Incoherent scattering of light by a Bose – Einstein condensate of interacting atoms

We demonstrate that incoherent photon scattering by a Bose–Einstein condensate of non-ideal atomic gas is enhanced due to bosonic stimulation of spontaneous emission, similarly to coherent scattering in forward direction. Necessary initial population of non-condensate states is provided by quantum depletion of a condensate caused by interatomic repulsion. Since the most reliable methods of diagnostics of a Bose–Einstein condensate (BEC) of a dilute atomic gas are based on laser spectroscopic techniques, the optical properties of BEC are of geat interest. One of the most important features of the interaction of BEC with resonant light is the enhancement of scattering in the forward direction [1, 2]. If an excited atom returns, after spontaneous emission of a photon, to the state occupied by a large number N of atoms, the probability of such a process is increased in proportion to N +1 by the effects of quantum Bose–Einstein statistics. A degenerate atomic sample interacts with external light as an integral object, so this process is coherent. Because of momentum conservation, photons are scattered mostly into the forward direction. The corresponding solid angle Ω coh is small but finite, because the atomic cloud size R is finite, and is of order of (kR) −2 , where k is the resonant photon wavenumber. On the other hand, it is commonly believed, that the photon scattering into modes lying outside of Ω coh , that leads to an escape of atoms from the condensate and heating of the atomic sample, is not modified with respect to the usual single-atom case [2, 3]. But such a conclusion is valid for an ideal gas only. In the present paper, we show how repulsive interaction of atoms composing BEC modifies incoherent photon scattering. Let us define, firstly, the initial |i and final |f states of the system. Initially, we have BEC of atoms in their internal ground state (the BEC chemical potential 1