Features of dynamics of stimulated atomic-molecular Raman conversion in a Bose-Einstein condensate
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Features of Dynamics of Stimulated Atomic–Molecular Raman Conversion in a Bose–Einstein Condensate P. I. Khadzhi and D. V. Tkachenko Institute of Applied Physics, Academy of Science of Moldova, Kishinev, MD 2800 Moldova Pridnestrovskiœ State University, Tiraspol’, MD 3300 Moldova e-mail: [email protected]; [email protected] Received September 19, 2006
Abstract—A set of nonlinear evolution equations describing the dynamics of atoms, molecules, and photons in the course of stimulated atomic–molecular conversion in a Bose–Einstein condensate is derived and studied in the mean-field approximation. It is shown that conversion can be periodic or aperiodic in time, the rate of the process being determined to a considerable extent by the initial density of particles and by the initial phase difference. Depending on the initial conditions, various conversion modes can be realized. The possibility of stabilization of a special state (of rest) of the system for nonzero initial number densities of particles is predicted. It is pointed out that coherence of a Bose condensate of atoms, molecules, and photons predetermines the possibility of phase control of the conversion process. PACS numbers: 03.75.Nt, 05.30.Jp, 42.50.Hz DOI: 10.1134/S1063776107030041
1. INTRODUCTION The first observation of Bose–Einstein condensation in low-density atomic vapors [1–5] stimulated substantial progress in experimental and theoretical studies of physical properties of Bose condensate in magnetic traps [6–9] and its dynamics in two-well traps [10–15]. In recent years, investigations into the dynamics of bound atomic–molecular condensates under the conditions when Feschbach resonances are manifested or under the conditions of the atomic–molecular Raman conversion involving two electromagnetic radiation pulses have been attracting special attention. If the total energy of two colliding atoms is equal to the energy of a quasi-bound diatomic state (a molecule in a strongly excited state), the emergence of resonant bonding of atoms is referred to as Feschbach resonance. The dependence of the Feschbach resonance position on the applied magnetic field determines the unique possibility of continuous variation of interatomic scattering length and even sign reversal of the interatomic interaction upon a variation of the field [16]. The magnetic field tunes the levels of the diatomic molecular system so that pairs of atoms are combined into a molecule in a strongly excited state. It was noted in [17] that the concepts “atomic pair” and “molecule” in a strongly interacting many-particle system in the region of the Feschbach resonance become conditional to a certain extent. Such resonances were observed, for example, in the Bose condensate of sodium atoms in magnetic fields of 853 and 907 G [18] and in the cold
gas of 85Rb in a field of 164 G [19]. In sodium, the scattering length a as a function of magnetic field B varied in accordance with theoretical predictions [16]. It was shown in [20–22] that the lifetime of the molecules formed in a
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