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arXiv:1006.5805 · Journal of Physics B Atomic Molecular and Optical Physics

Effective Hamiltonian study of excitations in a boson–fermion mixture with attraction between components

A. M. Belemuk, Valentin Nikolaevich Ryzhov

Published Oct 29, 2010• 2 citations
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Abstract

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.

DOI
10.1088/0953-4075/43/22/225301

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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.
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.
We study the collective modes of a confined gaseous cloud of bosons and fermions with mutual attractive interactions at zero temperature. The cloud consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a spherical harmonic trap and the coupling between the two species is varied by increasing either the magnitude of the interspecies sss-wave scattering length or the number of bosons. The mode frequencies are obtained in the collisional regime by solving the equations of generalized hydrodynamics and are compared with the spectra calculated in the collisionless regime within a random-phase approximation. We find that, as the mixture is driven towards the collapse instability, the frequencies of the modes of fermionic origin show a blue shift which can become very significant for large numbers of bosons. Instead the modes of bosonic origin show a softening, which becomes most pronounced in the very proximity of collapse. Explicit illustrations of these trends are given for the monopolar spectra, but similar trends are found for the dipolar and quadrupolar spectra except for the surface (n=0)(n=0)(n=0) modes which are essentially unaffected by the interactions.
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.
The structure of trapped binary mixtures of bosonic and fermionic atoms at zero temperature is studied using a modified Gross-Pitaevskii equation for the bosons which self-consistently includes the mean-field interaction generated by the fermionic cloud. The density of the fermionic component is described within the Thomas-Fermi approximation. The influence of the boson-boson and the boson-fermion s-wave interaction on the density profiles and the stability of the mixture is investigated systematically. Critical particle numbers for the mean-field collapse caused either by attractive boson-boson or by attractive boson-fermion interactions and for the onset of spatial component separation are discussed. It is shown that the interplay between the boson-boson and the boson-fermion interaction generates a rich and complex phase diagram. Finally, the specific properties and prospects of the boson-fermion mixtures available in present experiments are addressed.