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Synthetically-charged Bose gas in the fast rotating regime

H. Abdulghani, A. H. Abbas, Ali Yehia Ellithi, Th. elsherbini, Ahmed S. Hassan

Published Mar 1, 2023• 0 citations
Publisher

Abstract

Abstract We address the thermodynamic properties of a rotating Bose gas in a 3D space in the rapid rotation regime. In such a rotation regime, the 3D system has the shape of a flat pancake and shows exotic features that can never be found in the original system. Using the semi-classical approximation, the temperature dependence of the magnetization of rotating Bose gas is investigated. In the degenerate limit, the system does not show a Bose-Einstein condensation (BEC) phase transition at a definite transition temperature. However, it exhibits a large Landau diamagnetism at low temperatures, which diminishes as the speed of rotation decreases. Our findings are compared with the previous results.

DOI
10.21203/rs.3.rs-2629440/v1

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Abstract We address the thermodynamic properties of a rotating Bose gas in a 3D space in the rapid rotation regime. In such a rotation regime, the 3D system has the shape of a flat pancake and shows exotic features that can never be found in the original system. Using the semi-classical approximation, the temperature dependence of the magnetization of rotating Bose gas is investigated. In the degenerate limit, the system does not show a Bose-Einstein condensation (BEC) phase transition at a definite transition temperature. However, it exhibits a large Landau diamagnetism at low temperatures, which diminishes as the speed of rotation decreases. Our findings are compared with the previous results.
We investigate thermodynamic properties of the rotating Bose gas in a trap, taking the charged ideal Bose gas in a magnetic field as an example. The system is equivalent to a neutral gas in a synthetic magnetic field. It is indicated that the Bose—Einstein condensation temperature is irrelevant to the magnetic field, conflicting with established intuition that the critical temperature decreases with the field increasing. The specific heat and Landau diamagnetization also exhibit intriguing behaviors.
We investigate the weak Bose-Einstein condensation (BEC) scenario of a noninteracting charged Bose gas simultaneously subjected to a strong magnetic field and rigid rotation. Using standard methods of finite-temperature quantum field theory and the generalized Fock-Schwinger formalism, we derive the corresponding thermodynamic potential in the nonrelativistic and lowest Landau level approximations. An appropriate modification of the effective chemical potential yields a consistent thermodynamic description and naturally introduces a magnetorotational fugacity. Within the high-temperature approximation, rigid rotation enters the thermodynamics solely through the Tolman-Ehrenfest local temperature. We demonstrate that rigid rotation does not qualitatively modify the weak BEC scenario induced by Landau quantization. The magnetorotational fugacity remains below unity throughout the phenomenologically relevant temperature range, while the continuous evolution of the ground state population and the absence of a singularity in the specific heat provide complementary signatures of the persistence of weak BEC. We further study the thermodynamic properties of the system under conditions relevant to quark-gluon plasma and neutron-star matter. We show that rotational effects are much more pronounced in the former. Our analysis reveals a new magnetic response to rigid rotation: while magnetic fields enhance diamagnetism, rotation drives it toward paramagnetism. This behavior reflects a competition between magnetic quantization and rotational orbital motion, emphasizing the role of rotation in shaping the magnetic response of bosonic matter.
We study the Bose-Einstein condensation (BEC) of a free Bose gas under rigid rotation. The aim is to explore the impact of rotation on the thermodynamic quantities associated with BEC, including the Bose-Einstein (BE) transition temperature and condensate fraction. We begin by introducing the rotation in the Lagrangian density of free charged Klein-Gordon fields and determine the corresponding grand canonical partition function at finite temperature, chemical potential, and finite angular velocity. Assuming slow rotation, we derive analytical expressions for the pressure, energy, number, and angular momentum densities of a free Bose gas in nonrelativistic and ultrarelativistic limits in terms of the corresponding fugacities. We then focus on the phenomenon of BEC. We calculate the critical temperature of BEC transition and the condensate fraction in a slowly rotating Bose gas including only particles. Our findings indicate that the critical exponent associated with the BE transition in a rotating gas is lower compared to that in a nonrotating Bose gas. We also determine the fugacity in a rotating Bose gas in the aforementioned limits and examine how rotation affects its temperature dependence, both below and above the critical temperature. By analyzing the behavior of heat capacity at these temperatures, we demonstrate that in a nonrelativistic Bose gas, the rotation transforms the nature of the BE phase transition from a continuous to a discontinuous transition. In general, we find that a nonrelativistic Bose gas under rotation behaves similarly to a nonrotating Bose gas in ultrarelativistic limit.
In this short review we present our recent results concerning the rotation of atomic Bose-Einstein condensates confined in quadratic or quartic potentials, and give an overview of the field. We first describe the procedure used to set an atomic gas in rotation and briefly discuss the physics of condensates containing a single vortex line. We then address the regime of fast rotation in harmonic traps, where the rotation frequency is close to the trapping frequency. In this limit the Landau Level formalism is well suited to describe the system. The problem of the condensation temperature of a fast rotating gas is discussed, as well as the equilibrium shape of the cloud and the structure of the vortex lattice. Finally we review results obtained with a quadratic + quartic potential, which allows to study a regime where the rotation frequency is equal to or larger than the harmonic trapping frequency.
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.
Abstract We study the effects of a uniform and constant magnetic field on the Bose–Einstein condensation (BEC) of relativistic charged scalar bosons. The condensation of magnetized charged bosons is usually discussed in the weak or strong field regimes separately, and in each case, the properties predicted for the condensate are different. Here, we develop a low‐temperature analysis suitable for any field that allows us to observe how the gas behaves for intermediate values of the magnetic field. We find that BEC may occur at finite magnetic fields, despite the gas becoming effectively one‐dimensional due to Landau quantization of the momentum perpendicular to the magnetic axis.