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arXiv:cond-mat/0005323

Finite Temperature Collapse of a Bose Gas with Attractive Interactions (extended version)

Erich J. Mueller, Gordon Baym

Published May 19, 2000• 0 citations
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Abstract

We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low temperature condensed regime to the high temperature classical regime. As we show, the non-condensed particles play a crucial role in determining the region of stability, even providing a mechanism for collapse in the non-condensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.

DOI
10.48550/arxiv.cond-mat/0005323

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We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low temperature condensed regime to the high temperature classical regime. As we show, the non-condensed particles play a crucial role in determining the region of stability, even providing a mechanism for collapse in the non-condensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.
We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low-temperature condensed regime to the high temperature classical regime. As we show, the noncondensed particles play a crucial role in determining the region of stability, including providing a mechanism for collapse in the noncondensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.
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We study the pairing instability and mechanical collapse of a dilute homogeneous Bose gas with an attractive interaction. The pairing phase is found to be a saddle point and is unstable against pairing fluctuations. This pairing saddle point exists above a critical temperature. Below this critical temperature, the system is totally unstable in the pairing channel. Thus the system could collapse in the pairing channel in addition to mechanical collapse. The critical temperatures of pairing instability and mechanical collapse are higher than the Bose-Einstein condensation (BEC) temperature of an ideal Bose gas with the same density. When fluctuations are taken into account, we find that the critical temperature of mechanical collapse is even higher. The difference between the collapse temperature and the BEC temperature is proportional to (n∣as∣3)2/9,(n|{a}_{s}{|}^{3}{)}^{2/9},(n∣as​∣3)2/9, where n is the density and as{a}_{s}as​ is the scattering length.
We investigate the mechanical instability toward density collapse and the transition temperature of Bose-Einstein condensation (BEC) in the weakly coupled boson-fermion many-body mixture of single-component boson and fermion gases, in the case of the repulsive boson-boson and attractive boson-fermion interactions; no fermion-fermion interaction is assumed to be originated from the Pauli exclusion because of the diluteness of the mixture. The mechanical instability occurs in the bosonic gas where the induced boson-boson attraction mediated by the fermion polarization overcomes the boson-boson repulsive interaction at low temperatures. We calculate the onset temperature of the mechanical instability and the BEC transition temperature for the interaction strength and the boson-fermion number ratio. We also discuss the relation between the mechanical instability and the BEC transition using a diagrammatic method.
The competition between particle and pair condensation in Bose liquids is studied using a mean field variational ground state that comprises both the Bogoliubov approximation for weakly interacting Bose gases and the Valatin-Butler pair state. We first consider structureless bosons, disregarding the fact that an attractive gas will necessarily collapse. We show that a pair state occurs only if the attraction is strong enough to bind two bosons together. The limit of low densities is treated exactly. At higher density, we use a separable interaction model and we show that the pairs dissociate at a critical density Nc (where their ionization gap vanishes). Past that threshold, ordinary particle condensation sets in. In order to cure collapse, we consider bosons with an internal spin structure : the interaction is binding in some states, repulsive on the average. Taking spin 1 particles as an example, we repeat the previous analysis, and we substantiate its conclusions while retaining a positive compressibility. In the pair regime the ground state is isotropic (singlet pairs). Past the dissociation threshold, an anisotropic one particle condensate appears. We show that it is linearly polarized (in an arbitrary direction), and non fragmented. We discuss briefly its physical properties, and we suggest that the transition from pair to particle condensation might be first order.
Abstract We have analytically explored both the zero temperature and the finite temperature scaling theory for the collapse of an attractively interacting 3D harmonically trapped Bose gas in a synthetic magnetic field. We have considered short ranged (contact) attractive inter-particle interactions and Hartree–Fock approximation for the same. We have separately studied the collapse of both the condensate and the thermal cloud below and above the condensation point, respectively. We have obtained an anisotropy, artificial magnetic field, and temperature dependent critical number of particles for the collapse of the condensate. We have found a dramatic change in the critical exponent (from α = 1 to 0) of the specific heat ( C v ∝ | T − T c | α ) when the thermal cloud is about to collapse with the critical number of particles ( N = N c ) just below and above the condensation point. All the results obtained by us below and around the condensation point are experimentally testable within the present-day experimental set-up for the ultracold systems in the magneto-optical traps.