Theory of collective Raman scattering from a Bose-Einstein condensate

Abstract

Recent experiments have demonstrated superradiant Raman scattering from a Bose-Einstein condensate driven by a single off-resonant laser beam. We present a quantum theory describing this phenomenon, showing Raman amplification of matter wave due to collective atomic recoil from 3-level atoms in a Λ-configuration. When atoms are initially in a single lower internal state, a closed two-level system is realized between atoms with different internal states, and entangled atom-photon pairs can be generated. When atoms are initially prepared in both the lower internal states, a fraction of atoms recoiling in the backward direction can be generated.PACS numbers: 42.50.Fx, 42.50.Vk, 42.65.Dr Important progress in the study of the coherent interaction between atoms and photons have been recently obtained using Bose-Einstein condensates (BEC) of low-density alkali atoms [1]. In the case where the atoms interact only with far off-resonant optical fields, the dominant atom-photon interaction is two-photon Rayleigh scattering. In this situation, collective atomic recoil lasing (CARL) [2,3,4,5] causes exponential enhancement of the number of scattered photons and atoms. Experimentally, CARL from a BEC has been observed so far in the Superradiant regime [6,7,8,9], in which photons are scattered into the end-fire modes along the major axis of an elongated condensate. In these experiments, the atoms after the collective scattering remain in the original internal, gaining a recoil momentum h( k 2 − k 1 ), where k 2 and k 1 are the wave vectors of the pump and scattered photons, respectively. The scattered atoms may experience further collective scattering, leading to the observed superradiant cascade [6].In two recent experiments [10,11] it has been observed superradiant Raman scattering, in which the atoms remain, after the process, in a different hyperfine state not resonant with the pump laser beam. As a consequence, no further scattering of pump photons occurs. In this Brief Report, we present a theory of the collective atomic recoil lasing from a 3-level atomic BEC which describes the observed phenomena. In particular, the theory demonstrates that maximum atom-photon entanglement can be generated in this system.We consider a cloud of BEC atoms which have three internal states labeled by |b , |c , and |e with energies E b < E c < E e , respectively. The two lower states |b and |c can be hyperfine states in each of which the atoms can live for a long time. They are coupled to the upper state |e via, respectively, a classical pump field and a quantized probe field of frequencies ω 2 and ω 1 in the Λ-configuration. The interaction scheme is shown in Fig. 1.The second quantized Hamiltonian to describe the system at zero temperature is given bŷwhereĤ atom gives the free evolution of the the atomic fields andĤ atom−f ield describes the dipole interactions between the atomic fields and the pump and probe fields. We assume the condensate to be sufficiently diluite in order to neglect the atom-atom interaction. The free atomic Hami...

Laser driving of superradiant scattering from a Bose-Einstein condensate at variable incidence angle

“…Since the trailblazing experiment of superradiant Rayleigh scattering from a Bose-Einstein condensate (BEC) [1], numerous experiments and theoretical developments have emerged in cooperative scattering of light and atoms in ultracold atomic gases concerning Rayleigh superradiant scattering [1][2][3][4][5][6][7][8][9][10], amplification of matter waves [11][12][13], coherent atomic recoil lasing (CARL) [14,15], Raman superradiance [16][17][18], and its application in probing the spatial coherence of an ultracold gas [19,20]. Why matter-wave superradiance can occur only when the pump laser is red-detuned has been explained recently [21,22].…”

On the theory of matter wave amplification in a Bose–Einstein condensate of dilute gas

“…It is interesting that, independently of the experiment [1], a possibility of the backward atomic recoil was theoretically predicted in [12] for the model of superradiant Raman scattering from a 3-level atom in Λ-configuration. In the present paper we use a semi-classical approach in the mean field approximation.…”

Coherent Logic Gate for Light Pulses Based on Storage in a Bose-Einstein Condensate

“…Upon mapping the new atomic momentum component back onto light, it creates population in a new optical momentum component. This light emission process is accompanied by Raman amplification of matter waves (AMW) [16,17]. The light emitted during Raman AMW and the phase coherence of this light have never been studied experimentally; despite related work in atomic FWM [18], Rayleigh AMW [19,20], and superradiant light scattering [21,22].…”

“…From a theoretical point of view [17], Raman AMW is analogous to a usual stimulated Raman process, except that the emission is bosonically stimulated not by application of a second laser beam but by the presence of a second BEC. Effectively the role of the second laser beam and the second BEC are exchanged.…”