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Europhysics Letters (EPL)

Controllable quantum phase transition in two-component Bose-Einstein condensates under periodic modulation

G. Chen, J.-Q. Liang, Z.-D. Chen

Published Jun 6, 2007• 2 citations
Publisher

Abstract

In this letter we predict a novel second-order quantum phase transition of two-component Bose-Einstein condensates coupled with a periodically driven laser field in the resonant case. It is shown that this quantum phase transition from the normal to the tunneling phases can be controlled by the interspecies nonlinear interaction tuned via the magnetic-field–dependent Feshbach resonance technique. Furthermore, it is also demonstrated that this quantum phase transition can be detected by measuring the ground-state population imbalance between two condensates.

DOI
10.1209/0295-5075/79/10001

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In this letter we predict a novel second-order quantum phase transition of two-component Bose-Einstein condensates coupled with a periodically driven laser field in the resonant case. It is shown that this quantum phase transition from the normal to the tunneling phases can be controlled by the interspecies nonlinear interaction tuned via the magnetic-field–dependent Feshbach resonance technique. Furthermore, it is also demonstrated that this quantum phase transition can be detected by measuring the ground-state population imbalance between two condensates.
We put forward a scheme for controlling Josephson-like tunneling in two-component Bose-Einstein condensates coupled with microwave field via Feshbach resonance and tuning aspect ratio of trapping potential. We prove how to realize a perfect periodic oscillation from a fast damped and irregular oscillation on relative number of atoms in future experiment. In particular, intensity of Josephson-like tunneling can be successfully controlled through controlling speed of recovering the initial value of intra-atomic interaction and aspect ratio of trapping potential. Interestingly, we find that relative number of atoms represents two different types of oscillation in respond to periodic modulation of attractive intra-atomic interaction.
For a weakly and periodically driven two-component Bose-Einstein condensate (BEC) the Melnikov chaotic solution and boundedness conditions are derived from a direct perturbation theory that leads to the chaotic regions in the parameter space. Differing from the usual results, the chaotic regions depend on the initial conditions directly and can be controlled by setting the initial phase and modulating the frequency and amplitude of laser. It is demonstrated that the order-chaos transitions can be controlled by tuning the laser frequency only.
Summary form only given. Dynamical control of the atomic tunneling between two Bose-Einstein condensates (BEC's) confined in a double-well potential is predicted to occur when laser pulses induce transition between one of the condensate state and the excited state which brings about phase shifts for the condensate wave function, leading to transition between macroscopic quantum self-trapping, which is a self-maintained population imbalance between two BEC's due to interatomic interaction, and large amplitude oscillations. We investigate this phenomenon for the case of a three-level system with two condensate states and an excited state.
An extended Dicke model, which includes atom-atom interactions and a driving classical laser field, is established for a Bose-Einstein condensate inside an ultrahigh-finesse optical cavity. A feasible experimental setup with a strong atom-field coupling is proposed, where most parameters are easily controllable and thus the predicted a second-order superradiant-normal phase transition may be detected by measuring the ground-state atomic population. More intriguingly, second-order phase transition from the superradiant phase to the ``Mott'' phase is also revealed. In addition, a rich and exotic phase diagram is presented.
We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the nthn\mathrm{th}nth LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.
We propose an experiment that would demonstrate nonlinear Josephson-type oscillations in the relative population of a driven, two-component Bose-Einstein condensate. An initial state is prepared in which two condensates exist in a magnetic trap, each in a different hyperfine state, where the initial populations and relative phase between condensates can be controlled within experimental uncertainty. A weak driving field is then applied, which couples the two internal states of the atom and consequently transfers atoms back and forth between condensates. We present a model of this system and investigate the effect of the mean field on the dynamical evolution.