Phase locking of two independent degenerate. coherent anti-stokes Raman scattering processes

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1 Phase locking of two indeendent degenerate coherent anti-tokes Raman scattering rocesses QUN Zhang* Hefei National Laboratory for Physical ciences at the Microscale and Deartment of Chemical Physics, University of cience and Technology of China, Hefei, Anhui 36, Peole s Reublic of China *qunzh@ustc.edu.cn We roose an elegant scheme towards hase locking of two indeendent degenerate coherent anti-tokes Raman scattering (CAR) rocesses. The otical imlementation involves a modified Mach-Zehnder interferometer that is utilized to transfer hase coherence from three totally uncorrelated laser beams into two degenerate CAR beams which are indeendently roduced in two distinct Raman active samles. uch a hase-transort interferometer allows for exlicit measurement and control of hase differences between the two hase-locked degenerate CAR rocesses, hence may lead to alications in other ertinent research fields. PAC number(s): 4.65.Dr timulated Raman scattering; CAR; 7.6.Ly Interferometers; 4.5.Hz Interference; 4.5.Kb Coherence; 4.5.Ex Otical imlementations of quantum information rocessing and transfer. - -

2 As a nonlinear four-wave-mixing rocess [-3], coherent anti-tokes Raman scattering (CAR) [4-7] emloys multile hotons ( um, tokes, and robe ) to address the molecular vibrations, and as a result roduces a signal in which the emitted light waves are coherent with one another. The um and robe fields are usually chosen to be identical, thereby rendering the resultant otical outut a so-called coherent anti-tokes (or CAR) signal. It is well known that the total CAR signal comes from a coherent addition of the signal from individual Raman active molecules. Although it is also well known that coherence can be generally defined by the correlation roerties between quantities of an otical field and that the simlest way to reveal correlations between light waves is making use of interference henomena [8], an interesting subject ertinent to hase coherence of CAR [9] has not been thoroughly exloited, i.e., is it ossible to achieve hase locking between two indeendent degenerate CAR rocesses arising from two distinct Raman active media? In other words, can we obtain the interference attern from such two indeendently roduced yet energetically degenerate CAR signals? In this Brief Reort, we exlore a unique aroach and design an otical system to this end, in the hoe that it may rovide useful insight into the above questions of fundamental interest as well as bring forth otential alications in CAR-related research and in quantum communication based on coherent hase transort. We start with a general case that involves two indeendent CAR rocesses generated from two distinct Raman active samles, (a) and (b), as schematically deicted in Fig.. Assume that the two samles have their own characteristic Raman modes, - - (i) fg (i = a, b), with g and f resectively designating the initial ground state and the final (vibrationally) excited state of the

3 samles. We aly a air of temorally and satially overlaed laser fields, the um and the tokes (i = a, b), on each samle, such that = (i = a, b) are fg satisfied, i.e., the joint action of the two simultaneously resent fields efficiently establish a couling between the g and f states, making the molecule reside in a coherent suerosition of states. We herein confine ourselves to only the situation that the um field also oerates as a robe which simultaneously romotes the system to a virtual state, hence CAR signals with frequencies of CAR = (i = a, b) are exected to emit out of the samles. To observe otical interference between such two CAR signals, one must ensure first their energy degeneracy. To do so, we roose an all-otical scenario as follows. Assume we have three indeendent laser sources with outut frequencies of,, and, resectively. We generate (i = a, b) by sum-frequency mixing (FM) i (i =, ) with in two FM nonlinear crystals: =, =, () and generate (i = a, b) by difference-frequency mixing (DFM) (i = a, b) with i (i =, ) in two DFM nonlinear crystals: = =, = =. () Thus we exlicitly obtain the following energy relationshis: = =, (3) CAR CAR i.e., the energy degeneracy condition for the two indeendently roduced CAR signals is automatically fulfilled through using only the facile nonlinear frequency mixing techniques. It is worth noting that the above scenario is not only interesting but ractically oerational - 3 -

4 considering that many nowadays commercially available lasers (e.g., the tunable nanosecond ulsed OPO systems) can routinely generate outut frequencies of and that match the required vibrational modes for a variety of Raman active molecules. Moreover, it is easy to envisage that the frequency range of thus obtained CAR signals is actually controllable by choosing any conveniently available frequencies of the common laser source at will, because the virtual states (indicated by four dashed-dotted lines in Fig. ) involved in the two CAR rocesses are not eigenstates of the Raman active molecules and hence could in rincile be anywhere energetically. To exercise the above scenario, we roceed to roose constructing an otical system, as shown schematically in Fig.. The entire system can be viewed as a modified tye of Mach-Zehnder interferometer [] that begins with a beam slitter (B in Fig. ) and ends with a beam recombiner (BR). We arrange this system in a nearly symmetrical fashion along the central dotted line which searates the entire otical layout into two segments, labeled (a) and (b) in Fig.. With the aid of the otical delay lines [Fig. only shows the delay line (DL) in one of the beam aths.], we can make identical the otical ath lengths of any laser beams between B and BR for both segments. Each segment consists of two nonlinear frequency conversion rocesses (FM and DFM) and one arametric rocess (CAR). As discussed below, such a method of construction will naturally make the two otical segments (a) and (b) corresond to the two otical athways (a) and (b) shown in Fig., resectively. For convenience of descrition, we focus only on the otical segment (a). The nonlinear - 4 -

5 FM crystal (labeled FMX(a) in Fig. ) is angle-tuned to mix only one-half of the beam (due to the 5% B) with one-half of the beam (due to the 5% B), roducing an FM beam of = ) (. Right behind FMX(a), a dichroic mirror (D) is used for transmitting the residual and beams to a beam dum (DP) while reflecting the roduced beam. uch an beam is subsequently mixed with one-half of the beam (due to the 5% B) in a nonlinear DFM crystal (labeled DFMX(a)) that is angle-tuned to roduce only the DFM beam of = = ). As a result, we have three ( collinearly roagating beams (i.e., the,, and residual beams []) in between DFMX(a) and the samle cell (a). Eventually a CAR signal with frequency of CAR ( = ) is exected to be roduced out of (a), rovided that the hase-matching condition is fulfilled. ince a collinear (instead of Boxcar) geometry is adoted in this aer, the CAR beam should roagate along the same direction as the collinearly roagating um (robe) and tokes beams. Because the frequency of thus obtained CAR signal is known a riori, which is equal to the frequency sum of the three source lasers used, we can readily ick only the desired CAR signal out of the unwanted residual beams by exlicitly using a narrow bandass filter (BPF in segment (a) of Fig. ) secified for the CAR wavelength range. It is obvious that the above descritions for segment (a) should also aly to segment (b). When the two CAR beams of identical frequencies [cf. Eq. (3)] roduced indeendently in the two otical segments are recombined (at BR in Fig. ), they are exected to form stable interference atterns therein. Both CAR beams can be detected by a linear CCD (charge couled device) array. Directing these beams to the same osition on the CCD array but at - 5 -

6 slightly different angles is exected to generate a series of fringes []. As in standard interferometry, interference is observed only if the ath-length difference between the two indeendent aths (a) and (b) is less than the coherence length. We adjust this ath-length difference by sliding the beam slitter (B in Fig. ) along a linear track with an accomanying mirror (M3), which together form a retroreflector (indicated by the dashed rectangular in Fig. ). It is noteworthy that here we adjust the ath-length difference in, desite the fact that interference is monitored between the two CAR beams. To analyze the interference, we now consider the relative hase of the two CAR beams. As demonstrated in our revious work [3], the hase-matching conditions for nonlinear frequency mixing ensure that the resective hases of (i = a, b) can be exlicitly written as the sum of the hases of the source lasers involved: =, =, (4) and that the resective hases of (i = a, b) can be written as the difference of the hases of the source lasers involved: b. (5) ( a ) ( ) = a =, ( ) ( ) = b = imilarly, the hase-matching conditions for four-wave mixing can lead to the following hase relationshis for the two CAR beams: CAR = CAR = ( Δ), (6a). (6b) Here the Δ term accounts for an additional hase that is due to different ath lengths for the - 6 -

7 beams between the beam slitter (B in Fig. ) and the two mixing crystals [FMX(a) and FMX(b)]. Although the individual hases of the three source lasers (,, and ) are totally uncorrelated because they all are stand-alone systems, the relative hase between the two CAR beams is fixed, since Δ [( = Δ. (7) CAR CAR CAR = Δ ) ] [ ] Because the hase coherence between the two CAR beams is automatically assured by the above otical imlementation, we have demonstrated herein that two degenerate CAR rocesses indeendently generated from two distinct Raman active media can be hase-locked, a feat that would be otherwise difficult to attain and that has, to the best of our knowledge, not yet been achieved rior to this aer. Remarkably, thus established hase coherence between the two indeendent CAR rocesses will not be destroyed by random hase fluctuations in any of the source lasers, simly because both rocesses deend on the same light sources [recall Eqs. (3) and (6)], thereby making any hase fluctuations in them automatically cancel. In addition, our method of construction allows for control of the CAR interference by variation of Δ, the hase difference in the common laser source of frequency. To change the hase difference between the two athways [(a) and (b) in Fig. ] at will, we can insert a rotatable glass hase late ( Φ P in Fig. ) in one of the beam aths. One would exect alternating movement (i.e., hase modulation) of the CAR fringe attern on the CCD array when rotating the glass late. Consequently, the relative hase difference is not only measurable but controllable by exlicit adjustment of a hase-deendent roerty (here the otical thickness of a simle glass - 7 -

8 late) known in advance, rather than inferred from other sohisticated indirect hase modulation measurements (see, e.g., [4]). imilar to our revious work [3] in which an interruted Mach-Zehnder-tye interferometer was constructed towards the goal of coherently controlling chemical reactions [5] by interfering two hase-locked two-hoton rocesses, the unique interferometer described in this aer also serves as a hase-transort interferometer because the hase characteristics of an inut laser beam ( ) are faithfully transferred (in a controllable manner) to two indeendently roduced CAR beams of identical frequencies. uch a hase-transort interferometer may find otential alications in the field of quantum information rocessing and transfer that makes use of hase coherence roerties. For instance, one can encode the hase information ( Δ ) in one otical arm of the common inut source, and then decode (retrieve) it with high fidelity from the CAR interference attern in a remote detector. We exect also that this interferometer can be emloyed to evaluate the hase coherence of CAR rocesses, e.g., to see how the hase modulation deth (contrast of the fringe attern) varies when certain external conditions (e.g., temerature variations in the two Raman active samles) are changed and how the inherent non-resonant CAR background affects the observed interference. Obviously, to fully answer these interesting questions requires further exerimental investigations. Based on our revious successful exerience [3], we believe that such exeriments (which are under way in our laboratory) using the elegant scheme roosed in this aer are feasible

9 In summary, we have resented a unique aroach towards hase locking of two indeendent degenerate CAR rocesses. An interesting tye of Mach-Zehnder interferometer is elaborately designed towards this goal, which itself reresents an extension of the well known Young s double-slit exeriment to the condensed-hase all-otical imlementation of interfering two indeendently generated arametric rocesses in a hase-coherence-controllable manner. The author is indebted to Professor Mark Keil (Ben-Gurion University, Israel) and Professor Moshe hairo (The University of British Columbia, Canada) for many stimulating discussions, and also thanks suort from the National Natural cience Foundation of China (Grant No ), the Ministry of cience and Technology of China (Grant No. 7CB853), and the University of cience and Technology of China

10 REFERENCE AND NOTE [] D. C. Hanna, M. A. Yuratich, and D. Cotter, Nonlinear Otics of Free Atoms and Molecules (ringer-verlag, 979). [] Y. R. hen, Princiles of Nonlinear Otics (Wiley, 984). [3] M. O. cully and M.. Zubairy, Quantum Otics (Cambridge U. Press, 997). [4] M. D. Maker and R. W. Terhune, Phys. Rev. 37, A8 (965). [5] R. F. Begley, A. B. Harvey, and R. L. Byer, Al. Phys. Lett. 5, 387 (974). [6] W. M. Tolles, J. W. Nibler, J. R. McDonald, and A. B. Harvey, Al. ectrosc. 3, 53 (977). [7] A. M. Zheltikov, J. Raman ectrosc. 3, 653 (). [8] W. Lauterborn, T. Kurz, and M. Wiesenfeldt, Coherent Otics: Fundamentals and Alications (ringer-verlag, 993). [9] ee, e.g., C. Vinegoni, J.. Bredfeldt, D. L. Marks, and. A. Boart, Ot. Exress,, 33 (4); C. L. Evans, E. O. Potma, and X.. Xie, Ot. Lett. 9, 93 (4), and references therein. [] P. I. Hariharan, Basics of Interferometry (Academic, 99). [] It may also contain a small amount of residual and beams that results from the non-ideal roerties of the dichroic mirror (D in Fig. ), which however will not affect the CAR beam later roduced. [] J. H. Yi,. H. Kim, and Y. K. Kwak, Meas. ci. Technol., 35 (). [3] Q. Zhang, M. Keil, and M. hairo, J. Ot. oc. Am. B, 55 (3). [4] R. J. Gordon,. P. Lu,. M. Park, K. Trentelman, Y. Xie, L. Zhu, A. Kumar, and W. J. Meath, J. Chem. Phys. 98, 948 (993). [5] M. hairo and P. Brumer, Princiles of the Quantum Control of Molecular Processes (Wiley, 3). - -

11 FIGURE CAPTION FIG. : (Color online) chematic diagram for two indeendent degenerate CAR rocesses which are hase-locked by otical rocedures described in the text. FIG. : (Color online) chematic diagram of the otical layout. B, beam slitter; BR, beam recombiner; D, dichroic mirror; M, high reflecting mirror; Φ P, glass hase late; DL, delay line; FMX, sum-frequency-mixing crystal; DFMX, difference-frequency-mixing crystal;, Raman active samle; BPF, bandass filter; DP, laser beam dum; CCD, charge-couled-device linear-array detector. - -

12 FIG. Q. Zhang - -

13 FIG. Q. Zhang - 3 -