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arXiv:cond-mat/0606624

Asymmetric two-component Fermi gas with unequal masses

M. Iskin, C. A. R. Sá de Melo

Published Jun 23, 2006• 3 citations
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Abstract

We analyze the zero temperature phase diagram for an asymmetric two-component Fermi gas as a function of mass anisotropy and population imbalance. We identify regions corresponding to normal, or uniform/non-uniform superfluid phases, and discuss topological quantum phase transitions in the Bardeen-Cooper-Schrieffer (BCS), unitarity and Bose-Einstein condensation (BEC) limits. Lastly, we derive the zero temperature low frequency and long wavelength collective excitation spectrum, and recover the Bogoliubov relation for weakly interacting dilute bosons in the BEC limit.

DOI
10.48550/arxiv.cond-mat/0606624

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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 $s$-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.

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We analyze the zero temperature phase diagram for an asymmetric two-component Fermi gas as a function of mass anisotropy and population imbalance. We identify regions corresponding to normal, or uniform/non-uniform superfluid phases, and discuss topological quantum phase transitions in the Bardeen-Cooper-Schrieffer (BCS), unitarity and Bose-Einstein condensation (BEC) limits. Lastly, we derive the zero temperature low frequency and long wavelength collective excitation spectrum, and recover the Bogoliubov relation for weakly interacting dilute bosons in the BEC limit.
We analyze the phase diagram of superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) limit as a function of scattering parameter, population imbalance, and mass anisotropy. We identify regions corresponding to normal, or uniform or nonuniform superfluid phases, and discuss topological quantum phase transitions in the BCS, unitarity, and BEC limits. We derive the Ginzburg-Landau equation near the critical temperature, and show that it describes a dilute mixture of paired and unpaired fermions in the BEC limit. We also obtain the zero temperature low frequency and long wavelength collective excitation spectrum, and recover the Bogoliubov relation for weakly interacting dilute bosons in the BEC limit. Lastly, we discuss the effects of harmonic traps and the resulting density profiles in the BEC regime.
We analytically investigate superfluid phase in two dimension at zero temperature for asymmetric Fermi gas. Analytic expressions for both gap and chemical potentials at mean-field level are obtained as a function of binding energy and population imbalance when mass of different types of fermions is equal. We identify regions corresponding to normal, Sarma phase for different polarization, or mass ratio and discuss topological phase diagram in the BCS-BEC crossover and find that energy gap and chemical potential behave differently in these topological quantum phase. We also obtain the low-frequency and long-wavelength collective excitation spectrum and find sound velocity has a maximum when two types of mass are equal.
We analyze the phase diagram of uniform superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BEC) limit as a function of the scattering parameter and population imbalance. We find at zero temperature that the phase diagram of population imbalance versus scattering parameter is asymmetric for unequal masses, having a larger stability region for uniform superfluidity when the lighter fermions are in excess. In addition, we find topological quantum phase transitions associated with the disappearance or appearance of momentum space regions of zero quasiparticle energies. Lastly, near the critical temperature, we derive the Ginzburg-Landau equation and show that it describes a dilute mixture of composite bosons and unpaired fermions in the BEC limit.
We in this paper investigate the phase diagram associated with the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover of a three-component ultracold superfluid Fermi gas of different chemical potentials and equal masses in two dimensions. The gap-order parameter and number densities are found analytically by using the functional-path-integral method. The balance of pairing will be broken in the free space due to the unequal chemical potentials. We obtain the same particle-number density and condensed fraction in the BCS-superfluid phase as those in a recent paper [Phys. Rev. A 83, 033630 (2011)] while the Sarma phase of the coexistence of normal and superfluid Fermi gases is characteristic of an inhomogeneous system. The minimum ratio of the BCS-superfluid phase becomes 1/3 in the BCS limit corresponding to the zero ratio in the two-component system in which the critical point of phase separation is ${\ensuremath{\epsilon}}_{B}/{\ensuremath{\epsilon}}_{F}=2$, but it becomes 3 in the three-component case.
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.