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Journal of Physics B Atomic Molecular and Optical Physics

Molecular Bose–Einstein condensates: effects of molecular rotations on transition temperature and heat capacity

C. H. Raymond Ooi, W M Liu

Published Feb 20, 2019• 2 citations
Publisher

Abstract

Abstract We study the effects of molecular rotations on the transition temperature of molecular Bose–Einstein condensates (BEC). A semi-analytical method that includes the translation and rotational degrees of freedom is introduced to compute the temperature dependence of the mean condensate number and the heat capacity. Rotating molecules show a lower transition temperature and smaller heat capacity compared to an atomic BEC. The transition temperature increases with increased rotational frequency. These findings are explained and verified by analytical expressions that we derive. The results for three-, two- and one-dimensional harmonic traps are compared, showing a higher transition temperature for molecules in a lower dimensional trap. We discuss the possibility of realizing the trapping and rotational parameters.

DOI
10.1088/1361-6455/ab08b0

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Abstract We study the effects of molecular rotations on the transition temperature of molecular Bose–Einstein condensates (BEC). A semi-analytical method that includes the translation and rotational degrees of freedom is introduced to compute the temperature dependence of the mean condensate number and the heat capacity. Rotating molecules show a lower transition temperature and smaller heat capacity compared to an atomic BEC. The transition temperature increases with increased rotational frequency. These findings are explained and verified by analytical expressions that we derive. The results for three-, two- and one-dimensional harmonic traps are compared, showing a higher transition temperature for molecules in a lower dimensional trap. We discuss the possibility of realizing the trapping and rotational parameters.
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Bose-Einstein condensation (BEC) of an ideal gas is investigated for a finite number of particles. In three dimensions, we find a transition temperature which is lower than in the thermodynamic limit. Lowering the dimension increases the transition temperature and is therefore favorable for BEC. This is in contrast to the standard result obtained in the thermodynamic limit which states that BEC is not possible in, e.g., a one-dimensional (1D) harmonic potential. As a result, 1D atom traps, such as radially tightly confining magnetic traps or optical dipole traps, are promising for studying BEC. \textcopyright{} 1996 The American Physical Society.
One of the most interesting properties of boson gases is that under special conditions, there is a possibility of a phase transition, in a critical temperature below which all bosons condensate into the ground state. This phenomenon is called Bose – Einstein Condensation (BEC). In this paper, we investigate BEC in a harmonic oscillator trap. We conclude that, in contrast to a free boson gas, there is no critical temperature for phase transition in a harmonic oscillator trap. However , by numerical and analytical calculation, it is possible to obtain a temperature at which the heat capacity is maximum. We call this the critical temperature . Possible explanation for all these features will be explained in this paper.
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.
We study the thermodynamic behavior of an ideal gas of bosons trapped in a three-dimensional anisotropic harmonic-oscillator potential. The condensate fraction as well as the specific heat is calculated using the Euler-Maclaurin approximation. For a finite number of particles there is no phase transition, but there is a well-defined temperature at which the condensation starts. We also consider condensation in lower dimensions, and, for one-dimensional systems, we discuss the dependence of the condensate fraction and heat capacity on the ensemble used.
We consider the properties of a gas of bosonic diatomic molecules in the limit when few of the molecules are dissociated. Taking into account the effects of dissociation and scattering among molecules and atoms, we calculate the dispersion relation for a molecule, and the thermal depletion of the condensate. We calculate the dependence of the Bose-Einstein-condensation (BEC) temperature of a uniform gas on the atom-atom scattering length, and conclude that, for a broad Feshbach resonance, the condensation temperature increases as the molecular state becomes less strongly bound, thereby giving rise to a maximum in the transition temperature in the BEC-BCS crossover. We also argue on general grounds that, for a gas in a harmonic trap and for a narrow Feshbach resonance, the condensation temperature will decrease with increasing scattering length.