Observation of Autler-Townes splitting in six-wave mixing

We report an observation of the selfand 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. ©2011 Optical Society of America OCIS codes: (190.4380) Nonlinear optics, four-wave mixing; (270.4180) Multiphoton processes; (300.2570) Four-wave mixing; (030.1670) Coherent optical effects. References and links 1. S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955). 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). 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). 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). 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). 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). 7. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997). 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). 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). 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). 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). 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). 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). 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). 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). 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). #142477 $15.00 USD Received 15 Feb 2011; revised 28 Mar 2011; accepted 29 Mar 2011; published 6 Apr 2011 (C) 2011 OSA 11 April 2011 / Vol. 19, No. 8 / OPTICS EXPRESS 7769 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). 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). 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). 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).


Introduction
Aulter-Townes (AT) splitting was first observed on a radio-frequency transition more than sixty years ago [1].Such effect has been clearly demonstrated in a four-wave mixing on a simple atomic system dressed with a single laser beam [2].With the cw triple-resonant spectroscopy and the ultrashort intense laser pulses, respectively, the AT splitting effect in lithium molecules [3] and a semiconductor material [4] was investigated.Theoretical studies also indicate that the AT-split Rydberg population can lead to an antiblockade effect [5] and such phenomenon was experimentally demonstrated with two-photon excitation in a three-level atomic system [6].Recently, a great deal of attention has been paid to observe and understand the phenomenon of electromagnetically induced transparency (EIT) [7][8][9][10] and related effects in multi-level atomic systems interacting with two or more electromagnetic fields [11,12].
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].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].A similar result was obtained in the inverted-Y [15] and double-Λ [16] 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], we go further to investigate the complex AT splitting phenomena in the SWM process.

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 85 Rb.The energy levels of G ), which are split from a tapered-amplifier diode laser (Thorlabs TCLDM9) with equal power (  (3) For the five-level atomic system as shown in Fig.
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 2 E (connecting transition |1> to |2>) and 4 E (connecting the transition |1> to |4>) are added, two SWM processes will occur [11].First, without the strong coupling field 4  [11].When the power of 2 E 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): When the power of 4 E 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): Next, when both coupling fields ( 2 (5) 00 0 20 0 30 0 where , where  , and other parameters are the same as before.Then, we obtain the same eigenvalues (1)     , and Similarly, when 4 E induces the two primarily-dressed states, and 2 E acts as the external-dressing field, one can get the following corresponding eigenvalues: , ), and solve the coupled density-matrix equations to obtain (5)   10  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: (5) 10  and  ij 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: Similarly, for the SWM2 signal, the expression is simplified as: GG GG G .There exist two ladder-type EIT windows in Fig. 1(b), i -4).

Autler-Townes Splitting
When the external-dressing field 4 E 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 ( 1  ) for different field powers of 1 P , and 3 P with the same frequency detuning of 2 50MHz    .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 a0 20 30 G ), 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 2 E is blocked, we get the SWM2 signal in the EIT2 window.Figure 3  P 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 1 P 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 3 P 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 4 P power increases, the height of the right peak increases monotonously to approach the height of the middle peak.The two primarily-dressed states   and 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 2 P is increased, and the squares are the experimental results, while the solid lines in (b2, b4, b6) are the theoretical calculations.
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., 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 k k k k , respectively.These signals are in the same direction as F E (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 . 3 E 2 E
Fig. 1.(a) Phase-matching spatial beam geometry used in the experiment.(b) Five-level atomic system with one probe field , two pump fields 3 E and 3  E , and two coupling (dressing)

E
Fig. 1(b), there will be a corresponding FWM signal generated at frequency 1

2 E 4 E
This generates the secondary AT splitting for the SWM1 signal.The situation for the SWM2 ( S2 E ) process is similar.The two primarily-dressed states induced by can only couples to the dressed state |   , the secondarily-dressed states are then given by

4 E
level |   ) of |   , where only couples to the dressed state |   , the secondarily-  (induced by the coupling field 2 E ) and the |  (induced by the coupling field 4 E ).The EIT1 and EIT2 windows contain the SWM1 signal ( S1 E ) and the SWM2 signal ( S2 E ), respectively.Next, we will consider the AT splitting of the SWM signals within the EIT windows (Figs. 2

E versus 1 
presents the SWM2 signal intensity versus the probe field detuning ( 1  ) for different powers of 1 P , 3 P and 4 P with the same frequency detuning of 4 0MHz   .Figure3(a) depicts the measured EIT windows induced by the self-dressing field 4  ).Such EIT window increases with 4

4  2 
Figures 4(a1) -4(a3) present the interplay between the two SWM signals versus the probe field detuning ( 1  ) for different external-dressing field detunings ( 2  ) with 4 0MHz   .Here, we consider the case with 2 G G .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 (  ) is induced by the coupling field 4 E ,which contains the SWM2 signal ( S2 E ), and the right one ( | 0 |1 | ) is induced by the coupling field 2 E , which contains the SWM1 signal ( S1 E ).Since the right EIT window ( 2 150MHz    ) 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 2 E is tuned to move the right EIT window ( | 0 |1 | 2      ) towards the left one, the two EIT windows overlap at 2 15MHz   

is the coupling field 2 E
that couples the secondarily-dressed state   dressed by 3 E 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 |     , 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 1 and 4 E) are on at the same time, they can dress the energy level |1> together.For the SWM1 process ( S1 E ), 2 E first produces the primarily-dressed states  , then 4 E produces the secondarily-dressed states   at a proper frequency detuning (i.e.either tuned to the upper or lower dressed state, |   or |   ), ).
|   and |   are induced by 4