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arXiv:cond-mat/0002048 · Physical Review A

Induced instability for boson-fermion mixed condensates of alkali-metal atoms due to the attractive boson-fermion interaction

T. Miyakawa, T. Suzuki, Hiroyuki Yabu

Published Aug 17, 2001• 59 citations
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Abstract

Instabilities for boson-fermion mixed condensates of trapped alkali-metal atoms due to the boson-fermion attractive interaction are studied using a variational method. A stable, metastable, and unstable region as a function of the boson-fermion interaction exists. The stability condition is obtained analytically from the asymptotic expansion of the variational total energy. The lifetime of metastable states is discussed for tunneling decay and is estimated to be very long. It suggests that, except near the instability border, metastable mixed condensate should be almost stable against tunneling decay. The critical border between metastable and unstable phases is calculated numerically and is shown to be consistent with the M\o{}lmer scaling condition.

DOI
10.1103/physreva.64.033611

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Instabilities for boson-fermion mixed condensates of trapped alkali-metal atoms due to the boson-fermion attractive interaction are studied using a variational method. A stable, metastable, and unstable region as a function of the boson-fermion interaction exists. The stability condition is obtained analytically from the asymptotic expansion of the variational total energy. The lifetime of metastable states is discussed for tunneling decay and is estimated to be very long. It suggests that, except near the instability border, metastable mixed condensate should be almost stable against tunneling decay. The critical border between metastable and unstable phases is calculated numerically and is shown to be consistent with the M\o{}lmer scaling condition.
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Static properties of a bose-fermi mixture of trapped potassium atoms are studied in terms of coupled Gross-Pitaevskii and Thomas-Fermi equations for both repulsive and attractive bose-fermi interatomic potentials. Qualitative estimates are given for solutions of the coupled equations, and the parameter regions are obtained analytically for the boson-density profile change and for the boson/fermion phase separation. Especially, the parameter ratio RintR_{int}Rint​ is found that discriminates the region of the large boson-profile change. These estimates are applied for numerical results for the potassium atoms and checked their consistency. It is suggested that a small fraction of fermions could be trapped without an external potential for the system with an attractive boson-fermion interaction.
We investigate an ultracold Bose-Fermi mixture with a Feshbach resonance between two hyperfine states of fermions. Using a functional integral method, we calculate collective modes associated with fermion pairs and bosons in the superfluid phase. We derive a stability condition of the mixtures that is valid in the entire region of the BCS-BEC crossover. This stability condition, which smoothly connects the well-known results obtained in both the BCS and Bose-Einstein Condensate (BEC) limits, shows that sufficiently strong fermion-boson (FB) interactions destabilize the mixtures. In order to investigate the consequence of this instability, we study the ground-state energy of both the uniformly mixed and the phase-separated states. We find that FB repulsion induces a phase separation, whereas FB attraction should cause a collapse of the mixture. The possibilities for the experimental observation of such instabilities are also discussed.
The collapse of a trapped boson-fermion mixture with attraction between bosons and fermions is investigated in the framework of the effective Hamiltonian for the Bose system. The properties of an 87Rb^{87}\mathrm{Rb}87Rb and 40K^{40}\mathrm{K}40K mixture are analyzed quantitatively at T=0T=0T=0. We find numerically solutions of the modified Gross-Pitaevskii equation which continuously go from the stable to the unstable branch. We discuss how the conditions for the onset of collapse are related to the macroscopic properties of the system. A comparison with the case of a Bose condensate of the atomic 7Li^{7}\mathrm{Li}7Li system is given.
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Recent experiments with trapped cooled atoms have produced evidences for Bose-Einstein condensation. Among the atoms used are 7Li^7Li7Li ones, with attractive low energy interaction. Stability of their condensate is studied, with a conclusion that for a number of atoms below the critical value there exist a metastable minimum, separated from collapse by a potential barrier. The lifetime due to tunneling is estimated: it is unlikely to happen in the present experiment. Although in experimental conditions most of the atoms are not in the condensate, we argue that they only slightly affect the stability conditions for the condensate evaluated at T=0.