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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 5 — Mar. 11, 2013
  • pp: 5654–5670
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Observation of angle-modulated switch between enhancement and suppression of nonlinear optical processes

Zhiguo Wang, Zhengyang Zhao, Peiying Li, Jiamin Yuan, Huayan Lan, Huaibin Zheng, Yiqi Zhang, and Yanpeng Zhang  »View Author Affiliations


Optics Express, Vol. 21, Issue 5, pp. 5654-5670 (2013)
http://dx.doi.org/10.1364/OE.21.005654


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Abstract

We simultaneously investigate the four-wave mixing and the fluorescence signals via two cascade electromagnetically induced transparency (EIT) systems in atomic rubidium vapor. By manipulating the deflection angle between the probe beam and certain coupling beams, the dark state can extraordinarily switch to bright state, induced by the angle-modulation on the dressing effect. Besides, in the fluorescence signal, the peak of two-photon fluorescence due to classical emission and the dip of single-photon fluorescence due to dressing effect are distinguished, both in separate spectral curves and in the global profile of spectrum. Meanwhile, we observe and analyze the similarities and discrepancies between the two ground-state hyperfine levels F = 2 and F = 3 of Rb 85 for the first time.

© 2013 OSA

1. Introduction

The coherent superposition of atomic states forms the base for a great deal of interesting phenomena in nonlinear laser spectroscopy. One of these phenomena resulting from the quantum interference between dressed states [1

1. C. Li, Y. Zhang, H. Zheng, Z. Wang, H. Chen, S. Sang, R. Zhang, Z. Wu, L. Li, and P. Li, “Controlling cascade dressing interaction of four-wave mixing image,” Opt. Express 19(14), 13675–13685 (2011). [CrossRef] [PubMed]

,2

2. N. Li, Z. Zhao, H. Chen, P. Li, Y. Li, Y. Zhao, G. Zhou, S. Jia, and Y. Zhang, “Observation of dressed odd-order multi-wave mixing in five-level atomic medium,” Opt. Express 20(3), 1912–1929 (2012). [CrossRef] [PubMed]

] is electromagnetically induced transparency (EIT) [3

3. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997). [CrossRef]

7

7. A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57(4), 2996–3002 (1998). [CrossRef]

]. Under EIT condition, several higher-order nonlinear optical processes including four-wave mixing (FWM) [8

8. 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]

10

10. Y. 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]

] are allowed to occur in multi-level atomic systems, since the weak generated signals can be allowed to transmit through the resonant atomic medium with little absorption. Meanwhile, the fluorescence due to spontaneous emission can also generate within the EIT windows [11

11. J. Qi, G. Lazarov, X. 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]

,12

12. J. Qi and A. M. Lyyra, “Electromagnetically induced transparency and dark fluorescence in a cascade three-level diatomic lithium system,” Phys. Rev. A 73(4), 043810 (2006). [CrossRef]

] and the competition between amplified spontaneous emission and four-wave-mixing process has been studied [13

13. R. W. Boyd, M. S. Malcuit, D. J. Gauthier, and K. Rzaewski, “Competition between amplified spontaneous emission and the four-wave-mixing process,” Phys. Rev. A 35(4), 1648–1658 (1987). [CrossRef] [PubMed]

].

Furthermore, the suppression and enhancement of FWM, which are respectively corresponding to EIT and EIA (electromagnetically induced absorption) of probe transmission, also attracted the attention of many researchers [2

2. N. Li, Z. Zhao, H. Chen, P. Li, Y. Li, Y. Zhao, G. Zhou, S. Jia, and Y. Zhang, “Observation of dressed odd-order multi-wave mixing in five-level atomic medium,” Opt. Express 20(3), 1912–1929 (2012). [CrossRef] [PubMed]

,14

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

,15

15. Z. Wang, Y. Zhang, H. Zheng, C. Li, F. Wen, and H. Chen, “Switching enhancement and suppression of four-wave mixing via a dressing field,” J. Mod. Opt. 58(9), 802–809 (2011). [CrossRef]

]. By altering the frequency detunings of incident laser fields, the switch between dark state (EIT of probe transmission and suppression of FWM) and bright state (EIA of probe transmission and enhancement of FWM) is obtainable [2

2. N. Li, Z. Zhao, H. Chen, P. Li, Y. Li, Y. Zhao, G. Zhou, S. Jia, and Y. Zhang, “Observation of dressed odd-order multi-wave mixing in five-level atomic medium,” Opt. Express 20(3), 1912–1929 (2012). [CrossRef] [PubMed]

,13

13. R. W. Boyd, M. S. Malcuit, D. J. Gauthier, and K. Rzaewski, “Competition between amplified spontaneous emission and the four-wave-mixing process,” Phys. Rev. A 35(4), 1648–1658 (1987). [CrossRef] [PubMed]

,15

15. Z. Wang, Y. Zhang, H. Zheng, C. Li, F. Wen, and H. Chen, “Switching enhancement and suppression of four-wave mixing via a dressing field,” J. Mod. Opt. 58(9), 802–809 (2011). [CrossRef]

]. It is also reported recently by manipulating the phase difference between the two circularly polarized components of a single coherent field, the EIT-EIA switch could be realized [16

16. U. Khadka, Y. Zhang, and M. Xiao, “Control of multitransparency windows via dark-state phase manipulation,” Phys. Rev. A 81(2), 023830 (2010). [CrossRef]

].

2. Basic theory and experimental scheme

2.1 Experimental setup

The experiment is carried out in a rubidium vapor cell, whose energy levels of 5S1/2 (|0), 5P3/2 (|1), 5D5/2 (|2) and 5D3/2 (|3) form a four-level Y-type atomic system, as shown in Fig. 1(a)
Fig. 1 (a) Relevant four-level Y-type atomic system with one probe field E1, two coupling fields E2 and E2, and another two coupling fields E3 and E3. EF1 and EF2 are the generated FWM signals. R0, R1 and R2 are the generated fluorescence signals. (b) Normal phase-matching spatial beam geometry. (c)-(e) The abnormal propagation configurations for the ladder type subsystem and Y-type system, with the deflection angles α and β. The dash lines in (c)-(e) represent the direction of beams when the deflection angles equal 0.
. The resonant frequencies are Ω1, Ω2 and Ω3 for transitions|0 to |1, |1 to |2 and |1 to |3 respectively. The temperature of the atomic vapor cell is set at 60C. A weak probe beam E1 (with frequency ω1, wave vector k1, Rabi frequency G1 and frequency detuning Δ1, where Δi=Ωiωi) from an external cavity diode laser (ECDL), is horizontally polarized and probes the lower transition |0 to |1. Two coupling laser beams E2 (ω2, k2, G2 and Δ2) and E2 (ω2, k2, G2 and Δ2) splitting from a cw Ti:sapphire laser with vertical polarization, drive the upper transition |1 to |2. Another two coupling laser beams E3 (ω3, k3, G3 and Δ3) and E3 (ω3, k3, G3 and Δ3) splitting from an ECDL with vertical polarization, drive the upper transition |1 to |3. Using this experimental setup, we will study three kinds of signals simultaneously: the transmission of probe beam, the four-wave mixing signals EF1 and EF2, and the fluorescence signals R0, R1 and R2 (shown in Fig. 1(a)). Especially, we mainly focus on the control of signal patterns through varying the direction of incident beams.

In normal experimental configuration, the five laser beams are spatially designed in a square-box pattern as shown in Fig. 1(b), in which the coupling beams E2, E2, E3 and E3 propagate through the Rb vapor cell in the same direction with small angles (about 0.3) between one another, and the probe beam E1 propagates in the opposite direction of E2. In such beam geometric configuration, the two-photon Doppler-free conditions will be satisfied for the two ladder-type subsystems |0|1|2 and |0|1|3, thus two EIT windows appear in the probe transmission spectrum. Also, two FWM processes EF1 (generated by E1, E2 and E2) and EF2 (generated by E1, E3 and E3) can occur simultaneously within the two EIT windows, both propagating in the direction of kF (at the lower right corner of Fig. 1(b)) satisfying the phase-matching condition kF1=k1+k2k2 or kF2=k1k3+k3. In our experiments, we used a silicon photodiode to monitor the transmitted probe spectrum, and an avalanche photodiode detector to measure the generated FWM signals.

In addition to FWM signals induced by atomic coherence, three fluorescence signals due to spontaneous emission are studied simultaneously: the decay of photons from |1 to |0 generate single-photon fluorescence signal R0, and the decay of photons from |2 or |3 to |1 separately generate two-photon fluorescence signals R1 and R2, as shown in Fig. 1(a). These non-directional fluorescence signals are collected by a photodiode located at the side of the vapor cell. Similar to FWM signals, the two-photon fluorescence R1 and R2 also fall into the EIT windows and form the Doppler-free sharp peaks in frequency domain.

In our experiments, we especially focus on the angle-modulated switch on the probe transmission signal, FWM signals and fluorescence signals. When certain coupling beams are deflected with a small angle from their “normal” directions, the behaviors of the detected signals will change significantly: EIT peak in the probe transmission spectrum would switch to EIA dip; the suppression of FWM signal would alter to enhancement; and the pattern of fluorescence signals would also change correspondingly. We use the symbol α to represent the deflection of the coupling beams E2 and E2 from their normal directions (as shown in Fig. 1(c)-1(d)), and use the symbol β to represent the deflection of the coupling beams E3 and E3 from their normal directions (as shown in Fig. 1(e)). By altering the deflection angle α or β in different conditions, we can observe the switches of signals’ pattern we stated above. In the following we term such deflected spatial geometry (Fig. 1(c)-1(e)) the “abnormal” propagation configuration, to distinguish it from the “normal” spatial geometry shown in Fig. 1(b).

2.2 Basic theory

Via the Liouville pathway (perturbation chain) ρ00(0)E1ρ10(1), the element ρ10(1) can be written as:
ρ10(1)=iG1/d1,
(1a)
with d1=Γ10+iΔ1 (Γij is the transverse relaxation rate between |i and |j). The opposite of the imaginary part of ρ10(1) is proportional to the transparency degree of probe beam. When further considering the strong dressing effect of coupling fields E2(E2) and E3(E3), the energy level |1 was split to two dressed states |+ and |, thereby ρ10(1) is revised as:
ρ10SD(1)=iG1/(d1+|G2|2/d2),
(1b)
ρ10DD(1)=iG1/(d1+|G2|2/d2+|G3|2/d3),
(1c)
with d2=Γ20+i(Δ1+Δ2) and d3=Γ30+i(Δ1+Δ3), (the subscript SD means single-dressed, DD means double-dressed). Via the pathway ρ00(0)E1ρ10(1)E2ρ20(2)(E2)*ρ10(3), the FWM process EF1 can be described by:
ρF1DD(3)=iG1G2(G2)*/[(d1+|G2|2/d2+|G3|2/d3)2d2]
(2)
with doubly dressing effect. Similarly, the FWM process EF2 can be described by:
ρF2DD(3)=iG1G3(G3)*/[(d1+|G2|2/d2+|G3|2/d3)2d3]
(3)
with doubly dressing effect.

For the fluorescence signals, the intensity of single-photon fluorescence (R0) and two-photon fluorescence (R1 and R2) are separately proportional to the square of the module of second-order matrix element (ρ11(2)) and fourth-order matrix elements (ρ22(4) and ρ33(4)), since the square of the module of diagonal elements represent the density of particles in corresponding states. First of all, with only probe beam E1 turned on, the single-photon fluorescence signal R0 generates, the process of which is described by the pathway ρ00(0)E1ρ10(1)(E1)*ρ11(2). Guided by the pathway, we can easily obtain the expression of ρ11(2) from the density-matrix equations, as:
ρ11(2)=|G1|2/(Γ11d1).
(4a)
With E2(E2) and E3(E3) also turned on, R0 can get singly or doubly dressed:
ρ11SD(2)=|G1|2/[Γ11(d1+|G2|2/d2)],
(4b)
ρ11DD(2)=|G1|2/[Γ11(d1+|G2|2/d2+|G3|2/d3)].
(4c)
Especially, if we further simplify Eqs. (1a)-(1c) and Eqs. (4a)-(4c), we discover the square of the module of ρ11(2) and the imaginary part of ρ10(1) behave similarly. Therefore we assume the single-photon fluorescence signal and the probe transmission signal behave in corresponding manners. This hypothesis would be verified by both experimental results and simulations in the following sections.

ρ33SD(4)=|G1|2|G3|2/[Γ33d1d5(d3+|G3|2/d1)]
(6b)

When the coupling beams are deflected with a small angle α or β, because of phase matching conditions, the coupling strength (Rabi frequency) becomes a function of the angles. As is known, Rabi frequency Gi is defined as Gi=μiEicosθ/ where Ei represents the electric field, μi is the dipole moment of transition the light field excites, and θ represents the angle between the polarization of the light and the transition dipole moment. Now, when the additional deflection angle α between E2 and the opposite direction of E1 is introduced in, the orientation of electric field E2 changes, and the Rabi frequency G2 should be modified as G2=μ2E2cos(θ±α)/. Similarly, when the beam E3 is deflected with the angle β, the Rabi frequency G3 should be modified as G3=μ3E3cos(θ±β)/. In a word, by manipulating the deflection angles, we can control the coupling strength, and thereby control the switch between dark state and bright state. Although the angles α or β are relatively small, we will find the signals are strikingly sensitive to their alterations.

3. Observation of angle modulation in ladder type subsystem

We first consider the angle modulation in the |0|1|2 ladder type subsystem when three beams E1, E2 and E2 are turned on (as shown in Fig. 1(c)). We separately show the results with the two ground-state hyperfine levels (GSHL) of 85Rb: 5S1/2F=3 in Fig. 2
Fig. 2 (a)-(c) Measured signals versus Δ2 at discrete probe detuning Δ1 and discrete deflection angle α, the ground-state is 5S1/2F=3. The top curves ((a1)-(a4)) are probe transmission; the middle curves ((b1)-(b4)) are FWM signal; and the bottom curves ((c1)-(c4)) are fluorescence signal. The experimental parameters are P1=8mW, P2=10mW and P2=10mW. (d1)-(d3) Calculated probe transmission versus α at three typical detunings.
and 5S1/2F=2 in Fig. 3
Fig. 3 (a)-(c) Measured signals versus Δ2 at discrete Δ1 and α, the ground state is 5S1/2F=2. The experimental parameters are the same as Fig. 2. (d1)-(d2) Magnified sub-graphs for 5S1/2F=3 and F=2 of 85Rb. (e) Realistic energy level diagram showing the hyperfine levels of each driven state, where the FWM transitions with the least number of decay channels are presented.
. In both cases the angle modulation effect can be observed clearly, but some discrepancies can also be observed in the results with two different ground states.

As is known, the suppression of FWM is obtained in EIT window, and the enhancement of FWM is in company with EIA. Thus the switch between the suppression and enhancement of FWM will appear along with the EIT-EIA switch. In Figs. 2(b1)-2(b4), the suppression-enhancement switch of FWM is reflected in the variation in signal’s intensity with different angles. For instance, when α is set at 0.08 (Fig. 2(b1)) or 0 (Fig. 2(b2)), the FWM signal reaches its maximum at Δ1=300MHz; and when α is set at 0.08 (Fig. 2(b3)), it reaches the maximum around Δ1=450MHz. Admittedly, there’re some other factors which could also lead to the variation in the intensity of FWM. For instance, the FWM generally weakens with α increasing, because the effective overlap cross section of the beams generating FWM decreases. Therefore analyzing the variation in the intensity of FWM is not an ideal way to observe the suppression-enhancement switch. In Sec. 5, we will observe the switch in FWM directly using another method.

Now we turn to the results for the other ground state: 5S1/2F=2 of 85Rb (Figs. 3(a)-3(c)). The phenomenon of angle-modulation for F=2 is similar with F=3, except for some discrepancies. To show the details clearly, we magnified two typical sub-graphs from Figs. 2(a)-(c) and Figs. 3(a)-3(c) respectively, as shown in Figs. 3(d1)-3(d2). In the case of F=3 (Fig. 2(a)), when Δ1 is set at negative points (for example Δ1=300MHz), the probe transmission signal can change from strong EIT (α=0.08), to weak EIT (α=0), then to weak EIA (α=0.08), and finally to strong EIA (α=0.16). But when Δ1 is set at positive points, the switch process is not as striking as above. By contrast, in the case of F=2 (Fig. 3(a)), the striking EIA-EIT switch happens in positive probe detuning region. Besides, the strongest FWM generation also appears in positive probe detuning region for F=2 (Fig. 3(b)), which is different from the case of F=3 where the strongest FWM appears in negative detuning region (Fig. 2(b)). Moreover, the fluorescence signals for the two ground states are also different. Comparing the fluorescence signal for F=2 with that for F=3, we find the suppression dip of fluorescence disappears for F=2 ground state (Fig. 3(d2)). These discrepancies could be explained with the assistance of the realistic energy level diagram in Fig. 3(e). For the ground state F=3, the higher frequency transition F=3F=4 is closed; in other words the pathways involving F=4 have the fewest decay channels. Therefore the FWM generation and the switch for F=3 are strongest in the negative-detuned region where the F=4 level lies [20

20. U. Khadka, H. Zheng, and M. Xiao, “Four-wave-mixing between the upper excited states in a ladder-type atomic configuration,” Opt. Express 20(6), 6204–6214 (2012). [CrossRef] [PubMed]

]. On the contrary, for the ground state F=2, the lower frequency transition F=2F=1 is closed. That’s why for F=2 the strongest FWM and switch appear in positive-detuned region.

In following sections, the experiments are all performed with ground state F=3 of 85Rb.

4. Observation of angle modulation in Y-type subsystem

In this section, we emphasize on the angle modulation in the Y-type system where the doubly dressing effect should be considered. First in Fig. 4, with E1, E2, E2 and E3 turned on and E3 blocked (as the geometry shown in Fig. 1(d)), we study the signals by scanning Δ2 at different Δ3 points, with the angle α set at two typical values α=0.04 (Fig. 4(a)) and α=0.16 (Fig. 4(c)). The theoretical calculations corresponding to Figs. 4(a) and 4(c) are presented in Figs. 4(b) and (d).

Under the doubly dressing condition, two EIT would form simultaneously in the probe transmission spectrum: the |0|1|2 EIT and the |0|1|3 EIT. In the case of α=0.04, the global profile of the transmitted probe signal (Fig. 4(a1)) versus Δ3 reaches its summit at Δ3=Δ1=0, representing the |0|1|3 EIT window; on the other hand, the peak on each curve versus Δ2 is the |0|1|2 EIT window, satisfying Δ1+Δ2=0. When α is adjusted to α=0.16, the |0|1|2 EIT peaks can be observed totally switch to EIA dips, as shown in Fig. 4(c1). Notice the |0|1|3 EIT profile remains the same under the two angles, because changing the direction of E2 and E2 will not influence the dressing effect of E3.

In Fig. 4(a1) and 4(c1), when comparing the curves at Δ3=0MHz, Δ3=±30MHz and Δ3=±60MHz, one can discover that both the |0|1|2 EIT in Fig. 4(a1) and the |0|1|2 EIA in Fig. 4(c1) reach their minimum amplitude at Δ3=0MHz, matching the condition Δ1+Δ2=Δ1+Δ3=0. This is due to the strong sequential-cascade-dressing interaction between the two ladder type subsystems |0|1|2 and |0|1|3, according to the doubly dressed term d1+|G2|2/d2+|G3|2/d3 in Eq. (1c). Such interaction can be illustrated with the dressed state diagrams in Fig. 4(e). Figures 4(e1)-4(e5) separately present the diagrams of dressed states with Δ3 gradually altering from negative to positive. Due to the dressing effect of E3, the energy level |1 would be split into two dressed states |+ and |, the positions of which altering along with Δ3. As we know, the larger the relative frequency of a field to the transition it drives, the weaker the dressing effect is. When Δ3=0MHz (Fig. 4(e3)), the relative frequency of E2(E2) to the transition |+|2 or ||2 is large, therefore the dressing effect of E2(E2) is relatively weak and the |0|1|2 EIT/EIA is small; with |Δ3| increasing, the relative frequency of E2(E2) to one of the two transitions |+|2 and ||2 gets smaller, therefore the dressing effect of E2(E2) becomes larger and the |0|1|2 EIT/EIA becomes stronger.

For the FWM signal EF1 generated by E1, E2 and E2 shown in Fig. 4(a2), we can see its intensity is much weaker at resonant point (Δ3Δ1=0) than at detuned Δ3, for the suppression of the external dressing field E3 on EF1 is strongest around Δ3=Δ1. When α is adjusted to 0.16 (Fig. 4(c2)), EF1 is greatly strengthened at each Δ3 point. This is for the reason that the original suppression effect on EF1 induced by the self-dressing fields E2(E2) transforms to enhancement effect when α=0.16, corresponding to the switch from EIT to EIA of the transmitted probe field.

The fluorescence signal in Figs. 4(a3) and 4(c3) includes the doubly dressed single-photon fluorescence R0, and the two-photon fluorescence R1. For R0, on the one hand it is suppressed by E3 to its minimum around Δ3Δ1=0, corresponding to the |0|1|3 EIT profile in Figs. 4(a1) and (c1); on the other hand it is also suppressed by E2(E2), shown as the dip on each curve, corresponding to the |0|1|2 EIT peak. The sharp peak within each dip represents the emission of the two-photon fluorescence R1. It is obvious in Fig. 4(a3) that the suppression dip of R0 induced by E2(E2) gets much shallower when Δ3 approaches the resonant point, in agreement with the weakened |0|1|2 EIT peaks around Δ3=0 in Fig. 4(a1). Under the condition of α=0.16 (Fig. 4(c3)), the suppression dip on each curve become shallower compared with those in Fig. 4(a3). This corresponds to the behavior of probe transmission signal which changes from EIT (α=0.04) to EIA (α=0.16). To make the facts above more evident, we present the corresponding theoretical calculated results in Figs. 4(b) and 4(d), which are in good agreement with the experimental results in Figs. 4(a) and 4(c).

Next, the generated signals under a specific abnormal configuration (α=0.16) are present in Fig. 5
Fig. 5 (a) and (c) Measured probe transmission (top curves), FWM signal EF1 (middle curves), and fluorescence signals (bottom curves) versus Δ2 at discrete Δ3, with α=0.16, E3 blocked and Δ1 fixed at Δ1=0MHz for (a) and Δ1=150MHz for (c). The other parameters are P1=4mW, P2=12.6mW,P2=6.3mW and P3=40mW. (b) and (d) Calculated fluorescence signals corresponding to (a3) and (c3) separately.
, where we will put emphasis on the variation of fluorescence signals in particular. Figures 5(a) and (c) present the measured signals by scanning Δ2 at different Δ3 points with α=0.16, in which the probe detuning Δ1 is set at Δ1=0MHz for Fig. 5(a) and Δ1=150MHz for Fig. 5(c). Similar with the case in Fig. 4(c1), the abnormal EIA dip instead of normal EIT peak appears around Δ1+Δ3=0 in the transmitted probe spectrum, due to the modulation of angle α. However, we notice the EIA dip in Figs. 5(a1) and 5(c1) emerges only in a small region around Δ1+Δ3=0, whereas the EIA in Fig. 4(c1) appears in a extensive region, this is the result of the smaller probe field power P1 in Fig. 5 compared with Fig. 4. For the FWM signal in Figs. 5(a2) and 5(c2), it’s obvious that the intensity is greatly larger at the detuning point Δ1=150MHz (Fig. 5(c2)) than at Δ1=0MHz (Fig. 5(a2)), due to the different numbers of decay channels between transitions, which has already been discussed in Sec. 3.

When we turn to the fluorescence signals in Figs. 5(a3) and 5(c3), we find all three types of fluorescence (R0, R1 and R2) arise in the spectrum under such experimental condition. To discriminate them clearly, we present the corresponding calculated fluorescence signals as R0 (~|ρ11|2), R1 (~|ρ22|2), R2 (~|ρ33|2) and the total fluorescence signal (~|ρ11|2+|ρ22|2+|ρ33|2) separately in Figs. 5(b) and 5(d), among which the calculated total fluorescence signal in Figs. 5(b4) and 5(d4) is the simulation of the experimental detected fluorescence signal in Figs. 5(a3) and 5(c3). When Δ1=0MHz, the calculated single-photon fluorescence R0 is shown in Fig. 5(b1), where we can see each curve reveals as a dip resulting from the suppression effect of E2(E2). Besides, the global profile of the curves also reveals as a big dip (shown as the dash line), for R0 is also suppressed by E3. Figs. 5(b2) and 5(b3) show the two-photon fluorescence R1 and R2, respectively. Under the method of scanning Δ2 at different Δ3 points, the fluorescence signal R1 reveals as an emission peak on each spectral line (Fig. 5(b2)); while the fluorescence signal R2 reveals as an emission profile composed of a series of horizontal lines at each Δ3 point (Fig. 5(b3)). Therefore, when we turn to the total fluorescence signal in Fig. 5(b4), it is obvious that its intensity versus Δ2 (the curve at each Δ3 point) reveals as a dip (the suppression induced by E2(E2) on R0) containing a sharp peak (R1), and fluorescence intensity versus Δ3 (the global profile of curves at different Δ3 points) also behaves as a dip (the suppression induced by E3 on R0) containing a peak (R2).

When Δ1 is tuned away from resonance, the amplitudes of both the suppression dips and the emission peaks change, as shown in Fig. 5(d). First, the suppression dips of R0 both in the profile and in each curve become shallower in Fig. 5(d1) compared with those in Fig. 5(b1), since the dressing effect weakens with detuned probe field. On the other hand, both R1 peak (Fig. 5(d2)) and R2 peak (Fig. 5(d3)) get stronger, compared with those in Figs. 5(b2) and (b3). According to Eqs. (5b) and (6b), the two-photon fluorescence signals are under suppression around Δ1=0MHz, and such suppression effects weaken when |Δ1| increases. This is why R1 and R2 get strong with detuned Δ1.

Next, with all the five beams turned on, we investigate the function of deflection angle α in the interplay of two ladder type subsystems |0|1|2 and |0|1|3, as shown in Fig. 6
Fig. 6 Measured probe transmission (top curves), FWM (middle curves) and fluorescence (bottom curves) versus Δ1 when all the beams are turned on. The coupling detuning Δ2 is set at 80MHz ((a1) and (b1)), 60MHz ((a2) and (b2)), 40MHz ((a3) and (b3)), and 150MHz ((a4) and (b4)); Δ3 is fixed at Δ3=60MHz. α is set at α=0 for (a1)-(a4), and α=0.12 for (b1)-(b4). The other experimental parameters are P1=8.2mW, P2=18.3mW, P2=9.6mW, P3=29.0mW, and P3=25.0mW.
. Here, the probe detuning Δ1 is scanned with Δ2 set at four different values, and we present the experimental results with two different angles: α=0 for Figs. 6(a1)-6(a4); and α=0.12 for Figs. 6(b1)-6(b4).

Then, under the abnormal propagation configuration where E2 is deflected with α=0.12 (Figs. 6(b1)-6(b4)), the EIT peak of the |0|1|2 subsystem transforms to an EIA dip. Similar to the case of α=0, the EIA of |0|1|2 and EIT of |0|1|3 partially overlap (Figs. 6(b1) and 6(b3)), completely overlap (Fig. 6(b2)), and finally separate (Fig. 6(b4)). The two groups of characteristic signals still interact with each other. But the interaction behaves differently now. For example, for the FWM in Figs. 6(b1)-6(b3), the sum of EF1 and EF2 reaches the maximum amplitude when they completely overlap in Fig. 6(b2), which is different from the case in Figs. 6(a1)-6(a3) where the sum of EF1 and EF2 reaches the minimum amplitude when completely overlapping. This is because the FWM signal EF2 get enhancement instead of suppression in the case of α=0.12. With respect to the fluorescence signal, the two-photon emission peak of R1 is strengthened in the condition of α=0.12, corresponding to the |0|1|2 EIA.

5. Observation of angle modulated suppression-enhancement switch of FWM

In above sections the EIT-EIA switch modulated by angle α has been thoroughly discussed. The angle-modulated suppression-enhancement switch of FWM, on the other hand, only reflects in the variation of signal’s amplitude. In this section, we will modulate our spatial geometry so that the switch of FWM could be observed directly. In Fig. 7
Fig. 7 Measured probe transmission ((a1) and (b1)), FWM signal EF1 with enhancement and suppression ((a2) and (b2)), and fluorescence signal ((a3) and (b3)) versus Δ3 at discrete Δ1, with fixed Δ2=100MHz and E3 blocked. The deflection angle β is β=0 for (a1)-(a3), and β=0.12 for (b1)-(b3). The other experimental parameters are P1=4.5mW, P2=12.9mW, P2=8.2mW and P3=29.0mW.
and Fig. 8
Fig. 8 Measured probe transmission ((a1) and (b1)), the enhancement and suppression of FWM signal EF1 ((a2) and (b2)), and fluorescence ((a3) and (b3)) versus Δ3 with β=0.04, 0, 0.04, 0.08, 0.12 and 0.16 from top to bottom. (a) and (b) are separately the signals obtained at left peak and right peak of the FWM double-peak profile. The other parameters are P1=3.6mW, P2=30.6mW, P2=5.4mW and P3=14.0mW.
, we adopt the geometry shown in Fig. 1(e), where the external dressing field E3 instead of self-dressing field E2 is deflected with the angle β. The corresponding detuning Δ3 is scanned here.

Figure 7 shows concerning signals with two angle: β=0 (normal) for (a1)-(a3), and β=0.12 (abnormal) for (b1)-(b3). The behaviors of the probe transmission and the fluorescence signals are similar with above figures, so we mainly focus on the FWM. In Figs. 7(a2) and 7(b2), the curves at discrete Δ1 points form a double-peak profile (dash line), representing the AT-splitting of FWM signal EF1 induced by self dressing effect of E2(E2). The peak or dip on each baseline, on the other hand, means EF1 is enhanced or suppressed by the external dressing field E3. By manipulating the deflection angle β, we can observe the switch between enhancement and suppression directly. For instance, under the normal case (Fig. 7(a2)), the FWM signal undergoes suppression at the two global peaks (Δ1=70MHz and Δ1=115MHz) and the global valley (Δ1=100MHz), slight enhancement at two edges of the double-peak (Δ1=40MHz and Δ1=160MHz), and partial-suppression-partial-enhancement at other points. Now, with β altered to 0.12(Fig. 7(b2)), the original suppression dips around the left global peak are all replaced by pure enhancement, and around the right global peak the suppression also diminishes obviously. Such suppression-enhancement switch of FWM is in concord with the EIT-EIA switch in Sec. 3 and 4.

Besides, we notice that unlike the strong two-photon fluorescence peak (R1) in Fig. 4 and Fig. 5, in Figs. 7(a3) and 7(b3) the two-photon fluorescence peak (R2) is rather weak within each dip of single-photon fluorescence. This difference results from the discrepancy of spontaneous transition probability between the transitions |2|1 and |3|1. Theoretical calculation shows that the photons in the excited state |3(5D3/2) are more likely to transit to 5P1/2 rather than |1(5P3/2), while for the excited state |2(5D5/2) the transition |2(5D5/2)|1(5P3/2) is dominant [21

21. O. Heavens, “Radiative transition probabilities of the lower excited states of the alkali metals,” J. Opt. Soc. Am. 51(10), 1058–1061 (1961). [CrossRef]

], which results in R1 much stronger than R2.

In Fig. 8, we continuously change β from 0.04 to 0.16 with Δ3 scanned, so that the evolution of the signals versus the deflection angle can be observed more clearly. Figures 8(a) and (b) separately depict the signals at the left and right peaks (corresponding to Δ1=70MHz and Δ1=115MHz in Figs. 7(a) and 7(b)) of the FWM double-peak profile. When the angle β changes from negative to positive, the height of EIT for probe transmission signal increases from small to large in the beginning, and then decreases to small again, as shown in Figs. 8(a1) and 8(b1) from top to bottom. For fluorescence signal, we can see the suppression (dip) of it also changes from small to big, then to small with increasing β, as shown in Figs. 8(a3) and 8(b3), corresponding to the variation of probe transmission signal. The enhancement and suppression of the FWM signal EF1 are shown in Figs. 8(a2) and 8(b2). At the left peak of the AT splitting double-peak structure (Fig. 8(a2)), the dressing effect on EF1 evolutes from pure suppression, to partial-suppression-partial-enhancement, then to pure enhancement with β increasing. Especially, when β=0, the suppression dip gets deepest,corresponding to the case in Fig. 7(a2); when β=0.12, EF1 undergoes strong enhancement, corresponding to the case in Fig. 7(b2). At the right peak (Fig. 8(b2)), the FWM signal mainly shows the pattern of left-suppression and right-enhancement. Although the switch from suppression to enhancement in Fig. 8(b2) is not as prominent as that in Fig. 8(a2), the tendency could also be seen.

6. Conclusion

We have investigated the four-wave mixing (FWM), fluorescence and the probe transmission simultaneously in the atomic rubidium system. By manipulating the deflection angle of certain coupling beams, the switch between dark state (EIT of probe transmission and suppression of the nonlinear optical processes) and bright state (EIA of probe transmission and enhancement of the nonlinear optical processes) is obtained. We have separately investigated such angle-modulated switch in ladder-type atomic system with singly-dressing effect and Y-type system with doubly-dressing effect. Such angle-modulated switch could have potential applications in optical communication and quantum information processing. Moreover, in the ladder-type system, we have observed and analyzed similarities and discrepancies between the two ground-state hyperfine levels F = 2 and F = 3 of Rb 85.

Acknowledgments

This work was supported by the 973 Program (2012CB921804), NNSFC (10974151, 61078002, 61078020, 11104214, 61108017, 11104216), NCET (08-0431), RFDP (20110201110006, 20110201120005, 20100201120031), and FRFCU (2012jdhz05, 2011jdhz07, xjj2011083, xjj2011084, xjj20100151, xjj20100100, xjj2012080).

References and links

1.

C. Li, Y. Zhang, H. Zheng, Z. Wang, H. Chen, S. Sang, R. Zhang, Z. Wu, L. Li, and P. Li, “Controlling cascade dressing interaction of four-wave mixing image,” Opt. Express 19(14), 13675–13685 (2011). [CrossRef] [PubMed]

2.

N. Li, Z. Zhao, H. Chen, P. Li, Y. Li, Y. Zhao, G. Zhou, S. Jia, and Y. Zhang, “Observation of dressed odd-order multi-wave mixing in five-level atomic medium,” Opt. Express 20(3), 1912–1929 (2012). [CrossRef] [PubMed]

3.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997). [CrossRef]

4.

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]

5.

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]

6.

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

7.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A 57(4), 2996–3002 (1998). [CrossRef]

8.

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]

9.

Z. Zuo, J. Sun, X. Liu, Q. Jiang, G. Fu, L. A. Wu, and P. 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]

10.

Y. 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]

11.

J. Qi, G. Lazarov, X. 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]

12.

J. Qi and A. M. Lyyra, “Electromagnetically induced transparency and dark fluorescence in a cascade three-level diatomic lithium system,” Phys. Rev. A 73(4), 043810 (2006). [CrossRef]

13.

R. W. Boyd, M. S. Malcuit, D. J. Gauthier, and K. Rzaewski, “Competition between amplified spontaneous emission and the four-wave-mixing process,” Phys. Rev. A 35(4), 1648–1658 (1987). [CrossRef] [PubMed]

14.

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

15.

Z. Wang, Y. Zhang, H. Zheng, C. Li, F. Wen, and H. Chen, “Switching enhancement and suppression of four-wave mixing via a dressing field,” J. Mod. Opt. 58(9), 802–809 (2011). [CrossRef]

16.

U. Khadka, Y. Zhang, and M. Xiao, “Control of multitransparency windows via dark-state phase manipulation,” Phys. Rev. A 81(2), 023830 (2010). [CrossRef]

17.

P. R. S. Carvalho, L. de Araujo, and J. W. R. Tabosa, “Angular dependence of an electromagnetically induced transparency resonance in a Doppler-broadened atomic vapor,” Phys. Rev. A 70(6), 063818 (2004).

18.

M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A 76(2), 023813 (2007). [CrossRef]

19.

Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008). [CrossRef]

20.

U. Khadka, H. Zheng, and M. Xiao, “Four-wave-mixing between the upper excited states in a ladder-type atomic configuration,” Opt. Express 20(6), 6204–6214 (2012). [CrossRef] [PubMed]

21.

O. Heavens, “Radiative transition probabilities of the lower excited states of the alkali metals,” J. Opt. Soc. Am. 51(10), 1058–1061 (1961). [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 1, 2012
Revised Manuscript: December 15, 2012
Manuscript Accepted: January 28, 2013
Published: March 1, 2013

Citation
Zhiguo Wang, Zhengyang Zhao, Peiying Li, Jiamin Yuan, Huayan Lan, Huaibin Zheng, Yiqi Zhang, and Yanpeng Zhang, "Observation of angle-modulated switch between enhancement and suppression of nonlinear optical processes," Opt. Express 21, 5654-5670 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-5-5654


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References

  1. C. Li, Y. Zhang, H. Zheng, Z. Wang, H. Chen, S. Sang, R. Zhang, Z. Wu, L. Li, and P. Li, “Controlling cascade dressing interaction of four-wave mixing image,” Opt. Express19(14), 13675–13685 (2011). [CrossRef] [PubMed]
  2. N. Li, Z. Zhao, H. Chen, P. Li, Y. Li, Y. Zhao, G. Zhou, S. Jia, and Y. Zhang, “Observation of dressed odd-order multi-wave mixing in five-level atomic medium,” Opt. Express20(3), 1912–1929 (2012). [CrossRef] [PubMed]
  3. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today50(7), 36–42 (1997). [CrossRef]
  4. 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]
  5. 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]
  6. S. Wielandy and A. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A58(3), 2500–2505 (1998). [CrossRef]
  7. A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasidegenerate levels in Rb vapor,” Phys. Rev. A57(4), 2996–3002 (1998). [CrossRef]
  8. 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]
  9. Z. Zuo, J. Sun, X. Liu, Q. Jiang, G. Fu, L. A. Wu, and P. 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]
  10. Y. 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]
  11. J. Qi, G. Lazarov, X. 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]
  12. J. Qi and A. M. Lyyra, “Electromagnetically induced transparency and dark fluorescence in a cascade three-level diatomic lithium system,” Phys. Rev. A73(4), 043810 (2006). [CrossRef]
  13. R. W. Boyd, M. S. Malcuit, D. J. Gauthier, and K. Rzaewski, “Competition between amplified spontaneous emission and the four-wave-mixing process,” Phys. Rev. A35(4), 1648–1658 (1987). [CrossRef] [PubMed]
  14. C. Li, H. Zheng, Y. Zhang, Z. Nie, J. Song, and M. Xiao, “Observation of enhancement and suppression of four-wave mixing processes,” Appl. Phys. Lett.95(4), 041103 (2009). [CrossRef]
  15. Z. Wang, Y. Zhang, H. Zheng, C. Li, F. Wen, and H. Chen, “Switching enhancement and suppression of four-wave mixing via a dressing field,” J. Mod. Opt.58(9), 802–809 (2011). [CrossRef]
  16. U. Khadka, Y. Zhang, and M. Xiao, “Control of multitransparency windows via dark-state phase manipulation,” Phys. Rev. A81(2), 023830 (2010). [CrossRef]
  17. P. R. S. Carvalho, L. de Araujo, and J. W. R. Tabosa, “Angular dependence of an electromagnetically induced transparency resonance in a Doppler-broadened atomic vapor,” Phys. Rev. A70(6), 063818 (2004).
  18. M. Shuker, O. Firstenberg, R. Pugatch, A. Ben-Kish, A. Ron, and N. Davidson, “Angular dependence of Dicke-narrowed electromagnetically induced transparency resonances,” Phys. Rev. A76(2), 023813 (2007). [CrossRef]
  19. Z. Nie, H. Zheng, P. Li, Y. Yang, Y. Zhang, and M. Xiao, “Interacting multiwave mixing in a five-level atomic system,” Phys. Rev. A77(6), 063829 (2008). [CrossRef]
  20. U. Khadka, H. Zheng, and M. Xiao, “Four-wave-mixing between the upper excited states in a ladder-type atomic configuration,” Opt. Express20(6), 6204–6214 (2012). [CrossRef] [PubMed]
  21. O. Heavens, “Radiative transition probabilities of the lower excited states of the alkali metals,” J. Opt. Soc. Am.51(10), 1058–1061 (1961). [CrossRef]

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