Ultra-dispersive adaptive prism Vladimir A. Sautenkov,1,2 Hebin Li,1 Yuri V. Rostovtsev,1 and Marlan O. Scully1,3 1 Department of Physics and Institute for Quantum Studies, Texas A&M University, College Station, Texas 77843-4242 2 Lebedev Institute of Physics, Moscow 119991, Russia 3 Princeton Inst. for the Science and Technology of Materials and Dept. of Mech. & Aerospace Eng., Princeton University, 08544 (Dated: February 9, 2008) We have experimentally demonstrated an ultra-dispersive optical prism made from coherently driven Rb atomic vapor. The prism possesses spectral angular dispersion that is six orders of magnitude higher than that of a prism made of optical glass; it is the highest spectral angular dispersion that has ever been shown (such angular dispersion allows one to spatially resolve light 7 beams with different frequencies separated by a few kHz). The prism operates near the resonant 0 frequency of atomic vaporand its dispersion is optically controlled by a coherent drivingfield. 0 2 PACSnumbers: n a A single frequency ray of light is bent by a prism sorption,enhance the index ofrefraction[5, 6, 7], induce J upon an angle determined by the index of refraction,see chirality in nonchiral media [8], produce usually forbid- 0 Fig.1a. Aswasshownin[1],thedispersionoftheindexof denforwardBrillouinscatteringorstrongcoherentback- 3 refractionleadstospreadofdeviationanglesfordifferent wardscatteringinultra-dispersiveresonantmedia[9,10], 1 light frequencies. slow down or speed up light pulses [11, 12, 13], and the v Optical properties of matter, such as absorption, dis- optical analog of Stern-Gerlach experiment [14]. Opti- 9 persion, and a variety of nonlinear characteristics, can callycontrolledgiantnonlinearitiesmaygeneratenonlin- 2 be manipulated by electromagnetic fields [2, 3, 4]. For ear signals using single photons [15, 16]. The enhanced 2 example, the applied coherent fields can eliminate ab- nonlinearity can be employed for quantum information 1 0 storage [17] and for manipulating of light propagating 7 througha resonantmedium, suchas stationary pulses of 0 light in an atomic medium [18]. / Here we experimentally demonstrate an ultra- h p dispersive prism (we refer to it as “a prism” because it - deflects light, see Fig.1b) possessing the highest spectral t n angulardispersionthathaseverbeenexperimentallyob- a served (see Fig. 2,3). The prism is made of a coherently u driven atomic Rb vapor [4] that has a spectral angular q dispersion (dθ/dλ = 103 nm−1) six orders of magnitude v: higher than that of glass prisms (dθ/dλ = 10−4 nm−1) i or diffraction gratings (dθ/dλ=10−3 nm−1). X The physics ofrefractionofthe ultra-dispersivecoher- r a ently driven atomic medium is based on exciting quan- tum coherence. The wavevector k depends on the light frequency as ω k = n, (1) c where n is the index of refraction. Assuming that the driving field has an inhomogeneous profile, then the in- dex of refraction has a spatial gradient. The light ray trajectories in an inhomogeneous medium can be found by solving an eikonal equation [19] given by ω2 (∇Ψ)2 =k2 = n2 (2) c2 FIG.1: (a)Refractionoflightbytheprism. (b)Configuration of the probe and control laser beams inside the cell of Rb where Ψ is the phase of electromagnetic wave. Then the vapor. One can see that our setup can be viewed as a super- light turning angle can be estimated as high dispersive prism. (c) Simplified scheme of the energy levels of Rb atoms. θ ≃L∇n. (3) 2 Fig.1b, the practical details can be found in [20]. The laser frequency is tuned to the center of the Doppler broadened D line of Rb87 (transition F = 2−F = 1). 1 Two orthogonally polarized beams, control (P = 0.5 c mW) and probe (P = 0.5 mW), create coherence be- p tweengroundstateZeemansublevelsasshowninFig.1c. A heated Rubidium cell (l =7.5 cm, N =3 1011 cm−3) is installed in a magnetic shield and two-photon detun- ingisvariedbychangingthemagnitudeofalongitudinal magnetic field. Weemploytwoindependenttechniquestomeasurethe probebeampositionandtheangleofdeviation. Thefirst technique is basedonusing a CCDcameraanda remov- able mirror in front of the cell to measure the positions of the control and probe beams. The CCD camera is used to record an optical field distribution for selected two-photon detuning. In the second method, we use a positionsensitivedetector(PSD)[21]to accuratelymea- surethebeamdirectionversustwo-photondetuning. The distancefromthecenterofthecelltoPSDis1meterand totheCCDcamerais2.3meters. Measurementsbyboth techniques are consistent with each other. Before the cell, the control and probe beams are par- allel to each other. The probe beam can be adjusted to the left or to the right side of the control beam profile by tilting a parallel glass plate. Then, after the cell, the FIG. 2: (a) The spatial distributions of the control (1) and probeandcontrolbeamsarenotlongerparallel(seeFig. probe (2) fields at the input of the atomic cell. The probe 1b). When the probe beam is shifted to the right side, is shifted to the right with respect to the control field. The as shown in Fig. 2a, the observed probe beam profiles spatial distributions of the probe fields (2) and (2’) at the for twodetunings areshownin Fig.2b. The correspond- distanceof2.3metersafterpassingtheatomiccellfordifferent ing dependence of the angles of deviation on detuning is detunings corresponding to the maximal angles of deviation shown in Fig. 3a. The dependence corresponding to the (see Fig. 3a). shift of the probe field to the left side of the controlfield is shown in Fig. 3b. One can see that a different sign of the controlfield gradientchanges the dependence on the where n = p1+4πχ(ω), L is the length of a medium and∇n(ω)isthegradientoftheindexofrefractioninthe detuning. direction perpendicular to propagation. The atomic sus- Thewidthoftheprobebeam(0.7mmattheRbcell)is ceptibility of coherently driven medium χ(ω) [4] is given increasedtwiceat2.3meterdistancefromthecelldueto by diffraction (the diffraction opening for a Gaussian beam profile is given by 2λ/πd, where d is the diameter of the Ω2−γ2 −δω2 laser beam). For the data shown in Fig. 2b, the dis- ℜ[χ(ω)]=ηγ δω cb , r (Ω2+γ γ−δω2)2+δω2(γ +γ)2 placementduetotheultraprismeffectislargerthanthe cb cb (4) spread of the probe beam due to diffraction. whereη =3λ3N/16π2,N isthedensityofRbvapor,γ is In conclusion, we have experimentally demonstrated the relaxationrate at optical transition, γ is the relax- a EIT prism yielding large angular dispersion. The ob- cb ationrateatthelong-livedlowerfrequency(spin)transi- tained results show the dependence of the angle of devi- tion,ΩistheRabifrequencyofcontrolfield,δω =ω−ω ation on the detuning that is introduced by a magnetic ab is the detuning of the probe field from atomic transition field. It follows from Eq.(3), that the angle of deviation ω = 2πc/λ; and λ is the wavelength of resonant tran- isrelatedtodispersionofthe mediumandthe spacegra- ab sition. Then, for realistic parameters, such as δω ≃ 1 dient. Alternating the sign of the spacial gradient by kHz, γ = 1 kHz, N ≃ 1013 cm−3, L = 10 cm the es- shifting the probe beam, we can see the change of the cb timate yields θ ≃ 0.1, which shows a lot of potential for dependence of the angle of deviation on the two-photon implementation of the predicted effect. Note here that detuning. the spatial dependence of gradient of the driving field is Theschemeholdspromiseformanyapplications. Such important,andalsothatthe effectcanbe increasedeven ultra-highfrequency dispersion could be used for a com- more by using an enhanced index of refraction without pact high spectral resolution spectrometer, similar to absorption [5, 6, 7]. compact atomic clocks and magnetometers [24]. The The configuration of the laser beams is shown in prismhasahugeangulardispersion(dθ/dλ=103nm−1) 3 FIG.3: (1) Dependenceoftheangleof theprobebeam refraction on detuningfortheprobebeam initially shifted toright (a) and to theleft (b) with respect to thecontrol beam. (2) Dependenceof theprobe field transmission versusdetuning. which can spatially resolve spectral widths of a few kHz be easily extended to shortpulses by using the approach (spectral resolution R = λ/δλ ≃ 1012). We have ob- developed in [22]. servedtheangleofdeviationtobeanorderofmagnitude On the other hand, together with application to rel- larger than the one previously observedin an inhomoge- atively intense classical fields, the ultra-dispersive prism neous magnetic field [14]. We emphasis that the angle canhaveapplicationto weakfields, suchas asingle pho- can be increased even further by using the enhanced in- ton source, and controlling the flow of photons at the dex of refraction without absorption [5, 6, 7]. level of a single quanta [15, 16], Theabilitytocontrolthedirectionoflightpropagation We thank Hui Chen and M. Suhail Zubairy for useful byanotherlightbeamintransparentmediumcanbeap- discussions andgratefully acknowledgethe support from plied to optical imaging and to all-optical light steering the Defense Advanced Research Projects, the Office of [23]. Also, this prism can be used for all-optical con- NavalResearchunderAwardNo. N00014-03-1-0385,the trolled delay lines for radar systems. This technique can Robert A. Welch Foundation (Grant #A1261). [1] Isaac Newton, Opticks: Or a Treatise of the Reflections, netically induced coherent backscattering, Phys. Rev. Refrections, Inflections and Colours of Light, (4th ed. Lett., accepted to be published (2006). London) 1730; Reprinted by (NewYork,Dover) 1952. [11] A.B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G.R. [2] E. Arimondo, in Progress in Optics, edited by E. Wolf Welch,A.S.Zibrov,M.O.Scully,Slow,ultraslow,stored, (Elsevier, Amsterdam,1996), Vol. XXXV,pp.257-354. andfrozenlight,TheadvancesinAtomic,Molecular,and [3] S. E. Harris, Electromagnetically induced transparency, Optical Physics 46, 191 (2001), edited by B. Bederson Phys.Today 50, No.7, 36 (1997). and H.Walther. [4] M.O.ScullyandM.S.Zubairy,QuantumOptics,(Cam- [12] R.W. Boyd, ”Slow” and ”fast” light Prog. in Optics 43, bridge UniversityPress, Cambridge, England, 1997). 497 (2002). [5] M.O.Scully,Enhancementoftheindexofrefraction via [13] G.M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, quantumcoherence, Phys. Rev.Lett. 67, 1855 (1991). R.W. Boyd, Observation of backward pulse propagation [6] A. S. Zibrov, M. D. Lukin, L. Hollberg, D. E. Nikonov, throughamediumwithanegativegroupvelocity,Science M. O. Scully, H. G. Robinson, and V. L. Velichansky, 312, 895 (2006). Experimental Demonstration of Enhanced Index of Re- [14] L.Karpa,M.Weitz,AStern-Gerlachexperimentforslow fractionviaQuantumCoherenceinRb,Phys.Rev.Lett. light, NaturePhysics 2, 332 (2006). 76, 3935 (1996). [15] S. E. Harris and Y. Yamamoto, Photon Switching by [7] U.Rathe,M.Fleischhauer,S.-Y.Zhu,T.W.Hansch,and QuantumInterference,Phys.Rev.Lett.81,3611(1998). M.O.Scully,Nonlineartheoryofindexenhancementvia [16] V. Balic, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. quantum coherence and interference, Phys. Rev. A 47, Harris, Generation of Paired Photons with Controllable 4994 (1993). Waveforms, Phys.Rev. Lett.94, 183601 (2005) [8] V. A. Sautenkov, Y. V. Rostovtsev, H. Chen, P. Hsu, [17] C.H. van der Wal, M.D. Eisaman, A. Andre, R.L. G. S. Agarwal, and M. O. Scully, Electromagnetically Walsworth, D.F. Phillips, A.S. Zibrov, M.D. Lukin, inducedmagnetochiralanisotropyinaresonantmedium, AtomicmemoryforcorrelatedphotonstatesScience301, Phys.Rev.Lett. 94, 233601 (2005). 196 (2003). [9] A.B.Matsko,Y.V.Rostovtsev,M.Fleischhauer,andM. [18] M.Bajcsy, A.S.Zibrov and M.D.Lukin, Stationary pulses O.Scully,AnomalousstimulatedBrillouin scatteringvia of lightinan atomicmedium,Nature(London)426, 638 ultraslow light, Phys. Rev.Lett. 86, 2006-2009 (2001). (2003). [10] Y.Rostovtsev,Z.E.Sariyanni,M.O.Scully,Electromag- [19] Max Born and Emil Wolf, Principles of optics : electro- 4 magnetic theory of propagation, interference and diffrac- Zubairy, Optically controlled delays for broadband tion of light, (Cambridge, UK ; New York ; Cambridge pulses, Phys.Rev.A72, 031802 (2005). UniversityPress, 1997). [23] Q. Sun, Y. V. Rostovtsev, and M. S. Zubairy, All opti- [20] V. A. Sautenkov, Yu. V. Rostovtsev, and M. O. Scully, callycontrolledsteeringoflight,Proc.SPIE6130,61300S Switching between photon-photon correlations and Ra- (2006). man anticorrelations ina coherentlyprepared Rbvapor, [24] S. Knappe, P.D.D. Schwindt, V. Gerginov, V. Shah, L. Phys.Rev.A 72, 065801 (2005). Liew,J.Moreland,H.G.Robinson,L.Hollberg,J.Kitch- [21] R. Schlesser, A. Weis, Lifgt-beam deflection by cesium ing, Microfabricated atomic clocks and magnetometers, vapor in a transferse-magnetic field, Opt. Lett. 17, 1015 J. Opt.A: PureAppl.Opt. 8, S318 (2006). (1992). [22] Q. Sun, Y. Rostovtsev, J. Dowling, M.O. Scully, M.S.