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First and second global sound velocity of a Bose gas across the transition to Bose-Einstein condensation

A. R. Fritsch, P. E. S. Tavares, Franklin J. Vivanco, Gustavo Deczka Telles, Vanderlei Salvador Bagnato, E. A. L. Henn

Published Jun 21, 2016• 1 citation
OpenAlex

Abstract

We present an alternative approach for determining the sound modes in atomic Bose-Einstein condensates, based on thermodynamic global variables. The total number of trapped atoms was carefully studied as a function of temperature across the phase transition, at constant volume. It allowed us to evaluate the first and second sound independently resulting in consistent values from the quantum to classical regime, in good agreement with previous results found in the literature. We also provide some insight on the dominant mode, either thermal or superfluid, on each sound velocity depending on the temperature range

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We present an alternative approach for determining the sound modes in atomic Bose-Einstein condensates, based on thermodynamic global variables. The total number of trapped atoms was carefully studied as a function of temperature across the phase transition, at constant volume. It allowed us to evaluate the first and second sound independently resulting in consistent values from the quantum to classical regime, in good agreement with previous results found in the literature. We also provide some insight on the dominant mode, either thermal or superfluid, on each sound velocity depending on the temperature range
Abstract We present an alternative method for determining the sound velocity in atomic Bose–Einstein condensates, based on thermodynamic global variables. The total number of trapped atoms was as a function of temperature carefully studied across the phase transition, at constant volume. It allowed us to evaluate the sound velocity resulting in consistent values from the quantum to classical regime, in good agreement with previous results found in literature. We also provide some insight about the dominant sound mode (thermal or superfluid) across a wide temperature range.
In this thesis we present some studies that were done in a trapped 87Rb Bose-Einstein condensate using the thermodynamic global variables. We have measured the global sound velocity by studying the variation of the total number of trapped atoms as a function of temperature. This method allowed us to determine the contribution of thermal and BEC components at each temperature. In order to study the sound velocity in each component, we treated both fluids as they were completely independent and we found great similarity with a published work. In addition, we analyze theoretically the validity of the global variables by comparing this approach with other methods. The specific heat for an ideal gas was evaluated using the global variables and by using the usual statistical approach found in textbooks. After finding the same result for both methods, we used the simplicity to implement the interaction in the global approach, to study the variation in the specific heat when the interactions are taken into account. The last comparison was done between global variables and the local density approximation. We have obtained that, for the isothermal compressibility and a equation of state, both methods provide equivalent results.
We determine the temperature (T)(T)(T) dependence of first- and second-sound-like mode frequencies for trapped Fermi gases undergoing the BCS to Bose--Einstein condensation (BEC) crossover. Our results are based on numerical solution of the two-fluid equations in conjunction with a microscopic calculation of thermodynamical variables. As in experiment and at unitarity, we show that the lowest radial breathing mode is TTT independent. At finite TTT, higher-order breathing modes strongly mix with second sound. Their complex TTT dependence should provide an alternative way of measuring the transition temperature Tc{T}_{c}Tc​.
First and second sound speeds are calculated for a uniform superfluid gas of Fermi atoms as a function of temperature, density, and interaction strength. The second sound speed is of particular interest as it is a clear signal of a superfluid component and it determines the critical temperature. The sound modes and their dependence on density, scattering length, and temperature are calculated in the BCS, molecular Bose-Einstein condensate (BEC), and unitarity limits and a smooth crossover is extrapolated. It is found that first and second sounds undergo avoided crossing on the BEC side due to mixing. Consequently, they are detectable at crossover both as density and thermal waves in traps.
Abstract We study the propagation of the two sound modes in two-dimensional Bose gases across the Berezinksii–Kosterlitz–Thouless transition using classical-field dynamics, which is motivated by recent measurements of Christodoulou et al (2021 Nature 594 191). Based on the dynamic structure factor (DSF), we identify the two sound modes as the Bogoliubov (B) and the non-Bogoliubov (NB) sound mode below the transition, and as the diffusive and the normal sound mode above the transition. The NB sound mode velocity is higher than the B sound mode velocity, which we refer to as the weak-coupling regime of the sound modes. We excite the sound modes by driving the system as in the experiment and by perturbing the density with a step-pulse perturbation, as a secondary comparison. The driven response depends on the driving strength and results in higher velocities for the B sound mode at high temperatures near the transition, compared to the sound results of the DSF and step-pulse excitation. We show that the higher mode velocity has a weak temperature dependence across the transition, which is consistent with the experimental observation.
We apply the global thermodynamic variables approach to experimentally determine the isothermal compressibility parameter ${\ensuremath{\kappa}}_{T}$ of a trapped Bose gas across the phase transition. We demonstrate the behavior of ${\ensuremath{\kappa}}_{T}$ around the critical pressure, revealing the second-order nature of the phase transition. Compressibility is the most important susceptibility to characterize the system. The use of global variables shows advantages with respect to the usual local density approximation method and can be applied to a broad range of situations.