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Modern Physics Letters B

WAVE PACKET DYNAMICS AND RABI OSCILLATIONS IN TWO-COUPLED BOSE–EINSTEIN CONDENSATES CONFINED IN AN OPTICAL LATTICE

Aranya B. Bhattacherjee, Man Mohan

Published Apr 10, 2003• 0 citations
Publisher

Abstract

We predict the collapse and recurrence of Rabi oscillations in a two-component Bose–Einstein condensate trapped in an optical lattice. The optical trap creates a periodic potential with a periodic coupling. The collapse and revival sequence is explained on the basis of wave-packet dynamics. The collapse and revival sequence is found to be a consequence of competition between the potential energy difference and the driving frequency.

DOI
10.1142/s0217984903005160

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We study the Bloch oscillations (BOs) of two-component Bose-Einstein condensates (BECs) trapped in spin-dependent optical lattices. Based on the derived equations of motion of the wave packet in the basis of localized wave functions of the lattice sites, the damping effect induced by the intercomponent and intracomponent interactions to the BOs is explored analytically and numerically. We also show that such damping of the BOs can be suppressed entirely if all the atom-atom interactions are modulated synchronously and harmonically in time with suitable frequency via the Feshbach resonance. When the intercomponent and the intracomponent interactions have inverse signs, we find that the long-living BOs and even the revival of the BOs can be achieved via only statically modulating the configuration of optical lattices. The results provide a valuable guidance for achieving long-living BOs in the two-component BEC system by the Feshbach resonances and manipulating the configuration of the optical lattices.
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The center of mass dynamics of cold atoms and the Bose-Einstein condensate in one dimensional optical lattice is considered both in the absence and in the presence of external forcing. We discuss three situations for matter waves: first, the cold atoms; second, sufficiently dilute condensate where the dynamics are governed by the single particle wave packet dynamics; third, strong interaction regime, where, inter-atomic interaction can no longer be ignored. The analytical formalism developed for the two regimes, namely, deep optical lattice and shallow optical lattice. Parametric dependencies of energy spectrum and classical period, revival time and super revival are explained for the two regimes. The dynamics of condensate in driven optical lattice crystal are analyzed by studying dynamical stability of the condensate. The stability is determined by the dispersion behavior of the condensate excited in driven optical lattice. The recurrence behavior of the condensate close to the nonlinear resonances is analyzed as a function of time for delicate recurrences which take place for instance when lattice is weakly perturbed and robust recurrences which may manifest themselves for sufficiently strong external driving force. The analysis is not only valid for dilute condensate but also applicable for strongly interacting homogeneous condensate provided, the external modulation causes no significant change in density profile of the condensate. We explain parametric dependence of the dynamical recurrence times which can easily be realized in laboratory experiments. In addition, we find a good agreement between the obtained analytical results and numerical calculations. The stability of condensate is also explored in driven optical lattice numerically.
The Rabi oscillations in two-component Bose-Einstein condensates with a coupling drive are studied by means of a pair of bosonic operators. The coupling drive and initial phase difference, will affect the amplitude and the period of the Rabi oscillations. The Rabi oscillations will vanish in the evolution of the condensate density for some special initial phase differences (phi = 0 or pi). Our theory provides not only an analytical framework for quantitative predictions for two-component condensates, but also gives ail intuitive understanding of some mysterious features observed in experiments and numerical simulations.