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Egyptian Journal of Physics

Thermodynamic Parameters for Rotating Ultracold Atomic Fermi Gases

Ebtsam Ali Eid, Ahmed S. Hassan, Alyaa A. Mahmoud

Published Jul 22, 2025• 0 citations
Publisher

Abstract

in this paper, the thermodynamic parameters of a rotating ultracold atomic Fermi gas has been theoretically investigated. The analysis was based on a semiclassical approximation which is Sommerfeld expansion for the integral over the energy. Based on this result, several thermodynamic quantities are subsequently derived, such as the grand canonical thermodynamic potential, total energy, heat capacity and entropy. We subsequently explored how the rotation rate and interaction parameters influence various thermodynamic properties of the system. The results clearly indicate that these thermodynamic quantities are influenced by the rotation rate , while at the same time, they remain unaffected by the trap parameters across all temperature ranges. By using specific heat as an indicator, we also examined the phase transition from the gas phase to the degenerate phase. The methodology presented here can be extended to investigate the thermodynamic properties of a rotating Bose gas subjected to a combined harmonic and lattice potential.

DOI
10.21608/ejphysics.2025.405623.1114

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in this paper, the thermodynamic parameters of a rotating ultracold atomic Fermi gas has been theoretically investigated. The analysis was based on a semiclassical approximation which is Sommerfeld expansion for the integral over the energy. Based on this result, several thermodynamic quantities are subsequently derived, such as the grand canonical thermodynamic potential, total energy, heat capacity and entropy. We subsequently explored how the rotation rate and interaction parameters influence various thermodynamic properties of the system. The results clearly indicate that these thermodynamic quantities are influenced by the rotation rate , while at the same time, they remain unaffected by the trap parameters across all temperature ranges. By using specific heat as an indicator, we also examined the phase transition from the gas phase to the degenerate phase. The methodology presented here can be extended to investigate the thermodynamic properties of a rotating Bose gas subjected to a combined harmonic and lattice potential.
In a recent experiment, a Bose-Einstein condensate was trapped in an anharmonic potential that is well approximated by a harmonic and a quartic part. The condensate was set into such a fast rotation that the centrifugal force in the corotating frame overcompensates the harmonic part in the plane perpendicular to the rotation axis. Thus, the resulting trap potential becomes sombrero shaped. We present an analysis for an ideal Bose gas that is confined in such an anharmonic rotating trap within a semiclassical approximation, where we calculate the critical temperature, the condensate fraction, and the heat capacity. In particular, we examine in detail how these thermodynamical quantities depend on the rotation frequency.
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the sss-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
Thermodynamic properties of an ultracold Fermi gas in a harmonic trap are calculated within a local density approximation, using a conserving many-body formalism for the BCS to Bose-Einstein condensate crossover problem, which has been developed by Haussmann et al. [Phys. Rev. A 75, 023610 (2007)]. We focus on the unitary regime near a Feshbach resonance and determine the local density and entropy profiles and the global entropy S(E)S(E)S(E) as a function of the total energy EEE. Our results are in good agreement with both experimental data and previous analytical and numerical results for the thermodynamics of the unitary Fermi gas. The value of the Bertsch parameter at T=0T=0T=0 and the superfluid transition temperature, however, differ appreciably. We show that, well in the superfluid regime, removal of atoms near the cloud edge enables cooling far below temperatures that have been reached so far.
In this paper the thermodynamical parameters of a condensed Boson gas are calculated from the partial derivative of the grand potential. In particular, the analytical expressions for some important parameters, such as the condensed fraction, specific heat, critical temperature, effective size, and release energy are investigated. The mean effects which can be altered the ideal Bose gas, such as finite size, highly anisotropic of the external potential and interatomic interaction effects are considered simultaneously. Some new characteristics of the trapped interacting Bose gases in a highly anisotropic trap are revealed. The calculated result for the condensed fraction is compared with the ongoing Stuttgart experiment for 52Cr (Griesmaier et al., Phys. Rev. Lett. 94, 160401(2005)) directly. Good agreement between both the theoretical and experimental data are obtained.
In view of ongoing experiments to trap ultracold spin-polarized 6Li,{}^{6}\mathrm{Li},6Li, we study various properties of an interacting Fermi gas in a harmonic trap, taking the discrete nature of the unperturbed harmonic trap levels into account exactly. As 6Li{}^{6}\mathrm{Li}6Li has a rather large and negative scattering length, we focus on the effects of the attractive atom-atom interaction on several thermodynamic properties, and on the momentum and density distributions. The dependence of the chemical potential, the specific heat, and the density and momentum distributions on the number of particles in the trap is obtained. We also calculate the energy of the gas. Comparison is made with results of a semiclassical calculation and with the properties of a noninteracting gas. We find that the effect of the interactions is rather large for realistic trap frequencies. Hence it is important to include these interactions in any quantitative predictions relevant for experiments.
We report on a superfluid properties of a Bose- Einstein condensate in a rotating harmonic trap. We employ the semiclassical approximation, which is the density of state approach. Our approach provided the finite size effect. The superfluid fraction of bosons and its heat capacity at constant volume are investigated. The calculated results provide a good qualitative agreement with the measured experimental results for superfluid helium 4H. Moreover, furnish useful qualitatively theoretical results for a spectroscopic measurement of the superfluid fraction of an ultracold atomic gas [N. R. Cooper and Z. Hadzibabic, Phys. Rev. Lett. 104, 030401 (2010)]. Our results show that both The superfluid fraction of bosons and its heat capacity depend on the number of the atoms. This significant dependence should be considered when the it in situ widths are used in extracting measurable experimental quantities. Our approach can be extended to consider the rotating condensate in optical potential .