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

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. ©2012 Optical Society of America OCIS codes: (190.4380) Nonlinear optics, four-wave mixing; (190.3270) Kerr effect; (190.4180) Multiphoton processes; (300.2570) Four-wave mixing; (270.1670) Coherent optical effects. 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). 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). 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). 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). 5. H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70(6), 061804 (2004). 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). 7. H. Ma and C. B. de Araujo, “Interference between thirdand fifth-order polarizations in semiconductor doped glasses,” Phys. Rev. Lett. 71(22), 3649–3652 (1993). 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). 9. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997). 10. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). 11. A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14(24), 1344–1346 (1989). 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). 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). 14. M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001). 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). 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). #157217 $15.00 USD Received 31 Oct 2011; revised 9 Dec 2011; accepted 6 Jan 2012; published 13 Jan 2012 (C) 2012 OSA 30 January 2012 / Vol. 20, No. 3 / OPTICS EXPRESS 1912 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). 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). 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). 20. B. Anderson, Y. P. Zhang, U. Khadka, and M. Xiao, “Spatial interference between fourand six-wave mixing signals,” Opt. Lett. 33(18), 2029–2031 (2008). 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).


Introduction
Recently a lot of attention has been concentrated on the four-wave mixing (FWM) [1][2][3][4][5] and six-wave-mixing (SWM) [6][7][8] under atomic coherence.And electromagnetically induced transparency (EIT) [9,10] 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], quantum communications [12], slow light [13], photon controlling and information storage [14][15][16].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].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 [18,19].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].
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.

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  E′ 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 1 E propagates in the opposite direction with a small angle from the other beams.In such beam geometric configuration, the two-photon Doppler-free conditions will be satisfied for the two ladder-type subsystems both 0

E
(satisfying the phase-matching condition and four SWM processes 2 S

E
(satisfying ) 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 perturbation chain (3) 00 10 20 10 we can obtain the third-order density element (3) , the amplitude of which determines the intensity of the simple FWM process, where  ( ) exp( )
In the experiments, these

By individually adjusting the frequency detunings 2
∆ and 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 E′ (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 3 E ( 3 E′ ) on FWM signal 2 F E .The dressed FWM process can be described by And the density-matrix element related to the SWM processes can be obtained as (5)    E′ 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 M ρ , where (5) (5)  ∆ (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).
When scanning 2 ∆ , the FWM signal shows the evolution from pure-enhancement ∆ , 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 2 E ( 2 E′ ), the energy level 1 will be split into two dressed states  On the other hand, when 2 ∆ is set at discrete values orderly from positive to negative and 1 ∆ is scanned, the probe transmission shows an EIT window on each curve in Fig. 3(a3) . Also, the FWM signal 2 F E presents double peaks (Fig. 3 G − , 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 2 ∆ at discrete 1 ∆ values, and scanning 1 ∆ at discrete 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 E appears correspondingly both in Fig. 3(b2) and 3(b5), as the left dash line expresses; when two-photon resonance occurs at the point 1 2 0 ∆ + ∆ = , a peak (EIT) is gotten both in Fig. 3(b1) and 3(b4), and a dip (suppression point) of 2 F E 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 2 G ± could not move across the original position of 1 and therefore only one of them can resonate with 1 E when scanning the dressing detuning.
Furthermore, the spectra of the doubly-dressed FWM process of (0) , we can obtain for the doubly-dressed FWM process.Firstly, the probe transmission and FWM signal E , 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 1 ∆ is set at discrete values orderly from negative to positive and 2 ∆ is scanned, the experimentally obtained 2 F E 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  ), finally to pure-enhancement ( 1 80MHz

∆ =
). 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 E and 2 E′ .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.   G − , 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

G G
− − 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 2 ∆ at discrete 1 ∆ values, and scanning 1 ∆ at discrete 2 ∆ values), the corresponding relationship could also be discovered, as expressed with the dash lines in Figs.4(a G G + + , a dip of probe transmission (EIA) is gotten both in Fig. 4(b1) and 4(b4), and a peak (enhancement point) of 2 F E signal appears both in Fig. 4(b2) and 4(b5), as the left dash line expresses; when two-photon resonance ( 1 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 1 =0 ∆ in Fig. 4(b2) corresponds to the center of primary AT splitting at 2 =0 ∆ in Fig. 4(b5); and the positions of the pure-suppression at 1 = 20 MHz ∆ ± in Fig. 4(b2) correspond to the center of secondary AT splitting at 2 = 20 MHz ∆ ± in Fig. 4(b5).We also notice that when 1 ∆ scanned, three enhancement points and two suppression points could be obtained, while when scanning  E could be detected directly, excluding the pure FWM component (Fig. 4(d2)).We can see that the enhancement and suppression of 2 F E in Fig. 4(d2) shows similar evolution with that in Fig. 4 E 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 1 0, 20, and 20 MHz ∆ = − (Fig. 4(b2) and 4(e2)), all of which reveals pure-suppression.The symmetric center at 1 =0 ∆ is caused by the primary dressing effect, while the two symmetric centers at 1 = 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 ( 2 .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 2  (3) ( , , where / { ( / / ) } exp( )

2.4fs − Ω =
in 85 Rb .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 3 ∆ is at large detuning, with 2 E′ and 4 E′ blocked (shown as Fig. 1(e)).When take the atomic velocity component and the dressing effect of 3 E ( 3 E′ ) into consideration, the enhancement and suppression of the SWM signal would be shifted far away from resonance, as shown in Fig. 6.When considering Doppler effect the atom moving towards the probe laser beam with velocity v , the frequency of 1 E is changed to via the self-dressed perturbation chain , where 1 1 , where . From the expressions of In Fig. 6(a), we present the probe transmission (Fig. 6(a1)) and the measured SWM signal (Fig. 6  ∆ >> ), the enhancement and suppression of SWM signal is no more symmetrical.Specifically, due to the optical pumping effect corresponding to the transition from 3 to 1 by 3 E and 3 E′ , the suppression will be intensified with 1 0 ∆ < (especially when ∆ is at large detuning (Fig. 6(b1) and 6(b5)), the enhancement and suppression of SWM will still exists in the region with 1 0 ∆ < .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 ( First we investigate the interplay between the two FWM signals  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 E′ 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.

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 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.

Fig. 1 . 3 E , 3
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 3E , 3 E′ , 4 E and 4 E′ are blocked and 1 E , 2 E and 2 E′ are turned on.(d) The diagram of the Y-type four-level atomic subsystem when the fields 3 E and 3 E′ are blocked and other beams are turned on.(e) The diagram of the K-type five-level atomic system when the fields 2 E′ and 4 E′ are blocked only.

Fig. 1 ( 3 E′E
c)), only the 2 F E signal with self-dressing effect could be generated in the ladder-type three-level subsystem 0 are blocked and other beams on (Fig.1(d)), two FWM signals 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 2 E′ and 4 E′ are blocked only (Fig.1(e))will coexist and interact with each other.

2 G 2 FE 2 GE 2 G 2 0
± , as shown in Figs.3(c1)-3(c5).When 2 ∆ is scanned at 1 0 ∆ = , on the one hand, EIT is obtained in Fig.3(a1) at the point 2 = is satisfied.On the other hand, a pure-suppression of is gotten in Fig.3(b2) because the probe field 1 E could not resonate with either of the two dressed energy levels ± , as shown in Fig.3(c3).In the region with 1 0 ∆ < , when 2 ∆ is scanned, the probe transmission shows EIA firstly and EIT afterwards in Fig.3is first enhanced when the EIA is gotten and next suppressed when the EIT is obtained, shown in Fig.3(b2) at 1 = 20MHz ∆ − .The reason for the first EIA and the corresponding enhancement of 2 F E is that the probe field 1 E resonates with the dressed state + at first, thus the enhancement condition satisfied.While the reason for the next EIT and the corresponding suppression of 2 FE is that two-photon resonance occurs so as to satisfy the suppression condition 1 ∆ + ∆ = (see Fig.

3 ( 2 0 2 F
c2)).When 1 ∆ changes to be positive, the curves at 1 =20MHz ∆ show symmetric evolution behavior with the curves at 1 = 20MHz ∆ − , i.e., EIT as well as a suppression of 2 F E are obtained due to the two-photon resonance which matched the suppression condition 1 ∆ + ∆ = firstly; and then EIA as well as an enhancement of depicted in Fig. 3(c4).When 1 ∆ is far away from resonance point ( 1 = 80MHz ∆ ± ), the pure-EIA as well as the pure-enhancement of 2 F E are obtained because the probe field can only resonate with one of the two dressed states 2 G ± (as shown in Figs.3(c1) and 3(c5)).

2 E′ ) versus probe detuning 1 ∆ 4 E at 1 4 =
(a1).The height of the baseline of each curve represents the probe transmission without dressing field 2 E ( .The profile of these baselines reveals an EIT window induced by external-dressing field ∆ − ∆ .While the peak and dip on each baseline of the curves represent EIT and EIA induced by self-dressing fields 2

2 FE 1 ∆ 2 0
represents the detuning of 2 E ( 2 E′ ) from 4 G − .When the enhancement condition is satisfied, the probe field 1 E resonates with one of the secondarily dressed states, leading to an EIA of probe transmission and enhancement of 2 F E .When the suppression condition is satisfied, two-photon resonance occurs, leading to an EIT and suppression of 2 F E .Especially, we notice the enhancement and suppression of in Fig. 4(b2) show symmetric behavior with three symmetric centers at 1 0, 20, and 20 MHz ∆ = − , all of which are pure-suppression.The pure-suppression at 1 0 MHz ∆ = is induced by primary dressing effect of 4 E , while pure-suppressions at 1 = 20 MHz ∆ ± are caused by the secondary dressing effect of 2 E ( 2 E′ ).On the other hand, when 2∆ is set at discrete values orderly from positive to negative and is scanned, the intensity of probe transmission shows double EIT windows on each curve in Fig.4(a3), which are EIT windows ∆ ), respectively.As 4∆ is fixed at 4 0 ∆ = and 2 ∆ is set at discrete values from positive to negative, the EIT window 0 from negative to positive.Especially, when 2∆ is set at ∆ = , the two EIT windows overlap as shown in Fig.
) 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 ( 1 ∆ ) domain correspond with the positions in the self-dressing frequency detuning ( 2 ∆ ) domain, satisfying same enhancement/suppression conditions.Take the curves at 1 40MHz ∆ = − in Figs.4(b1)-(b2) and the curves at 2 40MHz ∆ = 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 1 E resonates with the dressed state 4 2

Figure 4 ( 2 FE is dressed by both 2 E ( 2 E′ ) and 4 E+ ± could be created from 2 G 2 G 2 G
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 .Firstly, under the self-dressing effect of 2 E ( 2 E′ ), the state 1 will be broken into two primarily dressed states 2 G ± .Then in the region with 1 + by the external-dressing field 4 E , as shown in Fig. 4(f1)-4(f4).Symmetrically, in the region with − , as shown in Fig. 4(f6)-4(f9).Here we only give the enhancement and represents the detuning of 4 E from #157217 -$15.00USD Received 31 Oct 2011; revised 9 Dec 2011; accepted 6 Jan 2012; published 13 Jan 2012 (C) 2012 OSA 30 January 2012 / Vol. 20, No. 3 / OPTICS EXPRESS 1922 − .Unlike scanning self-dressing detuning (Fig. 4(a2)), by scanning the external-dressing detuning the enhancement and suppression of 2 F

E′ 2 F E and 4 FE
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 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 can be observed, as shown in Fig. 5.

Fig. 5 . 2 F E and 4 FE
Fig. 5.The spatiotemporal interferograms of 2 F E and 4 F E in the Y-type atomic subsystem.(a) A three-dimensional spatiotemporal interferogram of the total FWM signal intensity ( , ) I r τ versus time delay τ of beam 2 E′ and transverse position r .(b) The temporal interference with a much longer time delay of beam 2 E′ .(c) Measured beat signal intensity ( , ) I r τ

2 /
can see that the total signal has an ultrafast time oscillation with a period of 2 π ω and spatial interference with a period of 2 / k π ∆ , 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 2 E′ while Fig. 5(c) shows its projections on time.Figure 5(c) depicts a typical temporal interferogram with the temporal oscillation

Fig. 6 . 2 ∆ for different 1 ∆ with the laser beams 2 E′ and 4 E′ blocked when 3 ∆
Fig. 6. (a1) The probe transmission signal and (a2) the SWM signal with the enhancement and suppression effect versus 2 ∆ for different 1 ∆ with the laser beams 2 E′ and 4 E′ blocked

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

3 +
or split 4 G − into two dressed states 4 2 G G − ± , as shown in Fig. 6(b).When two-photon resonance occurs at the original states 4 (Fig. 6(b3)) or 4G − (Fig.6(b4)), the pure-suppressions of SWM can be obtained.When Doppler effect being considered, the dominant atomic velocity component 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 original4 3 + + G G state, and the right one is related to the original 4 G G − state.This inconsistence is because when the frequency of 3 E ( 3 E′ ) is at large detuning ( 3 0

Fig. 7 . 2 ∆ at discrete 1 ∆ 2 ∆ 3 E and 3
Fig. 7. (a) Measured total MWM signal versus 2 ∆ at discrete 1 ∆ when all seven laser beams subsystem (Fig.1(d)) by blocking the laser beams 3 E and 3E′ .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 ( 4 FE could be extracted since 2 FE 4 FE induced by 2 E 2 FE 4 FEE′ and 4 4 E , 3 EE 4 E
b1) shows the measured FWM signal versus 2 ∆ at discrete 1 mutual dressings.In Fig.7(b1), the global profile of baselines of all the curves represents the intensity variation of 4 F E at designated probe detuning values, and the peak and dip on each baseline include two components: the doubly-dressed 2 F E signal and the enhancement and suppression of 4 F E induced by 2 E ( 2 E′ ).These two components could be individually detected by additionally blocking 2E′ or 4 E′ , as shown in Fig.7(b2) and 7(b3) separately.When blocking 2 E′ , the information related to is turned off (Fig.7(b2)).The global profile of all the baselines in Fig.7(b2) reveals AT splitting of 4 F E , and the peak and dip of each curve represent the enhancement and suppression of , which show similar evolution to the curves in Fig.4(d2).On the other hand, when turning on 2 E′ and blocking4 E′ , the doubly-dressed 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 which mainly behaves dips (Fig. 7(b2)), and the dressed FWM signal 2 F E , which mainly behave peaks (Fig. 7(b3)).Next we investigate the interplay between two SWM signals E′ blocked (shown as Fig. 1(e)).When all the five laser beams ( 1 E , 2 E , #157217 -$15.00USD Received 31 Oct 2011; revised 9 Dec 2011; accepted 6 Jan 2012; published 13 Jan 2012 (C) 2012 OSA 30 January 2012 / Vol. 20, No. 3 / OPTICS EXPRESS 1928 and 3 E′ ) are turned on, two external-dressed SWM signals 2 simultaneously, as shown in Fig. 7(c1).The global baseline variation profile shows the intensity variation of the SWM signal 4 S E revealing AT splitting.The peak and dip on each baseline include the remains, as shown in Fig. 7(c3).By subtracting the SWM signal 2 S E (Fig. 7(c3)) and the height of each baseline from the total signal (Fig. 7(c1)), the sum of the signals dressing effect can be obtained, as shown in Fig. .On the one hand, we can see from the curve (c2) that when two-photon resonance occurs at 1 = 20MHz ∆ − and 1 =25MHz ∆ , the depth of the dip is approximately maximum, meaning that the suppression is most significant.On the other hand, when 1 the generated SWM signals are enhanced as shown by the small peaks.
(b1)), the SWM signal intensity (Fig.7(c1)) and the intensity of the SWM signals relate G′ and 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 1 E ( 1 G and 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 2 and ij Γ is the transverse relaxation rate between states i and j .Similarly, for the simple FWM process multi-wave mixing signals are researched by selectively blocking different laser beams.When the beams 3 are turned on (as shown in 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 2 E ( 2 E′ ) versus probe detuning 1 #157217 -$15.00USD Received 31 Oct 2011; revised 9 Dec 2011; accepted 6 Jan 2012; published 13 Jan 2012 (C) 2012 OSA 30 January 2012 / Vol. 20, No. 3 / OPTICS EXPRESS 1917 ), 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 ( 1 ∆ ) domain correspond with the positions in the (b2).The profile of all the baselines, which has two peaks, reveals AT splitting of 2 state unobtainable.In this way, we first demonstrate that the enhancement and suppression signal can be observed out of the EIT window ( 1 -80MHz<∆ <+80MHz ) through the Doppler frequency shift led by atomic velocity component and optical pumping.From the figures one can see that even 1 4G − 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 ∆ 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.