Dynamics of Magnetically Trapped Boson-Fermion Mixtures

Tsurumi, Takeya; Wadati, Miki

doi:10.1143/jpsj.69.97

Cited by 22 publications

(34 citation statements)

References 42 publications

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“…M is inertia mass for the collective variable R. The meanings of other parameters (F , G, Ω, R eq , R t ) can be read off in Fig. 3, and they are fixed in order that the potential V (R) reproduce the E(R) numerically obtained by (9). This approximation should be enough for the order estimation of the life time.…”

Section: Appendix A: Life Time Of Collective Tunneling Effect In Metamentioning

confidence: 99%

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

2001

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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

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Section: Appendix A: Life Time Of Collective Tunneling Effect In Metamentioning

confidence: 99%

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

2001

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“…The Pauli exclusion principle results in the extension of the fermion cloud in the transverse direction over distances comparable to the longitudinal dimension of the excitations. It has been shown recently, however, that the quasi-one-dimensional situation can nevertheless be realized in a Bose-Fermi mixture due to strong localization of the bosonic component [5,6]. With account of the effectiveness of the optical lattice in managing systems of cold atoms, their effect on the dynamics of Bose-Fermi mixtures is of obvious interest.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice

Kostov

Gerdjikov

Valchev

2007

SIGMA

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Abstract. We present two new families of stationary solutions for equations of Bose-Fermi mixtures with an elliptic function potential with modulus k. We also discuss particular cases when the quasiperiodic solutions become periodic ones. In the limit of a sinusoidal potential (k → 0) our solutions model a quasi-one dimensional quantum degenerate BoseFermi mixture trapped in optical lattice. In the limit k → 1 the solutions are expressed by hyperbolic function solutions (vector solitons). Thus we are able to obtain in an unified way quasi-periodic and periodic waves, and solitons. The precise conditions for existence of every class of solutions are derived. There are indications that such waves and localized objects may be observed in experiments with cold quantum degenerate gases.

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“…Various theoretical researches have been proposed. For instance, formation of stable strongly correlated boson-fermion pairs [2], instability of the mixture when there is an attraction between bosons and fermions [3,4], interspecies interactions induced attraction among bosons [5,6] and emergent supersymmetry (SUSY) from mixtures of cold Bose and Fermi atoms [7,8]. Recent developments in atomic experiments have made it possible to realize boson-fermion mixed gases in the laboratory.…”

Section: Introductionmentioning

confidence: 99%

One-Loop Renormalization Group Analysis of Bose–fermi Mixtures

Liu

2012

Int. J. Mod. Phys. B

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A weakly interacting boson-fermion mixture model was investigated using Wisonian renormalization group analysis.This model includes one boson-boson interaction term and one boson-fermion interaction term. The scaling dimensions of the two interaction coupling constants were calculated as 2 − D at tree level and the Gell-Mann-Low equations were derived at one-loop level. We find that in the Gell-Mann-Low equations the contributions from the fermion loops go to zero as the length scale approaches infinity. After ignoring the fermion loop contributions two fixed points were found in 3 dimensional case. One is the Gaussian fixed point and the other one is Wilson-Fisher fixed point. We find that the boson-fermion interaction decouples at the Wilson-Fisher fixed point. We also observe that under RG transformation the boson-fermion interaction coupling constant runs to negative infinity with a small negative initial value, which indicates a boson-fermion pairing instability. Furthermore, the possibility of emergent supersymmetry in this model was discussed.

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Dynamics of Magnetically Trapped Boson-Fermion Mixtures

Cited by 22 publications

References 42 publications

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

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

Exact Solutions for Equations of Bose-Fermi Mixtures in One-Dimensional Optical Lattice

One-Loop Renormalization Group Analysis of Bose–fermi Mixtures

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