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Physical Review A

Phase separation in atom-molecule mixtures near a Feshbach resonance

Xiaoqiang Xu, Li-Hua Lü, You‐Quan Li

Published Apr 8, 2009• 7 citations
Publisher

Abstract

We study the phase separation of a Bose-Einstein condensate system with the conversion of one-species bosonic atoms into molecules via Feshbach resonance. Adopting the Thomas-Fermi approximation, we plot the phase diagrams of the system in two different parameter spaces for different atom-molecule interactions. In the presence of an isotropic trap, the density profiles in spatial space with fixed total number of atoms are also plotted. The clear phase separation in spatial space enables one to determine the location of atoms in the trap, which may be used as a possible experimental probe method.

DOI
10.1103/physreva.79.043604

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We study the phase separation of a Bose-Einstein condensate system with the conversion of one-species bosonic atoms into molecules via Feshbach resonance. Adopting the Thomas-Fermi approximation, we plot the phase diagrams of the system in two different parameter spaces for different atom-molecule interactions. In the presence of an isotropic trap, the density profiles in spatial space with fixed total number of atoms are also plotted. The clear phase separation in spatial space enables one to determine the location of atoms in the trap, which may be used as a possible experimental probe method.
We investigate phase separation of Bose-Einstein condensates (BECs) of two-component atoms and one-component molecules with a homonuclear Feshbach resonance. We develop a full model for dilute atomic and molecular gases including correlation of the Feshbach resonance and all kinds of interparticle interactions, and numerically calculate order parameters of the BECs in spherical harmonic oscillator traps at zero temperature with the Bogoliubov's classical field approximation. As a result, we find out that the Feshbach resonance can induce two types of phase separation. The actual phase structures and density profiles of the trapped gases are predicted in the whole parameter region, from the atom-dominant regime to the molecule-dominant regime. We focus on the role of the molecules in the phase separation. Especially in the atom-dominant regime, the role of the molecules is described through effective interactions derived from our model. Furthermore we show that a perturbative and semiclassical limit of our model reproduces the conventional atomic BEC (single-channel) model.
We study a dilute mixture of degenerate bosons and fermions across a Feshbach resonance of the Fermi-Fermi scattering length aF{a}_{F}aF​. This scattering length is renormalized by the boson-induced interaction between fermions and its value is crucial to determine the phase diagram of the system. For the mixture in a box and a positive Bose-Fermi scattering length, we show that there are three possibilities: A single uniform mixed phase, a purely fermionic phase coexisting with a mixed phase, and a purely fermionic phase coexisting with a purely bosonic one. As 1∕aF1∕{a}_{F}1∕aF​ is increased from a negative value to the Feshbach resonance (1∕aF=0)(1∕{a}_{F}=0)(1∕aF​=0), the region of pure separation increases and the other two regions are strongly reduced. Above the Feshbach resonance (1∕aF>0)(1∕{a}_{F}>0)(1∕aF​>0), pairs of Fermi atoms become Bose-condensed molecules. We find that these molecules are fully spatially separated from the bosonic atoms when 1∕aF1∕{a}_{F}1∕aF​ exceeds a critical value. For a negative Bose-Fermi scattering length we deduce the condition for collapse, which coincides with the onset of dynamical instability of the fully mixed phase. We consider also the mixture in a harmonic trap and determine the conditions for partial demixing, full demixing, and collapse. The experimental implications of our results are investigated by analyzing mixtures of $^{6}\mathrm{Li}\text{\ensuremath{-}}^{23}\mathrm{Na}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ atoms.
We calculate the phase diagrams for a harmonically trapped ideal gas mixture of fermionic atoms and bosonic molecules in chemical and thermal equilibrium, where the internal energy of the molecules can be adjusted relative to that of the atoms by use of a tunable Feshbach resonance. We plot the molecule fraction and the fraction of Bose-condensed molecules as functions of the temperature and internal molecular energy. We show the paths traversed in the phase diagrams when the molecular energy is varied either suddenly or adiabatically. Our model calculation helps to interpret the adiabatic phase diagrams obtained in recent experiments on the Bose–Einstein condensation to Bardeen–Cooper–Schrieffer crossover, in which the condensate fraction is plotted as a function of the initial temperature of the Fermi gas measured before a sweep of the magnetic field through the resonance region.
We consider a mixture of two-species atomic Bose-Einstein condensates coupled to a bound molecular state at zero temperature via an interspecies Feshbach resonance. The interspecies Feshbach coupling precludes the possibility of doubly mixed phases while enables not only the pure molecular superfluid but also the pure atomic superfluids to exist as distinct phases. We show that this system is able to support a rich set of phase separations, including that between two distinct mixed atom-molecule phases. We pay particular attention to the effects of the Feschbach coupling and the particle collisions on the miscibility of this multicomponent condensate system.
We determine the adiabatic phase diagram of a resonantly-coupled system of Fermi atoms and Bose molecules confined in the harmonic trap by using the local density approximation. The adiabatic phase diagram shows the fermionic condensate fraction composed of condensed molecules and Cooper pair atoms. The key idea of our work is conservation of entropy through the adiabatic process, extending the study of Williams et al. [Williams et al., New J. Phys. 6, 123 (2004)] for an ideal gas mixture to include the resonant interaction in a mean-field theory. We also calculate the molecular conversion efficiency as a function of initial temperature. Our work helps to understand recent experiments on the BCS-BEC crossover, in terms of the initial temperature measured before a sweep of the magnetic field.
We consider a mixture of single-component bosonic and fermionic atoms with an interspecies interaction that is varied using a Feshbach resonance. By performing a mean-field analysis of a two-channel model, which describes both narrow and broad Feshbach resonances, we find an unexpectedly rich phase diagram at zero temperature: Bose-condensed and non-Bose-condensed phases form a variety of phase-separated states that are accompanied by both critical and tricritical points. We discuss the implications of our results for the experimentally observed collapse of Bose-Fermi mixtures on the attractive side of the Feshbach resonance, and we make predictions for future experiments on Bose-Fermi mixtures close to a Feshbach resonance.