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arXiv:1405.7187 · Physical Review A

Chandrasekhar-Clogston limit and critical polarization in a Fermi-Bose superfluid mixture

Tomoki Ozawa, Alessio Recati, Marion Delehaye, Frédéric Chevy, S. Stringari

Published Oct 8, 2014• 32 citations
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Abstract

We study mixtures of a population-imbalanced, strongly interacting Fermi gas and of a Bose-Einstein condensed gas at zero temperature. In the homogeneous case, we find that the Chandrasekhar-Clogston critical polarization for the onset of instability of Fermi superfluidity is enhanced due to the interaction with the bosons. Predictions for the critical polarization are also given in the trapped case, with a special focus on the situation of equal Fermi-Bose and Bose-Bose coupling constants, where the density of fermions becomes flat in the center of the trap. This regime can be realized experimentally using Feshbach resonances and is well suited to investigate the emergence of exotic configurations, such as the occurrence of spin domains or the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase.

DOI
10.1103/physreva.90.043608

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We study mixtures of a population-imbalanced, strongly interacting Fermi gas and of a Bose-Einstein condensed gas at zero temperature. In the homogeneous case, we find that the Chandrasekhar-Clogston critical polarization for the onset of instability of Fermi superfluidity is enhanced due to the interaction with the bosons. Predictions for the critical polarization are also given in the trapped case, with a special focus on the situation of equal Fermi-Bose and Bose-Bose coupling constants, where the density of fermions becomes flat in the center of the trap. This regime can be realized experimentally using Feshbach resonances and is well suited to investigate the emergence of exotic configurations, such as the occurrence of spin domains or the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase.
The evolution of an attractive polarized two-component Fermi gas at zero temperature is analyzed as its polarization is progressively decreased, from full polarization (corresponding to the polaronic limit) down to a critical polarization when superfluidity sets in. This critical polarization and the nature of the associated superfluid instability are determined within a fully self-consistent ttt-matrix approach implemented exactly at zero temperature. In this way, the polarization-vs-coupling phase diagram at zero temperature is constructed throughout the whole BCS-BEC crossover. Depending on the coupling strength of the interparticle interaction between the two components, the superfluid instability can be either toward a Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase or toward a standard polarized BCS phase. The evolution with polarization of the quasiparticle parameters in the normal Fermi gas turns out to be notably different in the two cases. When the instability is toward a polarized BCS superfluid, quasiparticles in the proximity of the two Fermi surfaces remain well defined for all polarizations. When the instability is instead toward an FFLO superfluid, precursor effects become apparent upon approaching the FFLO quantum critical point (QCP), where the quasiparticle residues vanish and the effective masses diverge. This behavior leads to a complete breakdown of the quasiparticle picture characteristic of a Fermi liquid, similarly to what occurs in heavy-fermion materials at an antiferromagnetic QCP. At unitarity, the system is further investigated at finite temperature, making it possible to identify a non-Fermi liquid region in the temperature-vs-polarization phase diagram associated with the underlying FFLO QCP.
In this thesis we first review the theory of the normal state of the unitary Fermi gas at T = 0 and the main properties of the normal-to-superfluid transition. Then we study the trapped gas under adiabatic rotation, i.e., avoiding the formation of vortices. We show that for polarized systems the rotation enhances the Chandrasekhar-Clogston limit due to pair breaking at the border between the superfluid and the normal phase, while it leaves the global critical polarization Pc of the trapped system unaffected. In the case of an unpolarized unitary superfluid the rotation causes a phase separation between a superfluid core and an unpolarized normal shell, in which the densities of the spin-up and spin-down atom numbers is equal. For both the polarized and the unpolarized systems we calculate experimental observables such as the density profiles and the angular momenta. From the study of Bose-Einstein condensates it is well known that an adiabatic rotation induces a quadrupole deformation of the trapped atomic cloud when the rotation exceeds a certain angular velocity. In Fermi gases the situation is different due to the phase separation discussed above, and the quadrupole instabilities are found to set on at smaller angular velocity than in the BEC case. This phenomenon together with a more general discussion concerning not only the energetic but also the dynamic instabilities of the phase separated system is presented. We use the present knowledge of the equation of state of Fermi mixtures with unequal masses to give quantitative predictions for the phase separation between the normal and superfluid components. The analysis is based on the study of the zero temperature μ-h phase diagram of the uniform two component gas. The phase diagram at unitarity is determined thanks to the knowledge of the equation of state available from diagrammatic techniques applied to highly polarized configurations and from Monte Carlo simulations. The phase diagram is then used, in the local density approximation, to calculate the density profiles of the two Fermi components in the presence of harmonic trapping. Eventually we investigate the polarization produced by the relative displacement of the potentials trapping two spin species of a unitary Fermi gas with population imbalance. We investigate the dipole polarizability of a polarized system both in the two-fluid and the three-fluid model at zero temperature and point out the major differences between the two treatments.
Using many-body results available from diagrammatic and ab initio Monte Carlo calculations we analyze the phase diagram $\ensuremath{\mu}=({\ensuremath{\mu}}_{\ensuremath{\uparrow}}+{\ensuremath{\mu}}_{\ensuremath{\downarrow}})/2$ versus $h=({\ensuremath{\mu}}_{\ensuremath{\uparrow}}\ensuremath{-}{\ensuremath{\mu}}_{\ensuremath{\downarrow}})/2$ of a unitary Fermi gas at zero temperature with population imbalance and unequal masses. We identify different regions where the gas is superfluid, partially polarized or fully polarized, and determine the corresponding coexistence conditions. The asymmetry in the phase diagram, caused by the mass imbalance, and its effect on the Chandrasekhar-Clogston limit for the critical polarization are explicitly discussed. The equation of state of the superfluid and normal phases is employed, within the local density approximation, to predict phase separated configurations in the presence of harmonic trapping potentials.
Based on the integrable Gaudin model and local density approximation, we discuss the ground state of a one-dimensional trapped Fermi gas with imbalanced spin population, for an arbitrary attractive interaction. A phase separation state, with a polarized superfluid core immersed in an unpolarized superfluid shell, emerges below a critical spin polarization. Above it, coexistence of polarized superfluid matter and a fully polarized normal gas is favored. These two exotic states could be realized experimentally in highly elongated atomic traps, and diagnosed by measuring the lowest density compressional mode. We identify the polarized superfluid as having an Fulde-Ferrell-Larkin-Ovchinnikov structure, and predict the resulting mode frequency as a function of the spin polarization.
We study the three-fermion problem within a 1D model of a Feshbach resonance in order to gain insight into how the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO)-like state at small negative scattering lengths evolves into a Bose-Fermi mixture at small positive scattering lengths. The FFLO state possesses an oscillating superfluid correlation function, while in a Bose-Fermi mixture correlations are monotonic. We find that this behavior is already present at the three-body level. We present an exact study of the three-body problem and gain extra insights by considering world lines of a path-integral Monte Carlo calculation.
We present a numerical study of the one-dimensional BCS-BEC crossover of a spin-imbalanced Fermi gas. The crossover is described by the Bose-Fermi resonance model in a real space representation. Our main interest is in the behavior of the pair correlations, which, in the BCS limit, are of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type, while in the Bose-Einstein condensate limit, a superfluid of diatomic molecules forms that exhibits quasi-condensation at zero momentum. We use the density matrix renormalization group method to compute the phase diagram as a function of the detuning of the molecular level and the polarization. As a main result, we show that FFLO-like correlations disappear well below full polarization close to the resonance. The critical polarization depends on both the detuning and the filling.