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Comprehensive classification for Bose–Fermi mixtures

Published Aug 8, 2017• 7 citations
Publisher

Abstract

Abstract We present analytical studies of a trapped boson-fermion mixture at zero temperature with spin-polarized fermions. Using the Thomas–Fermi approximation for bosons and the local-density approximation for fermions, we find a large variety of different density shapes. In the case of continuous density, we obtain analytic conditions for each configuration for attractive as well as repulsive boson-fermion interaction. Furthermore, we analytically show that all the scenarios we describe are minima of the grand-canonical energy functional. Finally, we provide a full classification of all possible ground states in the interpenetrative regime. Our results also apply to binary mixtures of bosons.

DOI
10.18725/oparu-54158

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Abstract We present analytical studies of a trapped boson-fermion mixture at zero temperature with spin-polarized fermions. Using the Thomas–Fermi approximation for bosons and the local-density approximation for fermions, we find a large variety of different density shapes. In the case of continuous density, we obtain analytic conditions for each configuration for attractive as well as repulsive boson-fermion interaction. Furthermore, we analytically show that all the scenarios we describe are minima of the grand-canonical energy functional. Finally, we provide a full classification of all possible ground states in the interpenetrative regime. Our results also apply to binary mixtures of bosons.
We present analytical studies of a trapped boson-fermion mixture at zero temperature with spin-polarized fermions. Using the Thomas–Fermi approximation for bosons and the local-density approximation for fermions, we find a large variety of different density shapes. In the case of continuous density, we obtain analytic conditions for each configuration for attractive as well as repulsive boson-fermion interaction. Furthermore, we analytically show that all the scenarios we describe are minima of the grand-canonical energy functional. Finally, we provide a full classification of all possible ground states in the interpenetrative regime. Our results also apply to binary mixtures of bosons.
We study one-dimensional (1D) strongly interacting Bose–Fermi mixtures by both the exact Bethe-ansatz method and variational perturbation theory within the degenerate ground state subspace of the system in the infinitely repulsive limit. Based on the exact solution of the 1D Bose–Fermi gas with equal boson–boson and boson–fermion interaction strengths, we demonstrate that the ground state energy is degenerate for different Bose–Fermi configurations and the degeneracy is lifted when the interaction deviates the infinitely interacting limit. We then show that the ground properties in the strongly interacting regime can be well characterized by using the variational perturbation method within the degenerate ground state subspace, which can be applied to deal with more general cases with anisotropic interactions and in external traps. Our results indicate that the total ground-state density profile in the strongly repulsive regime behaves like the polarized non-interacting fermions, whereas the density distributions of bosons and fermions display different properties for different Bose–Fermi configurations and are sensitive to the anisotropy of interactions.
We consider a one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in experiments with ultracold boson and fermion isotopes in optical lattices. We use the Bethe-ansatz technique to find the ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We prove that the mixture is always stable against demixing. Combining exact solution with the local density approximation, we calculate density profiles and collective oscillation modes in a harmonic trap. In the strongly interating regime, we use exact wave functions to calculate correlation functions for bosons and fermions under periodic boundary conditions.
In six different regimes for a spatial phase diagram of a trapped interacting Bose–Fermi gas mixture at low temperatures, we present the conditions for the spatial demixing and separation of bosons and fermions. Starting from a semiclassically thermodynamic model for the local density functional of thermal bosons and fermions, the explicit analytical expressions for the fugacities of bosons and fermions are derived in different regimes by means of a first-order perturbation method in a local-density approximation. The critical values of the fermion–boson interaction strength as a function of the fractional composition of fermions have a general feature: increase, extreme and decrease with increasing the fermionic composition slightly above Bose–Einstein critical temperature.
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.
Abstract In this paper we study a mixed system of bosons and fermions with up to six particles in total. All particles are assumed to have the same mass. The two-body interactions are repulsive and are assumed to have equal strength in both the Bose–Bose and the Fermi–Boson channels. The particles are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and density matrix renormalization group calculations using a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different states for strongly interacting mixtures. By moving to slightly larger systems, we find that the ground state of balanced mixtures of four to six particles tends to separate bosons and fermions for strong (repulsive) interactions. On the other hand, in imbalanced Bose–Fermi mixtures we find pronounced odd–even effects in systems of five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition, both for the ground state and the excited states.