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arXiv:1011.0467 · Physical Review A

Population imbalance and pairing in the BCS-BEC crossover of three-component ultracold fermions

Tomoki Ozawa, Gordon Baym

Published Dec 14, 2010• 49 citations
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Abstract

We investigate the phase diagram and the BCS-BEC crossover of a homogeneous three-component ultracold Fermi gas with a U(3)-invariant attractive interaction. We show that the system at sufficiently low temperatures exhibits population imbalance as well as fermionic pairing. We describe the crossover in this system, connecting the weakly interacting BCS regime of the partially population-imbalanced fermion pairing state and the BEC limit with three weakly interacting species of molecules, including pairing fluctuations within a $t$-matrix calculation of the particle self-energies.

DOI
10.1103/physreva.82.063615

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We investigate the phase diagram and the BCS-BEC crossover of a homogeneous three-component ultracold Fermi gas with a U(3)-invariant attractive interaction. We show that the system at sufficiently low temperatures exhibits population imbalance as well as fermionic pairing. We describe the crossover in this system, connecting the weakly interacting BCS regime of the partially population-imbalanced fermion pairing state and the BEC limit with three weakly interacting species of molecules, including pairing fluctuations within a ttt-matrix calculation of the particle self-energies.
We investigate the formation of Bose-Einstein condensation and a population imbalance in a three-component Fermi superfluid by increasing the U(3) invariant attractive interaction. We consider the system at zero temperature in three dimensions as well as in two dimensions. Within mean-field theory, we derive explicit formulas for the number densities, the gap order parameter, the condensate density, and the condensate fraction of the uniform system and analyze them in the crossover from the Bardeen-Cooper-Schrieffer (BCS) state of Cooper pairs to the Bose-Einstein condensate (BEC) of strongly bound molecular dimers. In addition we study this Fermi mixture trapped by a harmonic potential: We calculate the density profiles of the three components and the condensate density profile of Cooper pairs in the BCS-BEC crossover.
We analyze the BCS-BEC crossover for a Fermi gas made of neutral atoms in three hyperfine states with a SU(3) invariant attractive interaction. By solving the extended BCS equations for the total number of particles and the pairing gap, we calculate at zero temperature the pairing gap, the population imbalance, the condensate fraction and the first sound velocity of the uniform system as a function of the interaction strength in both three and two dimensions. Contrary to the three-dimensional case, in two dimensions the condensate fraction approaches the value 1 only for an extremely large interaction strength and, moreover, the sound velocity gives a clear signature of the disappearance of one of the three hyperfine components.
an atomic mass in the -component) in the BCS-BEC crossover region. Including pairing fluctuations within a self-consistent T -matrix theory, we examine how the superfluid instability is affected by the presence of mass imbalance. We determine the superfluid region in the phase diagram of a Fermi gas in terms of the temperature, the strength of a pairing interaction, and the ratio of mass imbalance. The superfluid phase transition is shown to always occur even when m m#. 2 This behavior of Tc is quite different from the previous result in an extended T -matrix theory, 3 where Tc vanishes at a certain value of m=m# > 0 in the BCS regime. Since Fermi condensates with mass imbalance have been discussed in various systems, such as a cold Fermi gas, an exciton(polariton) condensate, as well as color superconductivity, our results would be useful for further understandings of these novel Fermi superfluids.
This thesis focuses on the analysis of Bardeen-Cooper-Schrieffer (BCS) \nto Bose-Einstein condensation (BEC) evolution in ultracold superfluid \nFermi gases when the interaction between atoms is varied. The tuning of \nattractive interactions permits the ground state of the system to evolve from a weak \nfermion attraction BCS limit of loosely bound and largely overlapping Cooper pairs \nto a strong fermion attraction limit of tightly bound small bosonic molecules \nwhich undergo BEC. \nThis evolution is accompanied by anomalous behavior of many superfluid \nproperties, and reveals several quantum phase transitions. \nThis thesis has two parts: \nIn the first part, I analyze zero and nonzero orbital angular momentum \npairing effects, and show that a quantum phase transition occurs for \nnonzero angular momentum pairing, unlike the sss-wave case where the BCS \nto BEC evolution is just a crossover. \nIn the second part, I analyze two-species fermion mixtures with mass and \npopulation imbalance in continuum, trap and lattice models. In contrast with \nthe crossover physics found in the mass and population balanced mixtures, \nI demonstrate the existence of phase transitions between normal and \nsuperfluid phases, as well as phase separation between superfluid (paired) \nand normal (excess) fermions in imbalanced mixtures as a function of scattering \nparameter and mass and population imbalance.
In this paper, we study the effect of population imbalance and its interplay with pairing strength and lattice effect in atomic Fermi gases in a one-dimensional optical lattice. We compute various phase diagrams as the system undergoes BCS-BEC crossover, using the same pairing fluctuation theory as in Part I of this work [Phys. Rev. A 101, 053617 (2020)]. We find widespread pseudogap phenomena beyond the BCS regime and intermediate temperature superfluid states for relatively low population imbalances. The Fermi surface topology plays an important role in the behavior of Tc{T}_{\mathrm{c}}Tc​. For large ddd and/or small ttt, which yield an open Fermi surface, superfluidity can be readily destroyed by a small amount of population imbalance ppp. The superfluid phase, especially in the BEC regime, can exist only for a highly restricted volume of the parameter space. An open Fermi surface often leads to destruction of the superfluid ground state in the BEC regime. Due to the continuum-lattice mixing, population imbalance gives rise to a new mechanism for pair hopping, as assisted by excessive majority fermions, which may lead to significant enhancement of Tc{T}_{\mathrm{c}}Tc​ on the BEC side of the Feshbach resonance, and also render Tc{T}_{\mathrm{c}}Tc​ approaching a constant asymptote in the BEC limit, when it exists. Furthermore, we find that not all minority fermions will be paired up in BEC limit, unlike the 3D continuum case. These predictions can be tested in future experiments.