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arXiv:1804.03035 · Journal of Experimental and Theoretical Physics

Universal Phase Diagram and Scaling Functions of Imbalanced Fermi Gases

B. Frank, J. Lang, W. Zwerger

Published Nov 1, 2018• 37 citations
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Abstract

Abstract We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite imbalance. The existence of a quantum multicritical point for the unitary gas at vanishing chemical potential μ and effective magnetic field h, first discussed by Nikolić and Sachdev, gives rise to three different phase diagrams, depending on whether the inverse scattering length 1/a is negative, positive or zero. Within a Luttinger–Ward formalism, the phase diagram and pressure of the unitary gas is calculated as a function of the dimensionless scaling variables T/μ and h/μ. The results indicate that beyond the Clogston–Chandrasekhar limit at (h/μ)c ≃ 1.09, the unitary gas exhibits an inhomogeneous superfluid phase with FFLO order that can reach critical temperatures near unitarity of ≃0.03TF .

DOI
10.1134/s1063776118110031

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Abstract We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite imbalance. The existence of a quantum multicritical point for the unitary gas at vanishing chemical potential μ and effective magnetic field h, first discussed by Nikolić and Sachdev, gives rise to three different phase diagrams, depending on whether the inverse scattering length 1/a is negative, positive or zero. Within a Luttinger–Ward formalism, the phase diagram and pressure of the unitary gas is calculated as a function of the dimensionless scaling variables T/μ and h/μ. The results indicate that beyond the Clogston–Chandrasekhar limit at (h/μ)c ≃ 1.09, the unitary gas exhibits an inhomogeneous superfluid phase with FFLO order that can reach critical temperatures near unitarity of ≃0.03TF .
We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite imbalance.The existence of a quantum multicritical point for the unitary gas at vanishing chemical potential µ and effective magnetic field h, first discussed by Nikolić and Sachdev, gives rise to three different phase diagrams, depending on whether the inverse scattering length 1/a is negative, positive or zero.Within a Luttinger-Ward formalism, the phase diagram and pressure of the unitary gas is calculated as a function of the dimensionless scaling variables T /µ and h/µ.The results indicate that beyond the Clogston-Chandrasekhar limit at (h/µ)c 1.09, the unitary gas exhibits an inhomogeneous superfluid phase with FFLO order that can reach critical temperatures near unitarity of 0.03 TF .
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.
We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techniques. We thus obtain estimates for critical values of the temperature, mass and spin imbalance, above which the system is in the normal phase. In the unpolarized, equal-mass limit, our result for the critical temperature is in accordance with state-of-the-art Monte Carlo calculations. In addition, we estimate the location of regions in the phase diagram where inhomogeneous phases are likely to exist. We show that an intriguing relation exists between the general structure of the many-body phase diagram and the binding energies of the underlying two-body bound-state problem, which further supports our findings. Our results suggest that inhomogeneous condensates form for mass imbalances ${m}_{\ensuremath{\downarrow}}/{m}_{\ensuremath{\uparrow}}\ensuremath{\gtrsim}3$. The extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance.
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 k F a , where most of the current experiments are realized. For homogeneous systems, we determine the critical chemical potential imbalance h c at which possible phase transitions occur. In the case of trapped gases, we show how h c can be consistently determined from experimental observations.
Quantum criticality of strongly attractive Fermi gas with SU(3)SU(3)SU(3) symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential μμμ, effective magnetic field H1H_1H1​, H2H_2H2​ (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the thermodynamic Bethe ansatz equations in zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent z=2z=2z=2 and correlation length exponent ν=1/2ν=1/2ν=1/2 read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multi-component Fermi gases with SU(N)SU(N)SU(N) symmetry.
We investigated possible superfluid phases at finite temperature in a two-component Fermi gas with density imbalance. In the frame of a general four-fermion interaction theory, we solved in the BCS region the gap equations for the pairing gap and pairing momentum under the restriction of fixed number densities and analyzed the stability of different phases by calculating the superfluid density and number susceptibilities. The homogeneous superfluid is stable only at high temperature and low number asymmetry, the inhomogeneous Larkin-Ovchinnikov-Fudde-Ferrell state survives at low temperature and high number asymmetry, and in between them there exists another possible inhomogeneous phase, that of phase separation. The critical temperatures and the orders of the phase transitions among the superfluid phases and normal phase are calculated analytically and numerically. The phase diagram we obtained in the temperature and number asymmetry plane is quite different from the one in the temperature and chemical potential difference plane for a system with fixed chemical potentials.