Enhancement of four-wave mixing in Bose-Einstein condensate by introducing a mismatch

A recent experiment demonstrated four-wave mixing of wave packets in a sodium Bose-Einstein condensate [Deng , Nature (London) 398, 218 (1999)]. This was followed by a theoretical and numerical treatment of the experiment [Trippenbach , Phys. Rev. A 62, 023608 (2000)]. In the experiment, a short time of free expansion of the condensate, after it was released from the magnetic trap, was followed by a set of two Bragg pulses, which created moving wave packets. These wave packets, due to nonlinear interaction and under phase-matching conditions created a new momentum component in a four-wave mixing process. Here we suggest that, instead of exactly matching the frequencies as in the above-mentioned experiments, we admit a small mismatch in energies, and therefore frequencies Deltaomega. We show that such a small mismatch can compensate for the initial phases built on the condensate during free expansion. A physical explanation is offered. This compensation can be beneficial for the efficiency of the four-wave mixing, in some cases even increasing it by a factor of 2.