Raman amplification of matter waves

With the realization of coherent, laserlike atoms in the form of Bose-Einstein condensates it has become possible to explore matter-wave amplification, a process in which the number of atoms in a quantum state is amplified due to bosonic stimulation. Stimulation has been observed in the formation of condensates [1,2] and, more directly, has been used to realize coherent matter-wave amplifiers [3,4] based on superradiant Rayleigh scattering [5–13] in which the atomic momentum of the gain medium and the amplified atoms differ by a photon recoil. In these cases the atoms remained in the same internal state, a fact that severely limited the performance of superradiant atom amplifiers since the amplified atoms were scattered out of the final state or served as a gain medium for higher-order processes (superradiant cascades [7]). In this Rapid Communication we demonstrate a Raman atom amplifier in which the gain medium and the amplified atoms are in different internal states. Such a system has analogies to an optical laser in which different transitions are used for pumping and lasing, thus circumventing the above limitations. The gain mechanism for this amplifier is stimulated Raman scattering in a L-type atomic level structure which occurs in a superradiant way. This system also acts as a Stokes Raman laser for optical radiation. The amplification scheme is similar to that explored in previous work on Rayleigh superradiance in Bose-Einstein condensates [7,12] [cf. Fig. 1(a)]. A linearly polarized laser beam with wave vector k is incident on a magnetically trapped, cigar-shaped condensate, perpendicular to its long axis. Each scattering event creates a scattered photon with momentum "sk−qd and a recoiling atom with corresponding momentum "q. This scattering process is bosonically stimulated by atoms that are already present in the final state "q. For Rayleigh scattering, the mode with the highest gain is the so-called endfire mode, in which the scattered photons propagate along the long axis of the condensate, while the scattered atoms recoil at an angle of 45° [7]. Rayleigh superradiance is strongest when the electric-field vector of the incident beam is perpendicular to the long axis of the condensate and is suppressed when the field vector is parallel to it [7]. This parallel configuration is the experimental situation considered in this Rapid Communication. The angular distribution of spontaneously emitted light is dependent on its polarization. If we take the quantization axis ẑ along the long axis of the condensate (which is also the direction of the bias field in the magnetic trap), the incident beam is p polarized. If the emitted light is also p polarized (Rayleigh scattering) its angular distribution is that of an oscillating dipole, fpsud= s3/8pdsin2 u, where u is the angle between ẑ and the direction of propagation of the scattered light. The suppression of Rayleigh superradiance in this configuration is reflected in the fact that fp vanishes along ẑ, such that the endfire mode cannot be populated. If the emitted light is s polarized, the angular characteristics are those of a rotating dipole, fssud= s3/16pds1+cos2 ud and emission into the endfire mode is favored. The absorption of p light followed by the emission of s light corresponds to a Raman transition in which the z component of the atomic angular momentum changes by ". We now discuss the existence of superradiant gain for such a Raman process. For Rayleigh scattering an expression has been derived both semiclassically and quantum mechanically, using descriptions based on either atomic or optical stimulation [7,12,14]: