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Chinese Physics

Entanglement dynamics in two-component Bose–Einstein condensates

Hao Ya-Jiang, Liang Jiu-Qing

Published May 31, 2006• 10 citations
Publisher

Abstract

Based on the exact solution of the time-dependent Schrödinger equation for two-species Bose–Einstein condensates (BECs) consisting of two hyperfine states of the atoms coupled by a tuned adiabatic and time-varying Raman coupling, we obtain analytically the entanglement dynamics of the system with various initial states, particularly the SU(2) coherent state, for both of cases with and without the nonlinear interactions. It is shown that the effect of nonlinear interaction on the entanglement appears only in a longer time period depending on the BEC parameters.

DOI
10.1088/1009-1963/15/6/007

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Based on the exact solution of the time-dependent Schrödinger equation for two-species Bose–Einstein condensates (BECs) consisting of two hyperfine states of the atoms coupled by a tuned adiabatic and time-varying Raman coupling, we obtain analytically the entanglement dynamics of the system with various initial states, particularly the SU(2) coherent state, for both of cases with and without the nonlinear interactions. It is shown that the effect of nonlinear interaction on the entanglement appears only in a longer time period depending on the BEC parameters.
In terms of exact solutions of the time-dependent Schr\"odinger equation for an effective giant spin modeled from a coupled two-mode Bose-Einstein condensate (BEC) with adiabatic and cyclic time-varying Raman coupling between two hyperfine states of the BEC, we obtain analytic time-evolution formulas of the population imbalance and relative phase between two components with various initial states, especially the SU(2) coherent state. We find the Berry phase depending on the number parity of atoms, and particle number dependence of the collapse revival of population-imbalance oscillation. It is shown that self-trapping and phase locking can be achieved from initial SU(2) coherent states with proper parameters.
Dynamical evolution of quantum mechanical squeezing and entanglement in a two-mode Bose-Einstein condensate (TBEC) with an adiabatic, time-varying Raman coupling is studied by finding analytical expressions for these quantities. In particular, we study the entanglement between the atoms in the condensate as well as that between the two modes. The nature of the enhanced quantum correlations in TBEC is clarified by considering squeezing and entanglement both with and without the nonlinear interaction turned on; it is found that entanglement approaching maximal value can be achieved with the nonlinear interactions present. Somewhat counterintuitively, greater squeezing is found in the absence of nonlinear interactions. This is due to the collapses and revivals of the TBEC quantum state induced by the nonlinear interactions. In addition, results involving the self-trapping phase state of TBEC indicate potential for creating a dynamically stable, macroscopic entangled quantum state which is relatively robust with respect to atom number fluctuations.
We study analytically the generation of maximally entangled states (MESs) formed by a two-component Bose–Einstein condensate (BEC) trapped in an adiabatically driven single potential well. Under the condition of the linear interaction controlled by a driven field being much stronger than the effective nonlinear interaction between the components, MESs, as some particular cases of superpositions of spin coherent states (SSCS), may emerge periodically along with not only time evolution but also the equidifferent change of the linear coupling strength at a particular time.
An exactly solvable case of an interacting Hamiltonian of two bosonic modes is considered to study fundamental properties of the entanglement dynamics for coupled nonlinear oscillators. Such an interaction is of physical importance, either in a two-species Bose–Einstein condensate or in the case of two modes of electromagnetic fields interacting in Kerr media. The time-evolved state is obtained analytically for initial products of two Fock and two coherent states, and the purification times of the subsystems are determined. The possibility of dynamical generation of a quantum superposition state is discussed at such purification times. We also identify the existence of two regimes: the short time, phase spread regime where subsystem entropy rises monotonically and the self-interference regime where it oscillates and a purification phenomenon can be observed. Our results also show that the break time from the first regime to the second one becomes longer, as well as the purification and reversibility times, as the Planck constant becomes much smaller than a typical action in phase space.
We investigate the dynamics of an open Bose-Einstein condensate system consisting of two hyperfine states of the same atomic species which are coupled by a tunable Raman laser. It has already been suggested that the detuning between the laser frequency and transition frequency affect significantly the dynamics of the pure condensate. Here we show that the detuning effect is suppressed by noise and dissipation caused by the environment. The increase of coherence and purity are also displayed for specific parameters. As a verification of the lowest order approximation we derive the hierarchy of motion equations in the second-order approximation. It turns out that the former one can describe the dynamical evolution qualitatively for weak noise and dissipation and quantitatively for strong noise and dissipation.
We study the condensate dynamics of the so-called entangled Bose-Einstein condensation (EBEC), which is the ground state of a mixture of two species of pseudospin-12\frac{1}{2}21​ atoms with interspecies spin-exchange scattering in certain parameter regimes. EBEC leads to four interdependent superfluid components, each corresponding to the orbital wave function associated with a spin component of a species. The four superflows have various counter-relations, and altogether lead to a conserved total supercurrent and a conserved total spin supercurrent. In the homogeneous case, we also obtain the elementary excitations due to variations of the single-particle orbital wave functions, by exactly solving the generalized time-dependent Bogoliubov equations. There are three gapless Bogoliubov modes and one Klein-Gordon-like gapped mode. The origin of these excitations are also discussed from the perspective of spontaneous breaking of the symmetries possessed by the system.