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CONDENSATE OSCILLATIONS, KINETIC EQUATIONS AND TWO-FLUID HYDRODYNAMICS IN A BOSE GAS

Allan Griffin

Published Jan 1, 2000• 1 citation
OpenAlex

Abstract

Trapped Bose-condensed atomic gases 1,2 are remarkable because, in spite of the fact that these are very dilute systems, they exhibit robust coherent dynamic behaviour when perturbed. These quantum “wisps of matter ” are a new phase of highly coherent matter. While binary collisions are very infrequent,

Related papers

CONDENSATE OSCILLATIONS, KINETIC EQUATIONS AND TWO-FLUID HYDRODYNAMICS IN A BOSE GAS

Allan Griffin

•Dec 1, 2000•0 citations

Condensate dynamics at T = 0

Allan Griffin, Tetsuro Nikuni, E. Zaremba

Trapped Bose-condensed atomic gases are remarkable because, in spite of the fact that these are very dilute systems, they exhibit robust coherent dynamic behaviour when perturbed. These quantum “wisps of matter” are a new phase of highly coherent matter. While binary collisions are very infrequent, the large coherent mean field associated with the Bose condensate ensures that interactions play a crucial role in determining the collective response of these trapped superfluid gases. In our discussion of the theory of collective oscillations of atomic condensates, the macroscopic Bose wavefunction Φ( r , t ) plays a central role. This wavefunction is the BEC order parameter. As discussed in Chapter 1, the initial attempts at defining this order parameter began with the pioneering work of London (1938a), were further developed by Bogoliubov (1947) and finally extended to deal with any Bose superfluid using the general quantum field theoretic formalism developed by Beliaev (1958a). Almost all this early theoretical work was limited to T = 0 where, in a dilute weakly interacting Bose gas, all the atoms are in the condensate. The first extension of these ideas to nonuniform Bose condensates was by Pitaevskii (1961) and, independently, by Gross (1961), which led to the now famous Gross–Pitaevskii (GP) equation of motion for Φ( r , t ). Before the discovery of BEC in trapped gases, the time-dependent GP equation was mainly used to study vortices in Bose superfluids, which involve a spatially nonuniform ground state. Apart from this application, the GP equation was largely unknown. The situation changed overnight in 1995 with the creation of trapped nonuniform Bose condensates in atomic gases.

Cambridge University Press eBooks•Feb 19, 2009•0 citations

Two-Fluid Hydrodynamics in Trapped Bose Gases and in Superfluid Helium

Allan Griffin, Tetsuro Nikuni

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Coherent Versus Incoherent Dynamics During Bose-Einstein Condensation in Atomic Gases

Henk T. C. Stoof

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Bose-Condensed Gases at Finite Temperatures

Allan Griffin, Tetsuro Nikuni, E. Zaremba

The discovery of Bose Einstein condensation (BEC) in trapped ultracold atomic gases in 1995 has led to an explosion of theoretical and experimental research on the properties of Bose-condensed dilute gases. The first treatment of BEC at finite temperatures, this book presents a thorough account of the theory of two-component dynamics and nonequilibrium behaviour in superfluid Bose gases. It uses a simplified microscopic model to give a clear, explicit account of collective modes in both the collisionless and collision-dominated regions. Major topics such as kinetic equations, local equilibrium and two-fluid hydrodynamics are introduced at an elementary level. Explicit predictions are worked out and linked to experiments. Providing a platform for future experimental and theoretical studies on the finite temperature dynamics of trapped Bose gases, this book is ideal for researchers and graduate students in ultracold atom physics, atomic, molecular and optical physics and condensed matter physics.

Cambridge University Press eBooks•Feb 19, 2009•351 citations

BEC and the New World of Coherent Matter Waves

Allan Griffin

This paper is based on three tutorial lectures given at the CRM Summer School in Banff, Alberta, June 27-July 10, 1999 on "Theoretical Physics at the End of the Twentieth Century". They will be published by Springer-Verlag. Lecture I gives a quick overview of recent studies of BEC in trapped atomic gases and reviews some properties of a trapped non-interacting Bose gas. Lecture II mainly discusses the collective modes of a pure condensate, based on the T=0 GP equation of motion. The Stringari quantum hydrodynamic theory is introduced. Lecture III discusses the coupled dynamics of the condensate and non-condensate at finite temperatures. A recent derivation of the two-fluid hydrodynamic equations is sketched. This theory predicts a new relaxational mode associated with the fact that the condensate and non-condensate may not be in diffusive equilibrium.

arXiv:cond-mat/9911419•Nov 25, 1999•2 citations
Trapped Bose-condensed atomic gases are remarkable because, in spite of the fact that these are very dilute systems, they exhibit robust coherent dynamic behaviour when perturbed. These quantum “wisps of matter” are a new phase of highly coherent matter. While binary collisions are very infrequent, the large coherent mean field associated with the Bose condensate ensures that interactions play a crucial role in determining the collective response of these trapped superfluid gases. In our discussion of the theory of collective oscillations of atomic condensates, the macroscopic Bose wavefunction Φ( r , t ) plays a central role. This wavefunction is the BEC order parameter. As discussed in Chapter 1, the initial attempts at defining this order parameter began with the pioneering work of London (1938a), were further developed by Bogoliubov (1947) and finally extended to deal with any Bose superfluid using the general quantum field theoretic formalism developed by Beliaev (1958a). Almost all this early theoretical work was limited to T = 0 where, in a dilute weakly interacting Bose gas, all the atoms are in the condensate. The first extension of these ideas to nonuniform Bose condensates was by Pitaevskii (1961) and, independently, by Gross (1961), which led to the now famous Gross–Pitaevskii (GP) equation of motion for Φ( r , t ). Before the discovery of BEC in trapped gases, the time-dependent GP equation was mainly used to study vortices in Bose superfluids, which involve a spatially nonuniform ground state. Apart from this application, the GP equation was largely unknown. The situation changed overnight in 1995 with the creation of trapped nonuniform Bose condensates in atomic gases.
The discovery of Bose Einstein condensation (BEC) in trapped ultracold atomic gases in 1995 has led to an explosion of theoretical and experimental research on the properties of Bose-condensed dilute gases. The first treatment of BEC at finite temperatures, this book presents a thorough account of the theory of two-component dynamics and nonequilibrium behaviour in superfluid Bose gases. It uses a simplified microscopic model to give a clear, explicit account of collective modes in both the collisionless and collision-dominated regions. Major topics such as kinetic equations, local equilibrium and two-fluid hydrodynamics are introduced at an elementary level. Explicit predictions are worked out and linked to experiments. Providing a platform for future experimental and theoretical studies on the finite temperature dynamics of trapped Bose gases, this book is ideal for researchers and graduate students in ultracold atom physics, atomic, molecular and optical physics and condensed matter physics.
This paper is based on three tutorial lectures given at the CRM Summer School in Banff, Alberta, June 27-July 10, 1999 on "Theoretical Physics at the End of the Twentieth Century". They will be published by Springer-Verlag. Lecture I gives a quick overview of recent studies of BEC in trapped atomic gases and reviews some properties of a trapped non-interacting Bose gas. Lecture II mainly discusses the collective modes of a pure condensate, based on the T=0 GP equation of motion. The Stringari quantum hydrodynamic theory is introduced. Lecture III discusses the coupled dynamics of the condensate and non-condensate at finite temperatures. A recent derivation of the two-fluid hydrodynamic equations is sketched. This theory predicts a new relaxational mode associated with the fact that the condensate and non-condensate may not be in diffusive equilibrium.