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arXiv:cond-mat/0606654 · Laser Physics Letters

Nonequilibrium Bose systems and nonground-state Bose-Einstein condensates

Vyacheslav I. Yukalov

Published Apr 10, 2006• 31 citations
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Abstract

The theory of resonant generation of nonground-state Bose-Einstein condensates is extended to Bose-condensed systems at finite temperature. The generalization is based on the notion of representative statistical ensembles for Bose systems with broken global gauge symmetry. Self-consistent equations are derived describing an arbitrary nonequilibrium nonuniform Bose system. The notion of finite-temperature topological coherent modes, coexisting with a cloud of noncondensed atoms, is introduced. It is shown that resonant generation of these modes is feasible for a gas of trapped Bose atoms at finite temperature.

DOI
10.1002/lapl.200610023

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The theory of resonant generation of nonground-state Bose-Einstein condensates is extended to Bose-condensed systems at finite temperature. The generalization is based on the notion of representative statistical ensembles for Bose systems with broken global gauge symmetry. Self-consistent equations are derived describing an arbitrary nonequilibrium nonuniform Bose system. The notion of finite-temperature topological coherent modes, coexisting with a cloud of noncondensed atoms, is introduced. It is shown that resonant generation of these modes is feasible for a gas of trapped Bose atoms at finite temperature.
Trapped atoms cooled down to temperatures below the Bose-Einstein condensation temperature are considered. Stationary solutions to the Gross-Pitaevskii equation (GPE) define the topological coherent modes, representing nonground-state Bose-Einstein condensates. These modes can be generated by means of alternating fields whose frequencies are in resonance with the transition frequencies between two collective energy levels corresponding to two different topological modes. The theory of resonant generation of these modes is generalized in several aspects: Multiple-mode formation is described; a shape-conservation criterion is derived, imposing restrictions on the admissible spatial dependence of resonant fields; evolution equations for the case of three coherent modes are investigated; the complete stability analysis is accomplished; the effects of harmonic generation and parametric conversion for the topological coherent modes are predicted. All considerations are realized both by employing approximate analytical methods as well as by numerically solving the GPE. Numerical solutions confirm all conclusions following from analytical methods.
The review is devoted to the elucidation of the basic problems arising in the theoretical investigation of systems with Bose-Einstein condensate. Understanding these challenging problems is necessary for the correct description of Bose-condensed systems. The principal problems considered in the review are as follows: (i) What is the relation between Bose-Einstein condensation and global gauge symmetry breaking? (ii) How to resolve the Hohenberg-Martin dilemma of conserving versus gapless theories? (iii) How to describe Bose-condensed systems in strong spatially random potentials? (iv) Whether thermodynamically anomalous fluctuations in Bose systems are admissible? (v) How to create nonground-state condensates? Detailed answers to these questions are given in the review. As examples of nonequilibrium condensates, three cases are described: coherent modes, turbulent superfluids, and heterophase fluids.
The resonant formation of nonlinear coherent modes in trapped Bose-Einstein condensates is studied. These modes represent nonground-state Bose condensates. The methods of describing the spectrum of the nonlinear modes are discussed. The latter can be created by modulating the trapping potential with a frequency tuned close to the transition frequency between the two chosen modes. The requirement that the transition amplitudes be smaller than the transition frequency implies a constraint on the number of particles that can be transferred to an excited mode. The resonant Bose condensate serves as a collective analog of a single resonant atom. Such a condensate, displaying the coherent resonance, possesses several interesting features, among which are: mode locking, critical dynamics, interference patterns, interference current, atomic squeezing, and multiparticle entanglement.
The review is devoted to the elucidation of the basic problems arising in the theoretical investigation of systems with Bose-Einstein condensate. Understanding these challenging problems is necessary for the correct description of Bose-condensed systems. The principal problems considered in the review are as follows: (i) What is the relation between Bose-Einstein condensation and global gauge symmetry breaking? (ii) How to resolve the Hohenberg-Martin dilemma of conserving versus gapless theories? (iii) How to describe Bose-condensed systems in strong spatially random potentials? (iv) Whether thermodynamically anomalous fluctuations in Bose systems are admissible? (v) How to create nonground-statc condensates? Detailed answers to these questions are given in the review. As examples of nonequilibrium condensates, three cases are described: coherent modes, turbulent superfluids, and heterophase fluids.
Abstract The review presents the methods of generation of nonlinear coherent excitations in strongly nonequilibrium Bose-condensed systems of trapped atoms and their properties. Non-ground-state Bose–Einstein condensates are represented by nonlinear coherent modes. The principal difference of nonlinear coherent modes from linear collective excitations is emphasized. Methods of generating nonlinear modes and the properties of the latter are described. Matter-wave interferometry with coherent modes is discussed, including such effects as interference patterns, internal Josephson current, Rabi oscillations, Ramsey fringes, harmonic generation, and parametric conversion. Dynamic transition between mode-locked and mode-unlocked regimes is shown to be analogous to a phase transition. Atomic squeezing and entanglement in a lattice of condensed atomic clouds with coherent modes are considered. Nonequilibrium states of trapped Bose-condensed systems, starting from weakly nonequilibrium state, vortex state, vortex turbulence, droplet or grain turbulence, and wave turbulence, are classified by means of effective Fresnel and Mach numbers. The inverse Kibble–Zurek scenario is described. A method for the formation of directed beams from atom lasers is reported.