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Progress of Theoretical Physics

Spectral Weight, Excitation Stability and Critical Velocity in a Bose-Condensed Gas

Shinichiro Ohtsuka, K. Sano, Susumu Kurihara

Published May 1, 2002• 0 citations

Abstract

We study the excitation spectrum of a spatially homogeneous Bose-condensed gas. Using finite-temperature field theory, we derive the dependence of the excitation spectrum on both the gaseous parameter and the temperature. In particular, we derive the asymptotic forms of the spectral weight at finite temperature. We then discuss the effects of the interaction between the excitations on the dispersion relation, in particular on its curvature for small momentum. From the gaseous parameter dependence of the curvature at zero temperature, we find that there exists a threshold for the gaseous parameter, above which the spectrum becomes stable and no damping processes occur. The excitation stability is analyzed at finite temperature, and it is found that the effect of the finite temperature is to increase the stability of the excitation. We numerically calculated the ratio of the critical velocity to the sound velocity, finding that the critical velocity is small compared to the sound velocity for specific gaseous parameters and temperatures.

DOI: 10.1143/ptp.107.903

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We study the excitation spectrum of a spatially homogeneous Bose-condensed gas. Using finite-temperature field theory, we derive the dependence of the excitation spectrum on both the gaseous parameter and the temperature. In particular, we derive the asymptotic forms of the spectral weight at finite temperature. We then discuss the effects of the interaction between the excitations on the dispersion relation, in particular on its curvature for small momentum. From the gaseous parameter dependence of the curvature at zero temperature, we find that there exists a threshold for the gaseous parameter, above which the spectrum becomes stable and no damping processes occur. The excitation stability is analyzed at finite temperature, and it is found that the effect of the finite temperature is to increase the stability of the excitation. We numerically calculated the ratio of the critical velocity to the sound velocity, finding that the critical velocity is small compared to the sound velocity for specific gaseous parameters and temperatures.

We develop a finite-temperature perturbation theory (beyond the mean field) for a Bose-condensed gas and calculate temperature-dependent damping rates and energy shifts for Bogolyubov excitations of any energy. The theory is generalized for the case of excitations in a spatially inhomogeneous (trapped) Bose-condensed gas, where we emphasize the principal importance of inhomogeneity of the condensate density profile and develop the method of calculating the self-energy functions. The use of the theory is demonstrated by calculating the damping rates and energy shifts of low-energy quasiclassical excitations, i.e., the quasiclassical excitations with energies much smaller than the mean-field interaction between particles. In this case the boundary region of the condensate plays a crucial role and the result for the damping rates and energy shifts is completely different from that in spatially homogeneous gases. We also analyze the frequency shifts and damping of sound waves in cylindrical Bose condensates and discuss the role of damping in the recent MIT experiment on the sound propagation.

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Whole excitation spectrum is calculated within the Popov approximation of the Bogoliubov theory for a cylindrical symmetric Bose-Einstein gas trapped radially by a harmonic potential. The full dispersion relation and its temperature dependence of the zero sound mode propagating along the axial direction are evaluated in a self-consistent manner. The sound velocity is shown to depend not only on the peak density, but also on the axial area density. Recent sound velocity experiment on Na atom gas is discussed in light of the present theory.

In Bose superfluids, the single-particle Green's function can be directly related to the superfluid velocity-velocity correlation function in the hydrodynamic regime. An explicit expression for the single-particle spectral density was originally written down by Hohenberg and Martin in 1965, starting from the two-fluid equations for a superfluid. We give a simple derivation of their results. Using these results, we calculate the relative weights of first and second sound modes in the single-particle spectral density as a function of temperature in a uniform Bose gas. We show that the second sound mode makes a dominant contribution to the single-particle spectrum in a relatively high-temperature region. We also discuss the possibility of experimental observation of the second sound mode in a Bose gas by photoemission spectroscopy.

Based on the dielectric formalism in the generalized random phase approximation, we generalize the description of a Bose-Einstein condensed gas to allow for a relative velocity between the superfluid and normal fluid. In this model, we determine the critical velocity dynamically as the transition point between stable and unstable dynamics. Unlike the zero temperature case, at finite temperature the relative critical velocity of a dilute Bose-Einstein gas is lower than the sound velocity. The requirement of Galilean invariance essential to obtain an invariant result necessitates the use of a gapless and conserving approximation.