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arXiv:cond-mat/0106503

Collective Excitations of Dilute Bose-Fermi Superfluid Mixtures

Bernhard Hikaru Valtan, Munehiro Nishida, Susumu Kurihara

Published Jun 25, 2001• 1 citation
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Abstract

Using the effective action formalism, we investigate collective excitations of a dilute mixture of a Bose gas and a two component Fermi gas when both bosons and fermions have undergone superfluid transitions. We show that there is a repulsion between Bogoliubov and Anderson modes, which has important implications including disappearance of boson superfluidity. We derive an analytic expression for the long-wavelength dispersion relation of the mixture at zero temperature and give a condition for the instability. We also numerically calculate the damping rate due to boson-fermion interaction at finite temperatures and show that the two modes are stable at sufficiently low temperatures.

DOI
10.48550/arxiv.cond-mat/0106503

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We show that in dilute boson-fermion mixtures with fermions in two internal states, even when the bare fermion-fermion interaction is repulsive, the exchange of density fluctuations of the Bose condensate may lead to an effective fermion-fermion attraction, and thus to a Cooper instability in the s-wave channel. We give a simple condition to know when this is going to happen, and an analytic expression for the associated Tc{T}_{c}Tc​ in the most important limit where the phonon branch of the Bogoliubov excitation spectrum of the bosons is important. We find a Tc{T}_{c}Tc​ of the same order as for a pure Fermi gas with bare attraction.
Using an effective field theory we describe the low energy bosonic excitations in a three-dimensional ultracold mixture of spin-1 bosons and spin-1/2 fermions. We establish an interesting fermionic excitation induced generic damping of the usual undamped long-wavelength bosonic collective Goldstone modes. Two states with bosons forming either a ferromagnetic or polar superfluid are studied. The linear dispersion of the bosonic Bogoliubov excitations is preserved with a renormalized sound velocity. For the polar superfluid we find both gapless modes (density and spin) are damped, whereas in the ferromagnetic superfluid we find the density (spin) mode is (not) damped. We find that this holds for any mixture of bosons and fermions that are coupled through at least a density-density interaction. In addition, we predict the existence of the Kohn anomaly in the bosonic excitation spectrum of Bose-Fermi mixtures. We discuss the implications of our many-body interaction results for experiments on Bose-Fermi mixtures.
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.
We investigate the properties of a dilute boson-fermion mixture at zero temperature. The ground-state energy of the system is calculated to second order in the Bose-Fermi coupling constant. The Green's function formalism is applied to obtain results for the effect of Bose-Fermi interactions on the spectrum of phonon excitations, the momentum distribution, the condensate fraction, and the superfluid density of the bosonic component. A quantitative discussion of these effects is presented in the case of mixtures with attractive interspecies interaction.
The low-energy modes of a superfluid atomic Fermi gas at zero temperature are investigated. The Bose-Einstein-condensate (BEC) side of the superfluid phase is studied in detail. The atoms are assumed to be in only one internal state, so that for a sufficiently diluted gas the pairing of fermions can be considered effective in the l=1 channel only. In agreement with previous works on p-wave superfluidity in Fermi systems, it is found that the px+ipyp_x+ip_ypx​+ipy​ phase represents the lowest energy state in both the Bardeen-Cooper-Schrieffer (BCS) and BEC sides. Our calculations show that at low energy three branches of collective modes can emerge, with different species of dispersion relations: a phonon-like mode, a single-particle-like mode and a gapped mode. A comparison with the Bogoliubov excitations of the corresponding spinor Bose condensate is made. They reproduce the dispersion relations of the excitation modes of the p-wave superfluid Fermi gas to a high accuracy.