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arXiv:0910.4977 · Physical Review A

Breakdown of macroscopic quantum self-trapping in coupled mesoscopic one-dimensional Bose gases

Rafael Hipolito, Anatoli Polkovnikov

Published Jan 25, 2010• 20 citations

Abstract

Two coupled Bose-Einstein condensates with a large population imbalance exhibit macroscopic quantum self-trapping (MQST) if the ratio of interaction energy to tunneling energy is above a critical value. Here we investigate effect of quantum fluctuations on MQST. In particular, we analyze the dynamics of a system of two elongated Bose gases prepared with a large population imbalance, where due to the quasi-one-dimensional character of the gas we no longer have true long range order, and the effect of quantum fluctuations is much more important. We show that MQST is possible in this system, but even when it is achieved it is not always dynamically stable. Using this instability one can construct states with sharply peaked momentum distributions around characteristic momenta dependent on system parameters. Our other finding is the nonmonotonic oscillating dependence of the decay rate of the MQST on the length of the wires. We also address the interesting question of thermalization in this system and show that it occurs only in sufficiently long wires.

DOI: 10.1103/physreva.81.013621

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Two coupled Bose-Einstein condensates with a large population imbalance exhibit macroscopic quantum self-trapping (MQST) if the ratio of interaction energy to tunneling energy is above a critical value. Here we investigate effect of quantum fluctuations on MQST. In particular, we analyze the dynamics of a system of two elongated Bose gases prepared with a large population imbalance, where due to the quasi-one-dimensional character of the gas we no longer have true long range order, and the effect of quantum fluctuations is much more important. We show that MQST is possible in this system, but even when it is achieved it is not always dynamically stable. Using this instability one can construct states with sharply peaked momentum distributions around characteristic momenta dependent on system parameters. Our other finding is the nonmonotonic oscillating dependence of the decay rate of the MQST on the length of the wires. We also address the interesting question of thermalization in this system and show that it occurs only in sufficiently long wires.

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

ω

of the oscillating energy barrier. In the regime of periodic macroscopic quantum tunneling (PMQT) with frequency

ω_J

, the population imbalance of the condensate in the two wells can be enhanced under the condition of parametric resonance

ω= 2 ω_J

. 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

ω

of the energy barrier and the frequency

ω_{ST}

of oscillation through the barrier of the very small fraction of particles which remain untrapped during MQST.

We present a theoretical treatment of macroscopic quantum self-trapping (MQST) and quantum coherent atomic tunneling in a zero-temperature two-species Bose-Einstein condensate system in the presence of the nonlinear self-interaction of each species, the interspecies nonlinear interaction, and the Josephson-like tunneling interaction. It is shown that the nonlinear interactions can dramatically affect the MQST and the atomic tunneling, and lead to the collapses and revivals (CR) of the population imbalance between the two condensates. The competing effects between the self-interaction of each species and the interspecies interaction can lead to a quenching of the MQST and a suppression of the CR and the Shapiro-like steps of the atomic tunneling current. It is revealed that interatomic nonlinear interactions can induce coherent atomic tunneling between two condensates even though interspecies Josephson-like tunneling coupling does not exist.

Abstract We theoretically study the effects of trap-confinement and interatomic interactions on Josephson oscillations (JO) and macroscopic quantum self-trapping (MQST) for a Bose–Einstein condensate confined in a trap which has a symmetric double-well potential along z -axis and 2D harmonic potentials along x - and y -axis. We consider three types of model interaction potentials: contact, long-range dipolar and finite-range potentials. Our results show that by changing the aspect ratio between the axial and radial trap sizes, one can induce a transition from JO to MQST for contact interactions with a small scattering length. For long-range dipolar interatomic interactions, we analyze transition from Rabi to Josephson regime and Josephson to MQST regime by changing the aspect ratio of the trap for a particular dipolar orientation. For a finite-range interaction, we study the effects of relatively large scattering length and effective range on JO and MQST. We show that JO and MQST are possible even if scattering length is relatively large, particularly near a narrow Feshbach resonance due to the finite-range effects.

Macroscopic quantum tunneling of Bose-Einstein Condensate in a double-well potential is discussed in the frame of an experimentally realizable Hamiltonian with ϕ 6 interaction under the two-mode approximation. Concentrating on a special case Δ E = Λ = 0, we analyze the stationary states and dynamics of the system to find that such system possesses very small phase spaces for Josephson oscillation and usually lies in the macroscopic quantum self-trapping state (MQST). Importantly we obtain three kinds of MQSTs and in terms of them show the phase diagrams of the system.

We study the dynamics of a Bose-Einstein condensate in a double-well potential in the two-mode approximation. The dissipation of energy from the condensate is described by the coupling to a thermal reservoir of noncondensate modes. As a consequence of the coupling, the self-locked population imbalance in the macroscopic quantum self-trapping decays away. We show that a coherent state predicted by spontaneous symmetry breaking is not robust and decoheres rapidly into a statistical mixture due to the interactions between condensate and noncondensate atoms. However, via stochastic simulations we find that with a sufficiently fast measurement rate of the relative phase between the two wells the matter wave coherence is established even in the presence of the decoherence.