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arXiv:cond-mat/0110004 · Physical Review A

Pairing instability and mechanical collapse of a Bose gas with an attractive interaction

Gun Sang Jeon, Lan Yin, Sung Wu Rhee, D. J. Thouless

Published Jul 19, 2002• 21 citations
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Abstract

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 $(n|{a}_{s}{|}^{3}{)}^{2/9},$ where n is the density and ${a}_{s}$ is the scattering length.

DOI
10.1103/physreva.66.011603

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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 study the Evans-Imry pairing phase of dilute homogeneous bose gas with attractive interaction. We find that it is generally unstable against fluctuations in pairing. Therefore in addition to the well-known mechanical collapse, the system can also collapse due to the pairing instability. Under certain conditions the critical temperature of pairing instability can be higher than that of mechanical collapse. 1 The system of bose gas with attractive interaction has received a lot of attention recently due to the success in cooling 7 Li [1] and 85 Rb [2] systems. In these trapped systems, Bose Einstein condensation can be realized at zero temperature if the number of atoms in the condensate is below a critical value [3] due to finite size effect. In 7 Li system, the condensate experiences repetitive growth and collapse as the system is cooled down [1]. In 85 Rb system, the interaction can be tuned from being repulsive to being attractive by Feshbach resonance technique. During this process, the system loses particles until the critical number is reached [2].
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.
Abstract The BCS pairing state has been predicted to be stable in a symmetric binary Bose gas with the intraspecies repulsion and interspecies attraction. In experiments, the binary Bose gases are generally asymmetric. In this work, we study the pairing state in a dilute asymmetric binary Bose system with the intraspecies repulsions and interspecies attraction and show that it is stable in a certain region of the phase space. We find that there always exists a best density ratio for given total density and coupling constants, where the temperature width of the BCS region is maximized. At the best density ratio, both components have the almost same ideal BEC temperature. We also found that there are two critical density ratios where the BCS phase vanishes. The stability of the BCS state against pairing fluctuations is shown by expanding the Helmholtz free energy of BCS state near the normal state and proving that it is a local minimum point.
Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bose gas is studied at finite temperatures in a single-channel mean-field approach where the Hartree-Fock energy and pairing gap are determined self-consistently. In the molecular-BEC state, the atomic excitation is gapped and the molecular excitation is gapless. The binding energy of Feshbach molecules is shifted from the vacuum value by many-body effects. When the scattering length as{a}_{s}as​ of the atoms is negative, the system is subject to mechanical collapse due to negative compressibility. The system is stable in most regions with positive scattering lengths. However, at low temperatures near the resonance, the molecular-BEC state vanishes, and the coherent mixture of atomic and molecular BEC is subject to mechanical collapse.
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.