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arXiv:1202.4233 · Physical Review A

Universality in rotating strongly interacting gases

Brendan C. Mulkerin, C. J. Bradly, Harry M. Quiney, A. Martin

Published May 24, 2012• 9 citations
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Abstract

We analytically determine the properties of two interacting particles in a harmonic trap subject to a rotation or a uniform synthetic magnetic field, where the spherical symmetry of the relative Hamiltonian is preserved. Thermodynamic quantities such as the entropy and energy are calculated via the second-order quantum cluster expansion. We find that in the strongly interacting regime the energy is universal; however, the entropy changes as a function of the rotation or synthetic magnetic-field strength.

DOI
10.1103/physreva.85.053636

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We analytically determine the properties of two interacting particles in a harmonic trap subject to a rotation or a uniform synthetic magnetic field, where the spherical symmetry of the relative Hamiltonian is preserved. Thermodynamic quantities such as the entropy and energy are calculated via the second-order quantum cluster expansion. We find that in the strongly interacting regime the energy is universal; however, the entropy changes as a function of the rotation or synthetic magnetic-field strength.
We analytically determine the properties of three interacting fermions in a harmonic trap subject to an external rotation. Many-body thermodynamic quantities such as the entropy and energy are calculated from the third-order quantum virial expansion. As the external rotation is increased, the regime over which the virial expansion is valid is extended to lower temperatures. By parameterizing the solutions in the rotating frame we find that the energy and entropy are universal for all rotations in the strongly interacting regime. Additionally, we find that rotation suppresses the onset of itinerant ferromagnetism in strongly interacting repulsive three-body systems.
The report analyzes all the available experimental data from three laboratories on the entropy-energy relation of two different strongly interacting trapped Fermi gases, and compare this directly with a single universal theoretical prediction. A diagrammatic approach based on functional path-integrals is used together with the local density approximation to treat the inhomogeneous trap. Below the superfiuid transition, the calculations include pairing fluctuations, which are important in the strongly interacting regime, due to the onset of molecule formation.
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.
A hard-sphere (HS) Bose gas in a trap is investigated at finite temperatures in the weakly interacting regime and its thermodynamic properties are evaluated using the static fluctuation approximation. The energies are calculated with a second-quantized many-body Hamiltonian and a harmonic oscillator wave function. The specific heat capacity, internal energy, pressure, entropy, and the Bose–Einstein occupation number of the system are determined as functions of temperature and for various values of interaction strength and number of particles. It is found that the number of particles plays a more profound role in the determination of the thermodynamic properties of the system than the HS diameter characterizing the interaction, that the critical temperature drops with the increase of the repulsion between the bosons, and that the fluctuations in the energy are much smaller than the energy itself in the weakly interacting regime.
In this paper, the temperature dependence for synthetic magnetization \bar M of a rotating Bose gas in harmonic trap and the magnetic field dependence of the critical temperature are investigated. A simple semiclassical approximation for the density of state approach is used in this study. The suggested approach simultaneously gives corrections to quantities which arise from the finite size and interatomic interaction effects. The calculated results show that the critical temperature decreases due to the increase of the synthetic magnetic field. The synthetic magnetization also exhibits a characteristic temperature dependence. It is proportional to T^3 if \bar T < \bar T_c, while it is proportional to T if \bar T > \bar T_c. The calculated results provide a solid theoretical foundation of the current experiments.
We investigate universal properties of one-dimensional multicomponent systems composed of fermions, bosons, or an arbitrary mixture, with contact interactions and subjected to an external potential. The masses and the coupling strengths between different types of particles are allowed to be different and we also take into account the presence of an arbitrary magnetic field. We show that the momentum distribution of these systems exhibits a universal ${n}_{\ensuremath{\sigma}}(k)\ensuremath{\sim}{C}_{\ensuremath{\sigma}}/{k}^{4}$ decay with ${C}_{\ensuremath{\sigma}}$ being the contact of species $\ensuremath{\sigma}$ which can be computed from the derivatives of an appropriate thermodynamic potential with respect to the scattering lengths. In the case of integrable fermionic systems, we argue that at fixed density and repulsive interactions the total contact reaches its maximum in the balanced system and monotonically decreases to zero as we increase the magnetic field. The converse effect is present in integrable bosonic systems: the contact is largest in the fully polarized state and reaches its minimum when all states are equally populated. We obtain short distance expansions for the Green's function and pair distribution function and show that the coefficients of these expansions can be expressed in terms of the density, kinetic energy, and contact. In addition, we derive universal thermodynamic identities relating the total energy of the system, pressure, trapping energy, and contact. Our results are valid at zero and finite temperature for homogeneous or trapped systems and for few-body or many-body states.