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

Abstract

Instabilities for boson-fermion mixed condensates of trapped Alkali atoms due to the bosonfermion attractive interaction are studied using a variational method. Three regions are shown for their instabilities according to the boson-fermion interaction strength: stable, meta-stable and unstable ones. The stability condition is obtained analytically from the asymptotic expansion of the variational total energy. The life-time of metastable states is discussed for tunneling decay, and is estimated to be very long. It suggests that, except near the unstable border, meta-stable mixed condensate should be almost-stable against clusterizations. The critical border between meta-stable and unstable phases is calculated numerically and is shown to be consistent with the Mølmer scaling condition. [5][6][7], dynamical expansions after the removal of trapping potentials [8], and the instability changes of 7 Li-6 Li system with attractive boson-boson interaction [10]. Discoveries of theIn this paper, we study the instabilities and collapses of the polarized boson-fermion mixed condensates due to the attractive boson-fermion interaction. In BEC, such instabilities are observed in several systems: 1) the trapped meta-stable 7 Li BEC (observed experimentally [11]) equilibrated between the attractive boson-boson interaction and the kinetic pressure due to the finite confinement [12], 2) two-component uniform BEC (from bosons 1 and 2), whose stability condition is given by g 11 g 22 > g 2 12 (g ij : the coupling constant between bosons i and j). In the latter case, the stability condition depends only on the interaction strength, but the condition for the case 1) has also the particle number dependence [12].Let us consider the case of the trapped boson-fermion mixed condensate. In the present paper, we assume T = 0 and a spherical harmonic-oscillator for the trapping potential; extension to the deformed potential is straightforward. Using the Thomas-Fermi approximation for the fermion degree of freedom (appropriate for large N f condensate), the total energy of the system becomes a functional of the boson order-parameter Φ( r) and the fermion density distribution n f ( r): (1), the fermion-fermion interaction has been neglected; the elastic fermion-fermion s-wave scattering for a polarized gas is absent because of the Pauli blocking effects and the p-wave scattering is suppressed below 100 µK [14]. Evaluating the total energy with the variational method, we take the Gaussian ansatz for the boson order-parameter:where x = r/ξ is a radial distance scaled by the harmonic-oscillator length ξ = (h/mω) 1/2 , and N b = d 3 x|Φ(x; R)| 2 is total boson number. The variational parameter R in (2) corresponds to the root-mean-square (rms) radius of the boson density distribution. This kind of variational functions have also been used in the instability investigations of 1

Collisional oscillations of trapped boson-fermion mixtures in the approach to the collapse instability

“…Collapse has been observed experimentally in the 87 Rb-40 K mixture as a sudden disappearance of the fermion cloud when the number of bosons, and hence the coupling between the two species, is increased [18]. The equilibrium properties and the phase diagram of a mixture with attractive interactions have been investigated by several authors [19][20][21][22], finding good agreement between the experimental data and a mean-field theoretical description [23,24].…”

Collisionless and hydrodynamic excitations of trapped boson-fermion mixtures

“…The latter system is in particular interesting since it serves as one typical example in which the intermingled particles obey different statistics. Up to date the static property [10,11,12,13], the phase diagram and phase separation [14,15,16], stability conditions [17,18] and collective excitations [19,20,21,22,23,24,25,26] of trapped boson-fermion mixtures have been theoretically investigated. In a recent experiment, the collapse of a degenerated Fermi gas caused by the strong attractive interaction with a Bose-Einstein condensate has been observed in an atomic mixture of 40 K− 87 Rb [27], and measurements of collective excitations might be available soon also in such systems.…”

Comprehensive classification for Bose–Fermi mixtures

“…Thus, if the parameters do not allow the continuous configurations 4.1 or 4.2, there is no stable configuration possible and the system collapses, which happens exactly if the first equation in figure 9 is violated. This condition has already been obtained by [21,23] in order to determine the unstable regime in parameter space.…”