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Journal of Physics B Atomic Molecular and Optical Physics

Dipole oscillations of a Bose–Fermi mixture: effect of unequal masses of Bose and Fermi particles

Arup Banerjee

Published Nov 18, 2009• 9 citations
Publisher

Abstract

We investigate the effect of unequal masses of Bose and Fermi particles on the dipole collective oscillations of degenerate boson–fermion mixtures. In particular, we study the character and the frequency of the dipole mode by using the variational-sum-rule approach. We find that there exists a critical value of the ratio of boson–fermion mass below and above which the character and the frequency of the dipole mode are significantly different.

DOI
10.1088/0953-4075/42/23/235301

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We investigate the effect of unequal masses of Bose and Fermi particles on the dipole collective oscillations of degenerate boson–fermion mixtures. In particular, we study the character and the frequency of the dipole mode by using the variational-sum-rule approach. We find that there exists a critical value of the ratio of boson–fermion mass below and above which the character and the frequency of the dipole mode are significantly different.
We investigate the effect of unequal masses of the Bose and Fermi particles on the collective oscillations of the degenerate boson-fermion mixtures. In particular, we consider the monopole and the quadrupole modes of the oscillations and study their characters and the frequencies by using variational-sum-rule approach. We find that for both the modes there exist critical values of the ratio of boson-fermion masses below and above which the character and frequency of the respective modes are significantly different.
We study the dipole collective oscillations in Bose-Fermi mixtures in a dynamical time-dependent approach, which is formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation. While the Bose gas oscillates monotonously, the fermion oscillation shows a beat and damping. We find big differences in behaviors of fermion oscillation between the time-dependent approach and usual approaches such as the sum-rule approach. When the amplitude is not minimal, the dipole oscillation of the Fermi gas cannot be described with a simple center-of-mass motion.
We present a study for the collective dipole oscillations of a mixture of Bose and Fermi superfluids in the crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid to a molecular Bose–Einstein condensate (BEC) in the ENS experimental setup (Ferrier-Barbut et al 2014 Science 345 1035). The dynamics of the double superfluidity is described by coupled time-dependent order-parameter equations, which are Gross–Pitaevskii equations for the Bose superfluid, coupled to the order-parameter equation including the equation of state fitting from the experimental data for the Fermi superfluid in the BCS–BEC crossover. The numerical simulations show that due to the boson–fermion interaction, the frequencies of the dipole oscillations of the Bose and Fermi superfluids are both downshifted and the frequency shifts increase monotonically from the BCS side to BEC side, which are in agreement with the experiment. We further study the dependencies of the frequency shifts on the oscillation amplitudes and the nonlinear effects, in which the Bose and Fermi superfliuds show different features. The frequency shifts of the Bose superfluid increase linearly as the oscillation amplitudes increase, while the frequency shifts of the Fermi superfluid show a quadratical increase. It is found that the intrinsic dipole oscillations of the Bose (Fermi) superfluid can be triggered by only boosting the Fermi (Bose) superfluid.
In this paper, we investigate the quantum coherence of Bose–Fermi mixtures of ultracold dipolar particles trapped in a three-site Bose–Fermi–Hubbard model. We show that the interplay between the boson–boson on-site interaction, boson–fermion on-site interaction, and boson–fermion inter-site dipole–dipole interaction (DDI) results in interesting coherence characters. When boson–boson on-site interaction is present, the resonance character of coherence against both boson–fermion DDI and boson–fermion on-site interaction emerges, the coherence of the system can be enhanced at certain values of boson–fermion on-site interaction and boson–fermion DDI. DDI of fermion–fermion affects the coherence weak and the phase coherence decreases monotonically for all the values of fermion–fermion DDI. The obtained coherent characters are further confirmed within the variational analyzing of the ground state energy.
We consider a homogeneous Bose-Fermi mixture, with the boson-fermion interaction tuned by a Fano-Feshbach resonance, in the presence of mass and density imbalance between the two species. By using many-body diagrammatic methods, we first study the finite-temperature phase diagram for the specific case of the mass-imbalanced mixture 87{}^{87}87Rb-40{}^{40}40K for different values of the density imbalance. We then analyze the quantum phase transition associated with the disappearance at zero temperature of the boson condensate above a critical boson-fermion coupling. We find a pronounced dependence of the critical coupling on the mass ratio and a weak dependence on the density imbalance. For a vanishingly small boson density, we derive, within our approximation, the asymptotic expressions for the critical coupling in the limits of small and large mass ratios. These expressions are relevant also for the polaron-molecule transition in a Fermi mixture at small and large mass ratios. The analysis of the momentum distribution functions at sufficiently large density imbalances shows an interesting effect in the bosonic momentum distribution due to the simultaneous presence of composite fermions and unpaired fermions.