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

Robb, G.R.M. and McNeil, B.W.J. (2006) Sum-frequency generation in an ultracold atomic gas due to collective atomic recoil. Journal of Physics B: Atomic, Molecular and Optical Physics, 39 (22). ISSN 0953-4075

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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.