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arXiv:1006.3240 · Physical Review A

Hysteresis effects in Bose-Einstein condensates

Andrea Sacchetti

Published Jul 27, 2010• 1 citation
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Abstract

Here, we consider damped two-component Bose-Einstein condensates with many-body interactions. We show that, when the external trapping potential has a double-well shape and when the nonlinear coupling factors are modulated in time, hysteresis effects may appear under some circumstances. Such hysteresis phenomena are a result of the joint contribution of the appearance of saddle node bifurcations and the damping effect.

DOI
10.1103/physreva.82.013636

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Here, we consider damped two-component Bose-Einstein condensates with many-body interactions. We show that, when the external trapping potential has a double-well shape and when the nonlinear coupling factors are modulated in time, hysteresis effects may appear under some circumstances. Such hysteresis phenomena are a result of the joint contribution of the appearance of saddle node bifurcations and the damping effect.
We discuss thermal and dynamical properties of Bose condensates confined by an external potential. First we analyze the Bose-Einstein transition temperature for an ideal Bose gas in a generic power-law potential and d-dimensional space. Then we investigate the effect of the shape of the trapping potential on the properties of a weakly-interacting Bose condensate. We show that using exotic trapping potentials the condensate can exhibit interesting coherent quantum phenomena, like superfluidity and tunneling. In particular, we consider toroidal and double-well potentials. The theoretical results are compared with recent experiments.
The dynamics of two-component Bose–Einstein condensates (BECs) in a double-well potential is studied here. Interspecies (or component–component) couplings are taken into account. As a consequence of the couplings, more fixed points may appear in the BECs. We analyze the stability of the system around some special fixed points that are independent of the couplings. A critical interspecies coupling constant below which fixed points are stable is presented and analyzed. Numerical simulation of the dynamics of the two-component BECs is also presented and discussed.
We study the dynamics of a Bose-Einstein condensate in a double-well potential in the mean-field approximation. Decoherence effects are considered by analyzing the couplings of the condensate to the environment. Two kinds of coupling are taken into account. With the first kind of coupling dominating, decoherence can enhance self-trapping by increasing the damping of the oscillations in the dynamics, while decoherence from the second kind of condensate-environment coupling leads to spoiling of the quantum tunneling and self-trapping.
The influence of atomic interactions on time-dependent tunneling processes of Bose-Einstein condensates is investigated. In a variety of contexts the relevant condensate dynamics can be described by a Landau-Zener equation modified by the appearance of nonlinear contributions. Based on this equation it is discussed how the interactions modify the tunneling probability. In particular, it is shown that for certain parameter values, due to a nonlinear hysteresis effect, complete adiabatic population transfer is impossible however slowly the resonance is crossed. The results also indicate that the interactions can cause significant increase as well as decrease of tunneling probabilities that should be observable in currently feasible experiments.
Self-trapping of Bose-Einstein condensates (BEC) in double-well trap is investigated. Two kinds of self-trapping are discussed through phase space analysis in the mean-field approximation: 1) The number of atoms oscillates near an equilibrium point in the phase space, while relative phase increases monotonously with time (running-phase); 2) Both the number of particles and the relative phase oscillate near an equilibrium point in the phase space. In particular, we investigate how an external periodic filed influence the self-trapping. It is found that the external periodic field may dramatically modulate the critical points at which the transition to self-trapping occurs. With this, we can observe self-trapping phenomenon in a dilute Bose-Einstein condensate with a very weak interaction as well. Finally, the effect of many-body quantum fluctuation on self-trapping is also studied. We also discuss how to observe the self-trapping phenomenon with present experimental techniques.
We investigate the nonlinear dissipative coherence bifurcation and population dynamics of a two-component atomic Bose—Einstein condensate coupling with a continuum. The coupling between the two-component condensates and the continuum brings effective dissipations to the two-component condensates. The steady states and the coherence bifurcation depend on both dissipation and the nonlinear interaction between condensed atoms. The coherence among condensed atoms may be even enhanced by the effective dissipations. The combination of dissipation and nonlinearity allows one to control the switching between different self-trapped states or the switching between a self-trapped state and a non-self-trapped state.