Decoherence effects in Bose-Einstein condensate interferometry I. General theory

Journal Article · Tue Mar 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.10.006· OSTI ID:21579870

Dalton, B.J., E-mail: [e-mail] ^[1]

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1. ARC Centre for Quantum-Atom Optics and Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia)

Research Highlights: > Theory of dephasing, decoherence effects for Bose-Einstein condensate interferometry. > Applies to single component, two mode condensate in double potential well. > Phase space theory using Wigner, positive P representations for condensate, non-condensate fields. > Stochastic condensate, non-condensate field equations and properties of noise fields derived. > Based on mean field theory with condensate modes given by generalised Gross-Pitaevskii equations. - Abstract: The present paper outlines a basic theoretical treatment of decoherence and dephasing effects in interferometry based on single component Bose-Einstein condensates in double potential wells, where two condensate modes may be involved. Results for both two mode condensates and the simpler single mode condensate case are presented. The approach involves a hybrid phase space distribution functional method where the condensate modes are described via a truncated Wigner representation, whilst the basically unoccupied non-condensate modes are described via a positive P representation. The Hamiltonian for the system is described in terms of quantum field operators for the condensate and non-condensate modes. The functional Fokker-Planck equation for the double phase space distribution functional is derived. Equivalent Ito stochastic equations for the condensate and non-condensate fields that replace the field operators are obtained, and stochastic averages of products of these fields give the quantum correlation functions that can be used to interpret interferometry experiments. The stochastic field equations are the sum of a deterministic term obtained from the drift vector in the functional Fokker-Planck equation, and a noise field whose stochastic properties are determined from the diffusion matrix in the functional Fokker-Planck equation. The stochastic properties of the noise field terms are similar to those for Gaussian-Markov processes in that the stochastic averages of odd numbers of noise fields are zero and those for even numbers of noise field terms are the sums of products of stochastic averages associated with pairs of noise fields. However each pair is represented by an element of the diffusion matrix rather than products of the noise fields themselves, as in the case of Gaussian-Markov processes. The treatment starts from a generalised mean field theory for two condensate modes, where generalised coupled Gross-Pitaevskii equations are obtained for the modes and matrix mechanics equations are derived for the amplitudes describing possible fragmentations of the condensate between the two modes. These self-consistent sets of equations are derived via the Dirac-Frenkel variational principle. Numerical studies for interferometry experiments would involve using the solutions from the generalised mean field theory in calculations for the stochastic fields from the Ito stochastic field equations.

• OSTI ID: 21579870
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 3; Other Information: DOI: 10.1016/j.aop.2010.10.006; PII: S0003-4916(10)00183-1; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
BOSE-EINSTEIN CONDENSATION
CORRELATION FUNCTIONS
FIELD EQUATIONS
FIELD OPERATORS
FOKKER-PLANCK EQUATION
HAMILTONIANS
INTERFEROMETRY
MARKOV PROCESS
MATHEMATICAL SOLUTIONS
MATRICES
MEAN-FIELD THEORY
NUMERICAL ANALYSIS
PHASE SPACE
POTENTIALS
VARIATIONAL METHODS
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SPACE
STOCHASTIC PROCESSES