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arXiv:cond-mat/0005417 · Physical Review A

Four-wave mixing in degenerate atomic gases

Pierre Villain, Patrik Öhberg, Luis Santos, Anna Sanpera, Maciej Lewenstein

Published Jul 1, 2001• 22 citations
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Abstract

We study the process of four-wave mixing (FWM) in ultracold degenerate atomic gases. In particular, we address the problem of FWM in boson-fermion mixtures. We develop an approximate description of such processes using asymptotic analysis of high-order perturbation theory taking into account quantum statistics. We perform also numerical simulations of FWM in boson-fermion mixtures and obtain an analytic and numerical estimate of the efficiency of the process.

DOI
10.1103/physreva.64.023606

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We study the process of four-wave mixing (FWM) in ultracold degenerate atomic gases. In particular, we address the problem of FWM in boson-fermion mixtures. We develop an approximate description of such processes using asymptotic analysis of high-order perturbation theory taking into account quantum statistics. We perform also numerical simulations of FWM in boson-fermion mixtures and obtain an analytic and numerical estimate of the efficiency of the process.
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We analyze the full nonlinear dynamics of the four-wave mixing between an incident beam of fermions and a fermionic density grating. We find that when the number of atoms in the beam is comparable to the number of atoms forming the grating, the dephasing of that grating, which normally leads to the decay of its amplitude, is suppressed. Instead, the density grating and the beam density exhibit large nonlinear coupled amplitude oscillations. In this case, four-wave mixing can persist for much longer times compared to the case of negligible back action. We also evaluate the efficiency of the four-wave mixing and show that it can be enhanced by producing an initial density grating with an amplitude that is less than the maximum value. These results indicate that efficient four-wave mixing in fermionic alkali gases should be experimentally observable.
An analysis is made of four-wave mixing of laser radiation interacting with an ultracold degenerate ensemble of boson atoms trapped in a magnetic trap. It is shown that the existence of long-range order in this type of atomic system leads to a new mechanism for the generation of the reversed wave whose experimental manifestation should differ from four-wave mixing in a nondegenerate gas. A similar nonlinear optical effect may be used for diagnostics of an ultracold gas at temperatures not much lower than the phase transition temperature.
Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles. We also briefly review progress in the case of spinor Bose gases of a few atoms. For fermionic mixtures, we discuss a special role of spin and present a detailed discussion of the two- and three-atom cases. We discuss the advantages and disadvantages of different computation methods applied to systems with intermediate interactions. In the case of very strong repulsion, close to the infinite limit, we discuss approaches based on effective spin chain descriptions. We also report on recent studies on higher-spin mixtures and inter-component attractive forces. For both statistics, we pay particular attention to impurity problems and mass imbalance cases. Finally, we describe the recent advances on trapped Bose-Fermi mixtures, which allow for a theoretical combination of previous concepts, well illustrating the importance of quantum statistics and inter-particle interactions. Lastly, we report on fundamental questions related to the subject which we believe will inspire further theoretical developments and experimental verification.