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arXiv:quant-ph/0406076 · Physical Review A

Resonances for coupled Bose-Einstein condensates

H. L. Haroutyunyan, Gerard Nienhuis

Published Dec 7, 2004• 13 citations
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Abstract

The properties of a Bose-Einstein condensate in a two-well potential can be manipulated by periodic modulation of the potential parameters. We study the effects arising from modulating the barrier height and the difference in well depth. At certain modulation frequencies the system exhibits resonances, which may show up in an enhancement of the tunneling rate between the wells. Resonances can be used to control the particle distribution over the wells. Some of the effects occurring in the two-well system also arise for a Bose-Einstein condensate in an optical lattice.

DOI
10.1103/physreva.70.063603

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The properties of a Bose-Einstein condensate in a two-well potential can be manipulated by periodic modulation of the potential parameters. We study the effects arising from modulating the barrier height and the difference in well depth. At certain modulation frequencies the system exhibits resonances, which may show up in an enhancement of the tunneling rate between the wells. Resonances can be used to control the particle distribution over the wells. Some of the effects occurring in the two-well system also arise for a Bose-Einstein condensate in an optical lattice.
The dynamics of a Bose?Einstein condensate under the influence of a confining double-well potential and a periodic potential (optical lattice) is studied by the well-known variational method. The variational principle leads to coupled nonlinear differential equations for the amplitude (width), chirp, center position and the center frequency of the condensate. The interplay between the condensate parameters leads to various regimes of its time evolution which depend on the relative strengths of the double-well and the periodic potentials. In particular, we show that by adjusting the strengths of the applied potentials appropriately, one can control and manipulate the condensate in several ways including tunneling from one well to the other and the to-and-fro motion between the two wells.
With phase space analysis approach, we investigate the self-trapping phenomenon for two weakly coupled Bose-Einstein condensates (BECs) in a symmetric double well potential. We identify two kinds of self-trapping by their different relative phase behavior. By applying a periodic modulation on the energy bias of the system we find that the self-trapping can be controlled, in other words, the transition parameters can be adjusted effectively by the periodic modulation. Analytic expressions for the dependence of the transition parameters on the modulation parameters are derived for high- and low-frequency modulations. For an intermediate-frequency modulation, we find the resonance between the periodic modulation and nonlinear Rabi oscillation dramatically affect the tunneling dynamics and demonstrate many phenomena. Finally, we study the effects of many-body quantum fluctuation on the self-trapping and discuss the possible experimental realization.
We analyze the periodic tunneling of a Bose-Einstein condensate in a double-well potential which has an oscillating energy barrier. We show that the dynamics of the Bose condensate critically depends on the frequency ωωω of the oscillating energy barrier. In the regime of periodic macroscopic quantum tunneling (PMQT) with frequency ωJω_JωJ​, the population imbalance of the condensate in the two wells can be enhanced under the condition of parametric resonance ω=2ωJω= 2 ω_Jω=2ωJ​. Instead, in the regime of macroscopic quantum self-trapping (MQST), we find that MQST can be reduced or suppressed under the condition of parametric resonance between the frequency ωωω of the energy barrier and the frequency ωSTω_{ST}ωST​ of oscillation through the barrier of the very small fraction of particles which remain untrapped during MQST.
We investigate the quantum tunneling of a Bose-Einstein condensate confined in a optical trap. We show that periodic pulses of coherent matter are emitted from the trap by using an oscillating energy barrier. Moreover, the emitted fraction of condensed atoms strongly increases if the period of oscillation of the height of the energy barrier is in parametric resonance with the period of oscillation of the center of mass of the condensate inside the potential well. Our model is analyzed by numerically solving the nonpolynomial Schrodinger equation (NPSE), an effective one-dimensional equation which describes the macroscopic wavefunction of Bose condensates under transverse harmonic confinement. The range of validity of NPSE is discussed and compared with that of Gross-Pitaevskii equation.
We investigate theoretically the tunneling of a dilute Bose-Einstein condensate through a potential barrier. This scenario is closely related to recent experimental studies of condensates trapped in one-dimensional optical lattices. We derive analytical results for the tunneling rate of the condensate with emphasis on the effects of atom-atom interactions. Furthermore, we consider the effect of fluctuating barrier height to the tunneling rate. We have computed the tunneling rate as a function of the characteristic frequency of the noise. The result is seen to be closely related to the excitation spectrum of the condensate. These observations should be experimentally verifiable.