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Pairing Instability of Bose Gas with Attractive Interaction

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

Published Sep 28, 2001• 0 citations
OpenAlex

Abstract

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].

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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 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.
The point of instability of a Bose-Einstein condensate (BEC) due to attractive interactions was studied. Stable 85Rb BECs were created and then caused to collapse by slowly changing the atom-atom interaction from repulsive to attractive using a Feshbach resonance. At a critical value, an abrupt transition was observed in which atoms were ejected from the condensate. By measuring the onset of this transition as a function of number and attractive interaction strength, we determined the stability condition to be N(absolute value of a) / a(ho) = 0.459+/-0.012+/-0.054, slightly lower than the predicted value of 0.574.
Summary form only given. Bose-Einstein condensation (BEC) of trapped atomic vapor has been realized in several atomic species. The static and dynamical properties of BEC crucially depend on the sign of the interatomic interaction. When the interaction is attractive, BEC in a spatially uniform 3D system is unstable to collapse into a denser phase. In a spatially confined system, however, the zero-point energy serves as a kinetic obstacle against collapse, allowing metastable BEC to be formed if the number of BEC atoms is below a certain critical number. Above the critical number of atoms, BEC collapses. The BEC with attractive interactions, therefore, has been restricted to a small number of atoms (/spl sim/1000) and the number has not been controllable.
Summary form only given. Quantum theory predicts that Bose-Einstein condensation (BEC) of a spatially homogeneous gas with attractive interactions is precluded by a conventional phase transition into either a liquid or solid. When confined to a trap, however, such a condensate can form provided that its occupation number No does not exceed a limiting value. The stability limit is determined by a balance between self-attraction and a repulsion arising from position-momentum uncertainty under conditions of spatial confinement. Near the stability limit, self-attraction can overwhelm the repulsion, causing the condensate to collapse. Growth of the condensate, therefore, is punctuated by intermittent collapses, which are triggered either by macroscopic quantum tunneling or thermal fluctuation. The data presented here are the first direct observations of the growth and collapse of Bose Einstein condensates with attractive interactions.
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.
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.