Sum-frequency generation in an ultracold atomic gas due to collective atomic recoil

Abstract

We describe a method for sum-frequency generation via non-degenerate four-wave mixing in classical (thermal) and quantum ultracold atomic gases (BEC). An integral part of the sum-frequency generation process is a collective instability which spontaneously generates a periodic density modulation in the atomic gas with a period comparable to the wavelength of the generated high-frequency optical field. Due to the generation of this density modulation, phase matching between the pump and generated fields is not a necessary initial condition for this sum-frequency generation process to occur: rather the density modulation acts to ‘self-phase-match’ the fields during the course of the sum-frequency generation process. We describe a one-dimensional model of this process, and suggest a proof-of-principle experiment to demonstrate a regime where the sum-frequency generation process evolves quantum mechanically, with discrete emission of sum-frequency photons. This experiment would involve pumping ultracold Cs atoms in a high-finesse unidirectional cavity with three infrared pump fields to produce blue light as a series of hyperbolic secant pulses.