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arXiv:cond-mat/0412701

Collapse of Bose component in Bose-Fermi mixture with attraction between components

S. T. Chui, Valentin Nikolaevich Ryzhov, Elena E. Tareyeva

Published Dec 27, 2004• 1 citation
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Abstract

An effective Hamiltonian for the Bose system in the mixture of ultracold atomic clouds of bosons and fermions is obtained by integrating out the Fermi degrees of freedom. An instability of the Bose system is found in the case of attractive interaction between components in good agreement with the experiment on the bosonic $^{87}$Rb and fermionic $^{40}$K mixture.

DOI
10.48550/arxiv.cond-mat/0412701

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An effective Hamiltonian for the Bose system in the mixture of ultracold atomic clouds of bosons and fermions is obtained by integrating out the Fermi degrees of freedom. An instability of the Bose system is found in the case of attractive interaction between components in good agreement with the experiment on the bosonic 87^{87}87Rb and fermionic 40^{40}40K mixture.
An effective Hamiltonian for the Bose subsystem for the mixture of ultracold atomic clouds of bosons and fermions is obtained by integrating out the fermion degrees of freedom. Using the effective Hamiltonian, a collapse of the trapped boson-fermion mixture due to the boson-fermion attractive interaction without and in the presence of the quantized vortices is studied in the framework of variational Bose wave function and Thomas-Fermi approximation. The properties of the 87Rb^{87}\mathrm{Rb}87Rb and 40K^{40}\mathrm{K}40K mixture are analyzed quantitatively. The critical number of bosons for the collapse transition is estimated without and in the presence of the vortices as a function of the fermion number. It is shown that the critical number of bosons increases in the presence of the vortex. The vortex critical velocities are calculated as functions of the numbers of bosons and fermions.
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.
An effective Hamiltonian for the Bose subsystem in the mixture of ultracold atomic clouds of bosons and fermions with mutual attractive interaction is used for investigating the collective excitation spectrum. The ground state and mode frequencies of the 87 Rb and 40 K mixture are analysed quantitatively at zero temperature. We find analytically solutions of the hydrodynamics equations in the Thomas–Fermi approximation. We discuss the relation between the onset of collapse and collective modes softening and the dependence of collective oscillations on scattering length and number of boson atoms.
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.
This work is inspired by recent experimental observations in ultracold atomic Bose-Fermi mixtures [DeSalvo et al., Nature 568 (2019)]. These experiments reveal the emergence of an attractive fermion-mediated interaction between bosons, as well as a stability-instability transition. We give the first mathematical demonstration of this transition by studying the low-energy spectrum of a many-body interspecies Hamiltonian. More precisely, we show the convergence of its eigenvalues towards those of an effective Bose Hamiltonian, which includes fermion-mediated effects. Applying this result to a model with short-range potentials, we derive a stability-instability transition in the bosonic subsystem, driven by the Bose-Fermi coupling strength ggg. For small ∣g∣|g|∣g∣, the bosons form a stable Bose-Einstein condensate with the energy per particle uniformly bounded from below. For large ∣g∣|g|∣g∣, the energy per particle is no longer uniformly bounded from below, signaling the collapse of the condensate.