Bragg spectroscopy and superradiant Rayleigh scattering in a Bose–Einstein condensate

Two sets of studies concerning the interaction of off-resonant light with a sodium Bose–Einstein condensate are described. In the first set, properties of a Bose– Einstein condensate were studied using Bragg spectroscopy. The high momentum and energy resolution of this method allowed a spectroscopic measurement of the mean-field energy and of the intrinsic momentum distribution of the condensate. Depending on the momentum transfer, both the phonon regime as well as the free-particle regime could be explored. In the second set of studies, the cigarshaped condensate was exposed to a single off-resonant laser beam and highly directional scattering of light and atoms was observed. This collective light scattering was caused by the long coherence time of the quasi-particles in the condensate and resulted in a new form of matter wave amplification. PACS: 03.75.Fi; 32.80.Pj What does a trapped Bose–Einstein condensate look like? More precisely, how does it interact with light, and does this differ fundamentally from what one would naively expect from a similar collection of very cold atoms? The experiments reviewed here all study off-resonant light scattering from a condensate, either spontaneously (i.e. Rayleigh scattering) or when stimulated by a second laser beam (i.e. Bragg spectroscopy). Light scattering imparts momentum to the condensate and creates an excitation which can be either a phonon or a free particle. A detailed study of the scattered light [1, 2], should therefore reveal a detailed picture of the Bose–Einstein condensate similar to the case of superfluid helium, where neutron scattering was used to obtain the spectrum of elementary excitations [3]. Since the light scattered from a typical 107-atom condensate is hard to detect, we used a second laser beam stimulating the scattering of light with a frequency and direction, which was pre-determined by the laser beam rather than postdetermined by analyzing scattered light. This scheme, which we call Bragg Spectroscopy, establishes a high-resolution spectroscopic tool for Bose–Einstein condensates which is sensitive to the momentum distribution of the trapped condensate as well as the mean-field energy shift [4, 5]. We studied Bragg scattering in two regimes differing by the amount of momentum transfer. For large momentum excitations (free-particle regime) the resonance showed a Doppler broadening due to the zero-point motion of the condensate and a line shift and broadening due to the interactions within the condensate [4]. The observed Doppler broadening was consistent with the expected Heisenberg-uncertainty limited momentum distribution of a condensate with a coherence length equal to its physical size. For small momentum excitations (phonon regime) the light scattering rate was significantly reduced, providing evidence for the presence of correlated momentum excitations in the many-body condensate wavefunction [5]. More generally, Bragg spectroscopy can be used to determine the dynamic structure factor S(q, ν) over a wide range of frequencies ν and momentum transfers q [6]. In contrast, the conventional imaging techniques like timeof-flight imaging or phase contrast imaging are not sensitive to the momentum distribution of a trapped condensate [7]. The spatial density distribution of the trapped condensate can be resolved in phase contrast imaging, and the momentum distribution of the atoms after being released from the trap can be imaged in time-of-flight. This momentum distribution, however, predominantly results from the released mean-field energy but not from the zero-point motion. In a second set of studies we found that scattering of a single beam of light from the condensate led to a new process – self stimulated Rayleigh scattering – above a low threshold intensity [8]. We observed pulses of scattered light emanating from the ends of the condensate, establishing that this process is a new form of superradiance which occurs because the recoiling atoms remain coherent with the unscattered atoms, forming a matter wave grating which scatters subsequent photons in the same direction. The two sets of studies shall be discussed in more detail in the following.