Enhancement and suppression of spontaneous emission and light scattering by quantum degeneracy

For a long time, spontaneous emission and light scattering were regarded as intrinsic properties of atoms. However, quantum electrodynamics ~QED! revealed the connection between these phenomena and the electromagnetic modes of the vacuum. Spontaneous emission and scattering can only take place when a vacuum mode is available to accommodate the emitted or scattered photon. Cavity-QED experiments @1# exploit the fact that small cavities can be used to modify the vacuum, and thus emission and scattering of light. Recent breakthroughs in the experimental realization of gaseous quantum degenerate systems of bosons @2‐5# and fermions @6# have provided additional means to modify the emission and scattering behavior of atoms. On the one hand, this modification is due to the finite population in the final state of the scattering or emission process. On the other hand, interactions modify the nature of the final states for the recoiling atom, similar to a cavity that alters the mode structure for the photon. Generally, transition rates between an initial state with population N1 and a final state with population N2 are proportional to N1(11N2) for bosons and to N1(12N2) for fermions. This reflects the well-known fact that in a bosonic system the transition into an already occupied state is enhanced by bosonic stimulation, while in fermionic systems, occupation of a state prevents a transition into this state by Pauli blocking. This simple derivation of transition rates using occupation numbers becomes subtle or even invalid for correlated manybody states such as an interacting Bose-Einstein condensate ~BEC! ground state. In this Rapid Communication, we analyze under which circumstances the simple approach can be used to reproduce the correct results for the interaction between light and a BEC. We show theoretically that spontaneous emission in a weakly interacting BEC is enhanced, consistent with the description using occupation numbers, and calculate the enhancement factor. We compare this result to light scattering in a BEC, which is suppressed due to interference effects not included in the simple derivation, as we have shown experimentally and theoretically in previous work @7#. In contrast, in fermionic systems quantum degeneracy leads to a suppression of both spontaneous emission and light scattering @8‐11#.