Superfluid-normal quantum phase transitions in an imbalanced Fermi gas

Abstract

We investigate the superfluid-to-normal zero temperature quantum phase transitions of asymmetric two-component Fermi gases as a function of the chemical potential imbalance h. The calculations are performed for homogeneous and trapped imbalanced systems. We concentrate at unitarity, characterized by a divergent interaction parameter kF a, where most of the current experiments are realized. For homogeneous systems, we determine the critical chemical potential imbalance hc at which possible phase transitions occur. In the case of trapped gases, we show how hc can be consistently determined from experimental observations.

The Gor'kov and Melik-Barkhudarov correction to an imbalanced Fermi gas in the presence of impurities

“…Comparisons between different theoretical results obtained for the CC limit at unitarity can be found as, for example, in Refs. [47,62,63,71].…”

“…Our values of y CC for both clean and with impurities are within the results found by means of several theoretical approaches as, for instance, Lobo et al [79], who found (h/µ) c = 0.96 from QMC calculations; Boettcher et al [57], who obtained (h/µ) c = 0.83 by means of the functional renormalization group (FRG). With the FRG they were able to go beyond the mean-field approximation by including bosonic fluctuations on the many-body state; Land et al [47], who found (h/µ) c = 1.09 within a Luttinger-Ward formalism; and (h/µ) c = 0.88 in the work by Caldas [63], obtained by means of thermodynamic equilibrium between possible phases at the unitary limit. We would like to remark in passing, for reference only, that the experimental value obtained for the zero temperature CC limit of a (harmonically trapped) spin-polarized Fermi gas of 6 Li atoms at unitarity is (h/µ) c 0.95 [23,98].…”

The Gor'kov and Melik‐Barkhudarov Correction to an Imbalanced Fermi Gas in the Presence of Impurities

“…[56] Comparisons between different theoretical results obtained for the CC limit at unitarity can be found as, for example, in refs. [47,62,63,71].…”

“…Our values of $$y_{\text{CC}}$$ for both clean and with impurities are within the results found by means of several theoretical approaches as, for instance, Lobo et al., [ 79 ] who found $$(h/\mu )_{\rm c}=0.96$$ from QMC calculations; Boettcher et al., [ 57 ] who obtained $$(h/\mu )_{\rm c}=0.83$$ by means of the functional renormalization group (FRG). With the FRG they were able to go beyond the mean‐field approximation by including Bosonic fluctuations on the many‐body state; Land et al., [ 47 ] who found $$(h/\mu )_{\rm c}=1.09$$ within a Luttinger–Ward formalism; and $$(h/\mu )_{\rm c}=0.88$$ in the work by Caldas, [ 63 ] obtained by means of thermodynamic equilibrium between possible phases at the unitary limit. We would like to remark in passing, for reference only, that the experimental value obtained for the zero temperature CC limit of a (harmonically trapped) spin‐polarized Fermi gas of $${}^{6} \rm Li$$ atoms at unitarity is $$(h/\mu )_{\rm c} \simeq 0.95$$.…”

The normal state of attractive Fermi gases from coupled-cluster theory

“…An ongoing investigation concerns the fate of the paired superfluid in the presence of a spin polarization, with implications for superconductivity in solids. Specifically, at large polarizations, the superfluid is expected to exhibit an instability to a partially polarized or fully polarized normal state [38][39][40][41][42][43][44][45][46][47][48][49].…”