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arXiv:0912.4170 · Physical Review A

Quantum coherence for Bose-Einstein condensates induced by an imaginary potential

Hongwei Xiong

Published Nov 16, 2010• 11 citations
arXivHTMLPDF

Abstract

The single-body Schr\"odinger equation with complex potentials has been studied intensively. In this work, we investigate the dynamical process for Bose-Einstein condensed gases, based on the many-body Schr\"odinger equation with complex potentials. It is shown that a weakly imaginary periodic potential may induce perfect quantum coherence between different condensates, even without considering interatomic interactions. This imaginary-potential-induced quantum coherence may be tested with present experimental techniques. We also consider the quantum coherence in the presence of both the imaginary periodic potential and interatomic interactions.

DOI
10.1103/physreva.82.053615

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With the help of a set of exact closed-form solutions to the stationary Gross—Pitaevskii (GP) equation, we calculate the collective excitation and quantum depletion of a weakly interacting Bose gas in the presence of a periodic array of quantum wells. The excitation spectrum (Bogoliubov spectrum) is obtained from the solution of the linearized time-dependent GP equation, which develops energy bands ħω j ( p ) periodic in quasi-momentum space. Moreover, we calculate the excitation strengths Z j ( p ) relative to the density operator and then the dynamic structure factor S ( p , ω). Accordingly, the analytical expressions of quantum depletion of the system are obtained. We find that the quantum depletion is enhanced when the interatomic interactions become larger and the potential is sufficiently deep. The conditions for the possible experimental realization of our scenario are also proposed.
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Abstract We consider a system ofNbosons in the limit N→∞N \rightarrow \infty N→∞ N→∞ , interacting through singular potentials. For initial data exhibiting Bose–Einstein condensation, the many-body time evolution is well approximated through a quadratic fluctuation dynamics around a cubic nonlinear Schrödinger equation of the condensate wave function. We show that these fluctuations satisfy a (multi-variate) central limit theorem.
Matter waves inside periodic potentials are well known from solid-state physics, where electrons interacting with a crystal lattice are considered. Atomic Bose-Einstein condensates inside light-induced periodic potentials (optical lattices) share many features with electrons in solids, but also with light waves in nonlinear materials and other nonlinear systems. Generally, atom-atom interactions in Bose-Einstein condensates lead to rich and interesting nonlinear effects. Furthermore, the experimental control over the parameters of the periodic potential and the condensate make it possible to enter regimes inaccessible in other systems. In this review, an introduction to the physics of ultracold bosonic atoms in optical lattices is given and an overview of the theoretical and experimental advances to date.
Atomic interaction leads to dephasing and damping of Bloch oscillations (BOs) in optical lattices, which limits observation and applications of BOs. How to obtain persistent BOs is particularly important. Here, the nonlinear Bloch dynamics of the Bose–Einstein condensate with two-body and three-body interactions in deep optical lattices is studied. The damping rate induced by interactions is obtained. The damping induced by two-body interaction plays a dominant role, while the damping induced by three-body interaction is weak. However, when the two-body and three-body interactions satisfy a threshold, long-lived coherent BOs are observed. Furthermore, the Bloch dynamics with periodical modulation of linear force is studied. The frequencies of linear force corresponding to resonance and pseudoresonance are obtained, and rich dynamical phenomena, i.e., stable and strong BOs, drifting and dispersion of wave packet, are predicted. The controllable Bloch dynamics is provided with the periodic modulation of the linear force.