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Old and New Concepts of Physics

Bogoliubov Transformations and Quantum Decoherence in an Atomic Bose-Einstein Condensate

Turan Birol, Özgür Esat Müstecaplıoğlu

Published Jul 3, 2007• 1 citation
Publisher

Abstract

In this brief review, we discuss quantum decoherence of an atomic Bose-Einstein condensate using Bogoliubov transformation. In particular, condensate phase is introduced and its diusion is studied. Validity of the Bogoliubov prescription is investigated and restored via the condensate phase. Role of quantum state of the condensate on the phase collapse is examined. Relation between the uctuations in the condensate particle number and the dynamics of the condensate phase is claried.

DOI
10.2478/v10005-007-0014-y

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In this brief review, we discuss quantum decoherence of an atomic Bose-Einstein condensate using Bogoliubov transformation. In particular, condensate phase is introduced and its diusion is studied. Validity of the Bogoliubov prescription is investigated and restored via the condensate phase. Role of quantum state of the condensate on the phase collapse is examined. Relation between the uctuations in the condensate particle number and the dynamics of the condensate phase is claried.
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We analyze the mean-field equilibrium states of a homogeneous Bose-Einstein condensate of boson particles in different internal states, possibly in the presence of an internal Josephson interaction, and we describe the quantum fluctuations by constructing an explicit form of the Bogoliubov transformation that characterizes the quasiparticle excitations of the system. The derivation of the Bogoliubov transformation is based on a simple geometrical picture which leads to a convenient parametrization of the transformation. Our calculations of physical properties, such as depletions and phonon velocities, as well as our discussion of stability, indicate the sense and the extent to which the internal Josephson interaction controls the many-body physics of multicomponent phase coherent matter.
The evolution equation of a weakly interacting boson system is derived. The model includes the interaction between the atoms in the condensate and the surrounding gas of noncondensed particles. The Bogoliubov transformation is introduced in a full quantum context and the scattering kernel between dressed particles and the condensate phase is obtained. The final system is expressed by the Boltzmann evolution equation for noncondensed particles coupled to the Gross-Pitaevskii equation for the condensate. We consider an out-of-equilibrium situation that induces a fast production of condensed particles. We apply our model to study the condensation dynamics of positronium atoms by evaporation.
This chapter introduces the basic physics of Bose--Einstein condensation. We first start with why there is a difference between distinguishable and indistinguishable particles in terms of the number of states that are available in a composite system. Then Bose and Einstein's argument of why one expects a high probability of occupation of the ground state is discussed. This is derived then more rigorously for the grand canonical ensemble, showing that at some critical temperature there should be a macroscopic occupation of the ground state. Next, the low-lying energy spectrum of an interacting Bose--Einstein condensate is derived, leading to the Bogoliubov dispersion. The significance of the Bogoliubov dispersion as the origin of superfluidity is then discussed, in terms of superfluditysuperfluidity. Laudau'sLandau's criterion for superfluidity is derived, by general principles of Galilean transformations of Schrodinger's equation.