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arXiv:cond-mat/0004006

Moment of inertia of a trapped superfluid gas of Fermions

M. Farine, Peter Schuck, X. Viñas

Published Apr 1, 2000• 0 citations
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Abstract

The moment of inertia Q of a trapped superfluid gas of atomic Fermions (6Li) is calculated as a function of the temperature. At zero temperature the moment of inertia takes on the irrotational flow value. Only for T very close to Tc rigid rotation is attained. It is proposed that future measurements of the rotational energy will unambiguously reveal whether the system is in a superfluid state or not.

DOI
10.48550/arxiv.cond-mat/0004006

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The moment of inertia Q of a trapped superfluid gas of atomic Fermions (6Li) is calculated as a function of the temperature. At zero temperature the moment of inertia takes on the irrotational flow value. Only for T very close to Tc rigid rotation is attained. It is proposed that future measurements of the rotational energy will unambiguously reveal whether the system is in a superfluid state or not.
The moment of inertia \ensuremath{\Theta} of a trapped superfluid gas of atomic fermions (6Li){(}^{6}\mathrm{Li})(6Li) is calculated as a function of the temperature. At zero temperature the moment of inertia takes on the irrotational-flow value. Only for T very close to Tc{T}_{c}Tc​ is rigid rotation attained. It is proposed that future measurements of the rotational energy will unambiguously reveal whether the system is in a superfluid state or not.
Abstract This chapter is devoted to discussing some key superfluid properties exhibited by dilute Bose gases confined in external traps. Key issues concern the behaviour of the critical velocity and the applicability of Landau’s criterion for superfluidity, the moment of inertia and its quenching caused by the irrotationality of the superfluid motion, the scissors mode, and the expansion of a rotating superfluid cloud. Rotational effects at high angular velocities, with the appearance of quantized vortices and vortex lattices, are also considered. The chapter also discusses the consequences for vortices on the collective oscillations of the trapped gas, the stability and the precession of vortex lines, and the nature of the superfluid flow in toroidal traps.
The effects of possible superfluidity on the cranking moment of a large many-fermion system moving under periodic boundary conditions are investigated within the framework of the theory of superconductivity recently formulated by Bogolyubov. The Hamiltonian is initially subjected to Bogolyubov's general unitary transformation. The collective excitations of the fermions are then considered in the usual pair approximation; the appropriate cranking terms are linear in the boson pair operators. On performing a unitary transformation which transforms away these linear terms, one obtains an expression for the moment of inertia of the system which includes both the effects of possible superfluidity and collective excitation. This expression, by virtue of its being stationary with respect to arbitrary variations in the amplitude associated with the latter unitary transformation, is then utilized as a variational principle for the moment of inertia. For the normal state, the result previously obtained by the author, that the moment of inertia has the rigid value, is rederived in more compact form. For the superfluid state, one finds that collective excitations effect a marked increase in the superfluid moment at intermediate coupling strengths although the resulting moment is still quite small compared to the rigid value. In contrast to the normal state case, where particle-hole pairs play a major role, this increase is almost entirely due to excitations consisting of particle-pairs or hole-pairs. The precise magnitude of the apparent resonance in the moment produced by the ddd-wave part of the cranking interaction is dependent to some extent on the features of the particle-particle potential which leads to the superfluid state. Variational expressions for the moment are exhibited for both Yukawa and delta-function shell potentials. These results are identical in charged and neutral Fermi systems. A calculation of the cranking moment at finite temperatures is presented in an Appendix along with an interpretation of it in terms of Bardeen's two-fluid model of superconductivity.
Abstract In this work, the normal density ρ n and moment of inertia of a moving superfluid are investigated. We find that, even at zero temperature, there exists a finite normal density for the moving superfluid. When the velocity of superfluid reaches sound velocity, the normal density becomes total mass density ρ , which indicates that the system losses superfluidity. At the same time, the Landau’s critical velocity also becomes zero. The existence of the non-zero normal density is attributed to the coupling between the motion of superflow and density fluctuation in transverse directions. With Josephson relation, the superfluid density ρ s is also calculated and the identity ρ s + ρ n = ρ holds. Further more, we find that the finite normal density also results in a quantized moment of inertia in a moving superfluid trapped by a ring. The normal density and moment of inertia at zero temperature could be verified experimentally by measuring the angular momentum of a moving superfluid in a ring trap.