Entanglement and localization of a two-mode Bose-Einstein condensate

Journal Article · Mon Feb 15 00:00:00 EST 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2009.09.015· OSTI ID:21336091

Perez-Campos, Citlali; Gonzalez-Alonso, Jose Raul ^[1]; Castanos, Octavio ^[1]; Lopez-Pena, Ramon ^[1]

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1. Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, 04510 Mexico, DF (Mexico)

A simple second quantization model is used to describe a two-mode Bose-Einstein condensate (BEC), which can be written in terms of the generators of a SU(2) algebra with three parameters. We study the behavior of the entanglement entropy and localization of the system in the parameter space of the model. The phase transitions in the parameter space are determined by means of the coherent state formalism and the catastrophe theory, which besides let us get the best variational state that reproduces the ground state energy. This semiclassical method let us organize the energy spectrum in regions where there are crossings and anticrossings. The ground state of the two-mode BEC, depending on the values of the interaction strengths, is dominated by a single Dicke state, a spin collective coherent state, or a superposition of two spin collective coherent states. The entanglement entropy is determined for two recently proposed partitions of the two-mode BEC that are called separation by boxes and separation by modes of the atoms. The entanglement entropy in the boxes partition is strongly correlated to the properties of localization in phase space of the model, which is given by the evaluation of the second moment of the Husimi function. To compare the fitness of the trial wavefunction its overlap with the exact quantum solution is evaluated. The entanglement entropy for both partitions, the overlap and localization properties of the system get singular values along the separatrix of the two-mode BEC, which indicates the phase transitions which remain in the thermodynamical limit, in the parameter space.

• OSTI ID: 21336091
• Journal Information: Annals of Physics (New York), Vol. 325, Issue 2; Other Information: DOI: 10.1016/j.aop.2009.09.015; PII: S0003-4916(09)00190-0; Copyright (c) 2009 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
ANNIHILATION OPERATORS
BOSE-EINSTEIN CONDENSATION
COMPARATIVE EVALUATIONS
EIGENSTATES
ENERGY SPECTRA
ENTROPY
GROUND STATES
MATHEMATICAL SOLUTIONS
PHASE SPACE
PHASE TRANSFORMATIONS
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
SECOND QUANTIZATION
SEMICLASSICAL APPROXIMATION
SPIN
SU-2 GROUPS
VARIATIONAL METHODS
WAVE FUNCTIONS