_{3}^{'}

G_{3}^{'}

), which are split from a tapered-amplifier diode laser (Thorlabs TCLDM9) with equal power (

P_{3} \approx P_{3}^{'}

) and vertical polarization, drive the transition

5 S_{1 / 2} - 5 P_{3 / 2}

. The diameters of the probe, pump and coupling beams are about 0.3, 0.5, 0.5 mm at the cell center, respectively. The pump and coupling laser beams (

E_{3}

E_{3}^{'}

E_{2}

E_{4}

) are spatially aligned in a square-box pattern as shown in Fig. 1(a), which propagate through the atomic medium in the same direction with small angles (

~ 0 . 3^{\circ}

) between them (the angles are exaggerated in the figure). The probe beam (

E_{1}

) propagates in the opposite direction with a small angle from the other beams. Under this configuration the diffracted FWM signal (

E_{F}

) and two SWM signals (

E_{S 1}

and

E_{S 2}

) with same horizontal polarization are in the directions determined by the phase-matching conditions

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

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

and

k_{S 2} = k_{1} + k_{4} - k_{4} + k_{3} - k_{3}^{'}

, respectively. These signals are in the same direction as

E_{F}

(at the lower right corner of Fig. 1(a)), and are detected by an avalanche photodiode detector. The transmitted probe beam is simultaneously detected by a silicon photodiode.

Fig. 1 (a) Phase-matching spatial beam geometry used in the experiment. (b) Five-level atomic system with one probe field , two pump fields

E_{3}

and

E_{3}^{'}

, and two coupling (dressing) fields

E_{2}

and

E_{4}

E_{F}

is the generated FWM signal.

E_{S 1}

and

E_{S 2}

are the two generated SWM signals. (c)-(e) Corresponding dressed-state pictures of (b).

For the five-level atomic system as shown in Fig. 1(b), if two strong coupling laser fields (

E_{2}

and

E_{4}

) drive two separate upper transitions (|1> to |2> and |1> to |4>), respectively, and a weak laser field (..) probes the lower transition (|0> to |1>), two ladder-type EIT subsystems will form with two-photon Doppler-free configuration [8

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995). [CrossRef] [PubMed]

] and two EIT windows appear. Depending on the frequency detunings of the two coupling laser beams, these two EIT windows can either overlap or be separated in frequency on the probe beam transmission signal. On the other hand, if the probe field

E_{1}

drives the transition (|0> to |1>) and the two pump fields (

E_{3}

and

E_{3}^{'}

) drive another transition (|3> to |1>) in the three-level Λ-type subsystem, as shown in Fig. 1(b), there will be a corresponding FWM signal generated at frequency

ω_{1}

(satisfying

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

). However, the FWM signal without the EIT window (not satisfying the two-photon Doppler-free configuration [8

]) can be neglected. When the two coupling laser fields E₂ (connecting transition |1> to |2>) and

E_{4}

(connecting the transition |1> to |4>) are added, two SWM processes will occur [11

]. First, without the strong coupling field

E_{4}

, a simple SWM1 process (

E_{S 1}

) at frequency

ω_{1}

is generated from the probe beam (E₁), the coupling field (

E_{2}

), and two pump fields (

E_{3}

and

E_{3}^{'}

), via the perturbation chain (I):

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

(satisfying

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

) [11

]. When the power of

E_{2}

is strong enough, it will start to dress the energy level

| 1 〉

to create the primarily-dressed states

| + 〉

and

| - 〉

, as shown in Fig. 1(c). This dressed SWM1 process can be described via the perturbation chain (II):

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

. Such self-dressing effect, i.e. one of the participating fields for generating SWM dresses the involved energy level

| 1 〉

, which then modifies the SWM process itself, is unique for such multi-wave mixing processes in multi-level systems. Similarly, for another SWM process (with fields

E_{1}

E_{4}

E_{3}

and

E_{3}^{'}

), without the strong coupling field

E_{2}

, it will generate a signal field

E_{S 2}

at frequency

ω_{1}

via the perturbation chain (III):

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

(satisfying

k_{S 2} = k_{1} + k_{4} - k_{4} + k_{3} - k_{3}^{'}

). When the power of

E_{4}

is strong enough, it will start to dress the energy level

| 1 〉

to create the primarily-dressed states

| + 〉

and

| - 〉

, as shown in Fig. 1(d). This dressed SWM2 process can be described via the perturbation chain (IV):

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

Next, when both coupling fields (

E_{2}

and

E_{4}

) are on at the same time, they can dress the energy level |1> together. For the SWM1 process (

E_{S 1}

E_{2}

first produces the primarily-dressed states

| \pm 〉

, then

E_{4}

produces the secondarily-dressed states

| \pm \pm 〉

at a proper frequency detuning (i.e. either tuned to the upper or lower dressed state,

| + >

| - >

), as shown in Fig. 1(e) via the perturbation chain (V):

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

. This generates the secondary AT splitting for the SWM1 signal. The situation for the SWM2 (

E_{S 2}

) process is similar.

The two primarily-dressed states induced by

E_{2}

can be written as

| \pm > = \sin θ_{1 \pm} | 1 > + \cos θ_{1 \pm} | 2 >

(Fig. 1(c)). When

E_{4}

only couples to the dressed state

| + >

, the secondarily-dressed states are then given by

| + \pm > = \sin θ_{2 \pm} | + > + \cos θ_{2 \pm} | 4 >

(Fig. 1(e)), where

\tan θ_{1 \pm} = - a_{1 \pm} / G_{2}

\tan θ_{2 \pm} = - a_{2 \pm} / G_{4}

a_{1 \pm} = Δ_{2} - λ_{\pm}^{(1)}

and

a_{2 \pm} = Δ_{4} - λ_{+}^{(1)} - λ_{+ \pm}^{(1)}

. One can obtain the eigenvalues

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

(measured from level

| 1 >

) of

| \pm >

, and

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

(measured from level

| + >

) of

| + \pm >

, where

Δ_{4}^{'} = Δ_{4} - λ_{+}^{(1)}

. When

E_{4}

only couples to the dressed state

| - >

, the secondarily-dressed states are given by

| - \pm > = \sin θ_{2 \pm} | - > + \cos θ_{2 \pm} | 4 >

, where

a_{2 \pm} = Δ_{4} - λ_{-}^{(1)} - λ_{- \pm}^{(1)}

, and other parameters are the same as before. Then, we obtain the same eigenvalues

λ_{\pm}^{(1)}

, and

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

(measured from level

| - >

) of

| - \pm >

, where

Δ_{4}^{'} = Δ_{4} - λ_{-}^{(1)}

. Similarly, when

E_{4}

induces the two primarily-dressed states, and

E_{2}

acts as the external-dressing field, one can get the following corresponding eigenvalues: ,

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

(

Δ_{2}^{'} = Δ_{2} - λ_{+}^{(2)}

), and

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

(

Δ_{2}^{'} = Δ_{2} - λ_{-}^{(2)}

In general for arbitrary strengths of the fields

E_{1}

E_{3}

E_{3}^{'}

E_{2}

and

E_{4}

, one needs to solve the coupled density-matrix equations to obtain

ρ_{10}^{(5)}

for the SWM processes, which we have done in simulating the experimental results later on. For simplicity, we have solved the coupled equations with perturbation chain (I) to obtain the nonlinear density-matrix element for the multi-dressed SWM processes (including self-dressing and external-dressing) as:

ρ_{10}^{(5)} = i G_{S 1} / (A B C D E)

, where,

A = d_{1} + G_{1}^{2} / Γ_{1} + G_{1}^{2} / Γ_{0} + G_{2}^{2} / d_{2} + G_{4}^{2} / d_{4}

B = d_{2} + G_{1}^{2} / d_{2}^{'}

C = d_{1} + G_{1}^{2} / Γ_{1} + G_{2}^{2} / d_{2} + G_{3}^{2} / d_{3} + G_{4}^{2} / d_{4}

D = d_{3} + G_{1}^{2} / d_{'}^{3}

E = d_{1} + G_{1}^{2} / Γ_{1} + G_{1}^{2} / Γ_{0} + G_{3}^{2} / d_{3} + G_{4}^{2} / d_{4}

d_{1} = Γ_{10} + i Δ_{1}

d_{2} = Γ_{20} + i (Δ_{1} + Δ_{2})

d_{2}^{'} = i Δ_{2} + Γ_{21}

d_{3} = Γ_{30} + i (Δ_{1} - Δ_{3})

d_{'}^{3} = Γ_{31} - i Δ_{3}

d_{4} = Γ_{40} + i (Δ_{1} + Δ_{4})

with

Δ_{i} = Ω_{i} - ω_{i}

and

Γ_{i j}

being the transverse relaxation rate between states

| i 〉

and

| j 〉

. For the SWM1 signal (due to the weak probe field), the expression can be simplified as:

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

. Similarly, for the SWM2 signal, the expression is simplified as:

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

, where

G_{S 2} = G_{1} G_{3}^{'}^{*} G_{3} G_{4} G_{4}^{*}

There exist two ladder-type EIT windows in Fig. 1(b), i.e., the

| 0 > - | 1 > - | 2 >

EIT1 window satisfying

Δ_{1} + Δ_{2} = 0

(induced by the coupling field

E_{2}

) and the

| 0 > - | 1 > - | 4 >

EIT2 window satisfying

Δ_{1} + Δ_{4} = 0

(induced by the coupling field

E_{4}

). The EIT1 and EIT2 windows contain the SWM1 signal (

E_{S 1}

) and the SWM2 signal (

E_{S 2}

), respectively. Next, we will consider the AT splitting of the SWM signals within the EIT windows (Figs. 2 -4 ).

Fig. 2 (a1), (b1) and (c1) are the measured SWM1 self-dressing AT splitting signals versus

Δ_{1}

for

Δ_{2} = - 50 MHz

under different

P_{1}

P_{2}

and

P_{3}

powers, respectively. (a1) is increasing

P_{1} =

0.30, 0.36, 0.43, 0.90, 1.37, 1.85, 2.32, 3.66, 5.33, 8.18, 10.3, 13.61, 15.46, 22.5, 24.2, 25.3, 28.8 and 29.5mW from bottom to top. (b1) is increasing

P_{2} =

0.3, 0.6, 0.9, 1.2, 1.5, 2.1, 4.5, 7.5, 12.5, 17.2, 25.5 and 31.4mW from bottom to top. (c1) is increasing

P_{3} =

1.8, 3.9, 6.3, 7.7, 11.4, 16.7, 22.2, 33.1 and 52.2mW from bottom to top. (a2), (b2) and (c2) are the corresponding power dependences of (a1), (b1) and (c1), respectively. Here

Δ_{a}

Δ_{b}

and

Δ_{c}

are the increments of distance between the two A-T splitting peaks when

P_{1}

P_{2}

and

P_{3}

are increased, respectively, and the squares are the experimental results, while the solid lines in (a2, b2, c2) are the theoretical calculations. The fixed powers in (a1,2), (b1,2) and (c1,2) are (

P_{2} =

32.0mW &

P_{3} =

55.0mW), (

P_{1} =

13.0mW &

P_{3} =

55.0mW), and (

P_{1} =

13.0mW &

P_{2} =

32.0 mW), respectively.

Fig. 4 Measured SWM1 moving towards SWM2 signal (lower-curves) and the corresponding EIT (upper-curves) versus

Δ_{1}

for

Δ_{4} = 0

Δ_{2} = - 150

(a1),

Δ_{2} = - 15

(a2),

Δ_{2} = 15 MHz

(a3). (b3) is the SWM1 signal splitting the right peak of the SWM2 signal versus

Δ_{1}

for increasing , 2.5, 3.5, 4.5, 5.5 and 6.5 mW from bottom to top when

P_{1} =6
                              .5mW

P_{3} =38
                              .5mW

and

P_{4} =22
                              .6mW

. (b5) is the SWM1 splitting the left peak of SWM2 signals versus

Δ_{1}

under the same power of (b3). (b1) is the double-peaked SWM1 signals versus

Δ_{1}

with

Δ_{2} = - 150 M H z

. (b2), (b4) and (b6) are the corresponding power dependences. Here

Δ_{b1}

Δ_{b3}

and

Δ_{b5}

are the increments of the distances between the two large peaks in (b1), right two peaks in (b3), left two peaks in (b5), respectively, when

P_{2}

is increased, and the squares are the experimental results, while the solid lines in (b2, b4, b6) are the theoretical calculations.

3. Autler-Townes Splitting

When the external-dressing field

E_{4}

is blocked, we get the SWM1 signal within the EIT1 window (which is an inverted-Y system) [15

]. Figure 2 (a1, b1, c1) presents the SWM1 signal intensity versus the probe field detuning (

Δ_{1}

) for different field powers of

P_{1}

, and

P_{3}

with the same frequency detuning of

Δ_{2} = - 50 MHz

. Obviously, the SWM1 signal shows two peaks due to multi-dressing effects (Fig. 1(c)). With the power increases, the intensity of the SWM1 signal increases accordingly, while the left peak height is always greater than the height of the right peak. Meanwhile, the increments of the AT splitting separations

Δ_{i} = λ_{+}^{(1)} - λ_{-}^{(1)} \approx 2 \sqrt{{| G_{j} |}^{2} + {| G_{i 0} |}^{2}}

(

i =

a, b, c corresponds to

j =

1, 2, 3, respectively, and

{| G_{a0} |}^{2} = {| G_{20} |}^{2} + {| G_{30} |}^{2}

{| G_{b0} |}^{2} = {| G_{10} |}^{2} + {| G_{30} |}^{2}

{| G_{c0} |}^{2} = {| G_{10} |}^{2} + {| G_{20} |}^{2}

), increase obviously with increased powers (Rabi frequencies)

P_{1}

(

G_{1}

P_{2}

(

G_{2}

) and

P_{3}

(

G_{3}

), respectively and fixed

P_{2}

P_{3}

(

G_{20} & G_{30}

P_{1}

P_{3}

(

G_{10} & G_{30}

) and

P_{1}

P_{2}

(

G_{10} & G_{20}

), respectively. The two peaks of the double-peak SWM1 signal (Figs. 2(a1), (b1) and (c1)) correspond, from left to right, to the primarily-dressed states

| + 〉

and

| - 〉

, respectively (Fig. 1(c)). Moreover, the experimentally measured (peak separation) results in Figs. 2(a1), (b1) and (c1) are in good agreement with our theoretical calculations (solid curves), as shown in Figs. 2(a2), (b2) and (c2), respectively.

When the external-dressing field

E_{2}

is blocked, we get the SWM2 signal in the EIT2 window. Figure 3 presents the SWM2 signal intensity versus the probe field detuning (

Δ_{1}

) for different powers of

P_{1}

P_{3}

and

P_{4}

with the same frequency detuning of

Δ_{4} = 0 MHz

. Figure 3(a) depicts the measured EIT windows induced by the self-dressing field

E_{4}

versus

Δ_{1}

(satisfying

Δ_{1} + Δ_{4} = 0

). Such EIT window increases with

P_{4}

power increasing. The SWM2 signal has three peaks. In general, when the power increases, the intensity of the SWM2 signal also increases accordingly. However, the states of AT splittings change differently for different power changes. If only

P_{1}

power increases, the right peak first increases and then decreases, while the height of the middle peak is always larger than the height of either the left or right peak. If only

P_{3}

power increases, the right peak always increases, while the height of the middle peak is always larger than the height of either the left or right peak. If only

P_{4}

power increases, the height of the right peak increases monotonously to approach the height of the middle peak. The two primarily-dressed states

| + >

and

| - >

are induced by

E_{4}

. When

E_{1}

and

E_{3}

couples to the dressed state

| - >

, the secondarily-dressed states

| - + 〉

and

| - - 〉

appear. The three peaks in the SWM2 signal (Figs. 3(b1), (c1) and (d1)) correspond, from left to right, to the primarily-dressed state

| + >

, the secondarily-dressed states

| - + 〉

and

| - - 〉

, respectively (Fig. 1(d)). Based on our theoretical analysis, the two primarily-dressed states dressed by

E_{4}

can be written as

| \pm > = \sin α_{1 \pm} | 1 > + \cos α_{1 \pm} | 4 >

, and the secondarily-dressed states dressed by

E_{3}

are given by

| - \pm > = \sin α_{2 \pm} | - > + \cos α_{2 \pm} | 3 >

, where

\tan α_{1 \pm} = - b_{1 \pm} / G_{4}

\tan α_{2 \pm} = - b_{2 \pm} / \sqrt{{| G_{1} |}^{2} + {| G_{3} |}^{2}}

b_{1 \pm} = Δ_{4} - λ_{\pm}^{(3)}

, and

b_{2 \pm} = Δ_{3} - λ_{-}^{(3)} - λ_{- \pm}^{(3)}

. One can obtain the eigenvalues

λ_{\pm}^{(3)} = (Δ_{4} \pm \sqrt{Δ_{4}^{2} + 4 {| G_{4} |}^{2}}) / 2

(measured from level

| 1 >

) of

| \pm >

, and

λ_{- \pm}^{(3)} = (Δ_{3}^{'} \pm \sqrt{{Δ^{'}}_{3}^{2} + 4 ({| G_{1} |}^{2} + {| G_{3} |}^{2})}) / 2

(measured from level

| - >

) of

| - \pm >

, where

Δ_{3}^{'} = - Δ_{3} - λ_{-}^{(3)}

Fig. 3 (a) is the measured EIT2 induced by the field

E_{4}

versus

Δ_{1}

. (b1), (c1) and (d1) are the measured SWM2 self-dressing AT splitting signals versus

Δ_{1}

for

Δ_{4} = 0

under different

P_{1}

P_{3}

and

P_{4}

powers, respectively. (b1) is increasing

P_{1} =0
                              .4

, 0.9, 1.4, 1.8, 3.7, 5.3, 9.3, 10.3, 13.6, 15.5, 24.7 and 29.5 mW from bottom to top. (c1) is increasing

P_{3} = 1.2

, 1.4, 2.9, 4.6, 6.6, 8.2, 9.5 and 27.2 mW from bottom to top. (d1) is increasing

P_{4} =

0.12, 0.48, 0.6, 1.36, 2.47, 3.1, 5.4, 7.7, 14.0, 23.0, 39.0, 71.0, 116.0, 142.0, 184.0, 205.0, 225.0, 242.0 and 258.0 mW from bottom to top. (b2), (c2) and (d2) are the corresponding power dependences of (b1), (c1) and (d1), respectively. Here

Δ_{b}

Δ_{c}

and

Δ_{d}

are the increments of the distance between the right (for

Δ_{b}

and

Δ_{c}

) or left (for

Δ_{d}

) two A-T splitting peaks, respectively, when

P_{1}

P_{3}

and

P_{4}

are increased, respectively, and the squares are the experimental results, while the solid lines in (b2, c2, d2) are the theoretical calculations. The fixed powers in (b1, 2), (c1, 2) and (d1, 2) are (

P_{3} =

30.0mW &

P_{4} =

150.0mW), (

P_{1} =

1.0 mW &

P_{4} =

150.0mW), and (

P_{1} =

1.0 mW &

P_{3} =

30.0mW), respectively.

Meanwhile, the increments of the AT splitting separations

Δ_{b} = λ_{-+}^{(3)} - λ_{--}^{(3)} =2 \sqrt{{| G_{1} |}^{2} + {| G_{30} |}^{2}}

Δ_{c} = λ_{- +}^{(3)} - λ_{- -}^{(3)} = 2 \sqrt{{| G_{3} |}^{2} + {| G_{10} |}^{2}}

, and

Δ_{d} = λ_{+}^{(3)} - λ_{- +}^{(3)} = 2 G_{4} - \sqrt{{| G_{10} |}^{2} + {| G_{30} |}^{2}} \approx 2 G_{4}

(

G_{4} > > G_{10,30}

) increase obviously with increased powers (Rabi frequencies) of

P_{1}

(

G_{1}

P_{3}

(

G_{3}

) and

P_{4}

(

G_{4}

), respectively and fixed

P_{3}

P_{4}

(

G_{30} & G_{40}

P_{1}

P_{3}

(

G_{10} & G_{30}

) and

P_{1}

P_{4}

(

G_{10} & G_{40}

), respectively. When the self-dressing

P_{4}

power changes, the state of the AT splitting obviously has an essential distinction from the former two states as the powers of

P_{1}

and

P_{3}

change. The experimentally measured results in Figs. 3(b1), (c1) and (d1) are in good agreement with our theoretical calculations shown in Figs. 3(b2), (c2) and (d2), respectively.

After studying the self-dressing AT splitting of the individual SWM1 or SWM2 signal, we will now consider the cross-dressing AT splitting between the two SWM signals. Figures 4(a1) - 4(a3) present the interplay between the two SWM signals versus the probe field detuning (

Δ_{1}

) for different external-dressing field detunings (

Δ_{2}

) with

Δ_{4} = 0 MHz

. Here, we consider the case with

G_{2} < G_{4}

. The upper-curve in each figure is the probe transmission with two ladder-type EIT windows and the lower-curve gives the measured SWM signals. In Fig. 4(a1), the left EIT window (

| 0 > - | 1 > - | 4 >

satisfying

Δ_{1} + Δ_{4} = 0

) is induced by the coupling field

E_{4}

,which contains the SWM2 signal (

E_{S 2}

), and the right one (

| 0 > - | 1 > - | 2 >

satisfying

Δ_{1} + Δ_{2} = 0

, Δ₂ = -15MHZ) is induced by the coupling field

E_{2}

, which contains the SWM1 signal (

E_{S 1}

). Since the right EIT window (

Δ_{2} = - 150 MHz

) is quite far from the left EIT window, these two SWM signals have little effect on each other (Fig. 4(a1)). When the frequency of

E_{2}

is tuned to move the right EIT window (

| 0 > - | 1 > - | 2 >

) towards the left one, the two EIT windows overlap at

Δ_{2} = - 15 MHz

, which leads to the triple AT splitting for SWM2, i.e., the right peak of SWM2 signal is further split into two peaks (Fig. 4(a2), satisfying

Δ_{2} = λ_{- -}^{(3)}

). It is the coupling field

E_{2}

that couples the secondarily-dressed state

| - - 〉

dressed by

E_{3}

and splits it into two triply-dressed states

| - - + >

and

| - - - >

. The four peaks of the SWM2 signal in Fig. 4(a2) correspond, from left to right, to the primarily-dressed state

| + >

, the secondarily-dressed states

| - + 〉

, the triply-dressed states

| - - + >

and

| - - - >

, respectively (Fig. 1(e)). We can write the triply-dressed states as

| - - \pm > = \sin α_{3 \pm} | - - 〉 + \cos α_{3 \pm} | 2 >

, where

\tan α_{3 \pm} = - b_{3 \pm} / G_{2}

b_{3 \pm} = Δ_{2} - λ_{-}^{(3)} - λ_{- -}^{(3)} - λ_{- - \pm}^{(3)}

, and the other parameters are the same as before. One can obtain the eigenvalues

λ_{- - \pm}^{(3)} = (Δ_{2}^{'} \pm \sqrt{{Δ^{'}}_{2}^{2} + 4 {| G_{2} |}^{2}}) / 2

(measured from level

| - - 〉

) for the dressed states

| - - \pm >

, where

Δ_{2}^{'} = Δ_{2} - λ_{-}^{(3)} - λ_{- -}^{(3)}

. With the right EIT window (

| 0 > - | 1 > - | 2 >

) continuously moving to the left, the SWM1 signal splits the left peak of the SWM2 signal when

Δ_{2} = 15 MHz

, as shown in Fig. 4(a3). Corresponding to the moving SWM1 signal in Fig. 4(a1), Fig. 4(b1) presents the measured self-dressing double-peak SWM1 signal versus

Δ_{1}

with

Δ_{2} = 0 MHz

. Corresponding to the fixed SWM2 signal in Figs. 4(a2) and 4(a3), Figs. 4(b3) and 4(b5) show the measured SWM2 signals, whose right and left peaks are split by the SWM1 signal, versus

Δ_{1}

with an increasing external-dressing

P_{2}

power, respectively. Figures 4(b2), 4(b4) and 4(b6) give the corresponding power dependences of the AT-splitting separations. The corresponding separations are determined by

Δ_{b 1} = λ_{+}^{(1)} - λ_{-}^{(1)} \approx 2 G_{2}

Δ_{b 3} = λ_{- - +}^{(3)} - λ_{- - -}^{(3)} \approx 2 G_{2}

, and

Δ_{b 5} \approx 2 G_{2}

, respectively.

4. Conclusion

In summary, we have observed the self- and externally-dressed AT splittings of the SWM processes within EIT windows in a five-level atomic system. Such AT splitting demonstrates the interactions between two coexisting SWM processes. The controlled multi-channel splitting signals in nonlinear optical processes can find potential applications in optical communication and quantum information processing, such as wavelength-demultiplexer [18

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009). [CrossRef] [PubMed]

–20

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008). [CrossRef] [PubMed]

Acknowledgments

This work was supported by NSFC (10974151, 61078002, 61078020), NCET (08-0431), RFDP (20100201120031), 2009xjtujc08, XJJ20100100, XJJ20100151.

References and links

1.	S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955). [CrossRef]
2.	W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994). [CrossRef] [PubMed]
3.	J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999). [CrossRef]
4.	O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002). [CrossRef] [PubMed]
5.	C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007). [CrossRef] [PubMed]
6.	T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010). [CrossRef] [PubMed]
7.	S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]
8.	M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995). [CrossRef] [PubMed]
9.	R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995). [CrossRef] [PubMed]
10.	S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A 58(3), 2500–2505 (1998). [CrossRef]
11.	Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007). [CrossRef] [PubMed]
12.	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]
13.	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]
14.	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]
15.	R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009). [CrossRef]
16.	G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001). [CrossRef]
17.	Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010). [CrossRef] [PubMed]
18.	K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009). [CrossRef] [PubMed]
19.	R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009). [CrossRef]
20.	V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008). [CrossRef] [PubMed]

OCIS Codes
(030.1670) Coherence and statistical optics : Coherent optical effects
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(270.4180) Quantum optics : Multiphoton processes
(300.2570) Spectroscopy : Four-wave mixing

ToC Category:
Nonlinear Optics

History
Original Manuscript: February 15, 2011
Revised Manuscript: March 28, 2011
Manuscript Accepted: March 29, 2011
Published: April 6, 2011

Citation
Yanpeng Zhang, Peiying Li, Huaibin Zheng, Zhiguo Wang, Haixia Chen, Changbiao Li, Ruyi Zhang, and Min Xiao, "Observation of Autler-Townes splitting in six-wave mixing," Opt. Express 19, 7769-7777 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7769

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References

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955). [CrossRef]
W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994). [CrossRef] [PubMed]
J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999). [CrossRef]
O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002). [CrossRef] [PubMed]
C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007). [CrossRef] [PubMed]
T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010). [CrossRef] [PubMed]
S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]
M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995). [CrossRef] [PubMed]
R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995). [CrossRef] [PubMed]
S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A 58(3), 2500–2505 (1998). [CrossRef]
Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007). [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]
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]
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]
R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009). [CrossRef]
G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001). [CrossRef]
Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010). [CrossRef] [PubMed]
K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009). [CrossRef] [PubMed]
R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009). [CrossRef]
V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008). [CrossRef] [PubMed]

Amthor, T.
Ates, C.
Autler, S. H.
Boyd, R. W.
Boyer, V.
Brown, A. W.
Camacho, R. M.
Chalupczak, W.
Dolgaleva, K.
Drampyan, R.
Dunn, M. H.
Fleischhauer, M.
Fu, G. S.
Fu, P. M.
Fulton, D. J.
Gaeta, A. L.
Gawlik, W.
Gea-Banacloche, J.
Giese, C.
Harris, S. E.
Hofmann, C. S.
Howell, J. C.
Jiang, Q.
Jin, S.
Kärtner, F. X.
Kowal, Z.
Lazarov, G.
Lett, P. D.
Li, C. B.
Li, L.
Li, Y.
Liu, X.
Lukin, M. D.
Lyyra, A. M.
Marino, A. M.
Morgner, U.
Moseley, R. R.
Mücke, O. D.
Narducci, L. M.
Nie, Z. Q.
Pattard, T.
Pohl, T.
Pooser, R. C.
Pustelny, S.
Qi, J. B.
Rickey, E. G.
Rost, J. M.
Scully, M. O.
Shepherd, S.
Shin, H.
Sinclair, B. D.
Spano, F. C.
Sun, J.
Townes, C. H.
Tritschler, T.
Vudyasetu, P. K.
Wang, X. J.
Wang, Z. G.
Wasik, G.
Wegener, M.
Weidemüller, M.
Wen, F.
Wielandy, S.
Wu, L. A.
Xiao, M.
Yan, M.
Yelin, S. F.
Zachorowski, J.
Zhang, Y. P.
Zhu, Y. F.
Zuo, Z. C.

Nat. Photonics

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009). [CrossRef]

Opt. Lett.

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010). [CrossRef] [PubMed]

Phys. Rev.

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955). [CrossRef]

Phys. Rev. A

W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994). [CrossRef] [PubMed]
S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A 58(3), 2500–2505 (1998). [CrossRef]
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]
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]
R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009). [CrossRef]
G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001). [CrossRef]

Phys. Rev. Lett.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009). [CrossRef] [PubMed]
Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007). [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]
M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995). [CrossRef] [PubMed]
R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995). [CrossRef] [PubMed]
J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999). [CrossRef]
O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002). [CrossRef] [PubMed]
C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007). [CrossRef] [PubMed]
T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010). [CrossRef] [PubMed]

Phys. Today

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

Science

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008). [CrossRef] [PubMed]

2010, Amthor, Phys. Rev. Lett.
2010, Zhang, Opt. Lett.
2009, Dolgaleva, Phys. Rev. Lett.
2009, Camacho, Nat. Photonics
2009, Drampyan, Phys. Rev. A
2008, Boyer, Science
2007, Ates, Phys. Rev. Lett.
2007, Zhang, Phys. Rev. Lett.
2006, Zuo, Phys. Rev. Lett.
2002, Mücke, Phys. Rev. Lett.
2001, Wasik, Phys. Rev. A
2001, Yan, Phys. Rev. A
1999, Qi, Phys. Rev. Lett.
1999, Lukin, Phys. Rev. A
1998, Wielandy, Phys. Rev. A
1997, Harris, Phys. Today
1995, Xiao, Phys. Rev. Lett.
1995, Moseley, Phys. Rev. Lett.
1994, Chalupczak, Phys. Rev. A
1955, Autler, Phys. Rev.

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