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.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.

arXiv:cond-mat/0203192Physical Review AJul 29, 2002118 citations

BOSON-FERMION INTERACTIONS

V. A. Yatsun

Jan 1, 19920 citations

Vortex state in a Bose-Fermi mixture with attraction between bosons and fermions

A. M. Belemuk, N. M. Chtchelkatchev, Valentin Nikolaevich Ryzhov +1 more

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 $^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}$ 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.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 $^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}$ 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.

arXiv:cond-mat/0512344Physical Review AMay 11, 200610 citations

Fermion to boson mapping

Asis Basu, Jayprokas Chakrabarti

arXiv:math-ph/0503065Annals of PhysicsMay 25, 20050 citations

π Berry phase and topological excitation in interacting boson-fermion mixtures

Huaiming Guo

The topological property of a boson-fermion mixture in a one-dimensional optical superlattice is studied and the topological insulating phase of an interacting boson-fermion mixture characterized by a nontrivial Berry phase is identified. The single-particle and boson-fermion exchanging excitation spectrums are calculated and we identify the boson-fermion exchanging excitation as the gapless topological excitation in the topological phase of the mixture. The different kinds of excitations are explained explicitly from the competition among the bulk gap, the on-site boson-boson, and boson-fermion interactions. The Hamiltonian studied has been partly realized in the state-of-art cold atom experiments, and the results are very relevant to the experiments.The topological property of a boson-fermion mixture in a one-dimensional optical superlattice is studied and the topological insulating phase of an interacting boson-fermion mixture characterized by a nontrivial Berry phase is identified. The single-particle and boson-fermion exchanging excitation spectrums are calculated and we identify the boson-fermion exchanging excitation as the gapless topological excitation in the topological phase of the mixture. The different kinds of excitations are explained explicitly from the competition among the bulk gap, the on-site boson-boson, and boson-fermion interactions. The Hamiltonian studied has been partly realized in the state-of-art cold atom experiments, and the results are very relevant to the experiments.

arXiv:1509.03037Physical Review ASep 28, 20153 citations

Coupled Boson—Fermion Systems

C. B. Dover

Springer eBooksJan 1, 19690 citations

^{87}\mathrm{Rb}

and

^{40}\mathrm{K}

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.