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arXiv:1012.0484 · New Journal of Physics

Metastability in spin-polarized Fermi gases and quasiparticle decays

K Sadeghzadeh, Georg M. Bruun, C Lobo, Pietro Massignan, Alessio Recati

Published May 24, 2011• 5 citations
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Abstract

The metastability associated with the first-order transition from the normal to the superfluid phase is investigated in the phase diagram of two-component polarized Fermi gases. We begin by detailing the dominant decay processes of single quasiparticles, determining the momentum thresholds of each process and calculating their rates. This understanding is then applied to a Fermi sea of polarons, and we predict a region of metastability for the normal partially polarized phase. We propose experiments to observe the threshold of the metastable region, the interaction strength at which the quasiparticle ground state changes character, and the decay rate of polarons.

DOI
10.1088/1367-2630/13/5/055011

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The metastability associated with the first-order transition from the normal to the superfluid phase is investigated in the phase diagram of two-component polarized Fermi gases. We begin by detailing the dominant decay processes of single quasiparticles, determining the momentum thresholds of each process and calculating their rates. This understanding is then applied to a Fermi sea of polarons, and we predict a region of metastability for the normal partially polarized phase. We propose experiments to observe the threshold of the metastable region, the interaction strength at which the quasiparticle ground state changes character, and the decay rate of polarons.
The ground state of an impurity immersed in a Fermi sea changes from a polaron to a molecule as the interaction strength is increased. We show here that the coupling between these two states is strongly suppressed due to a combination of phase-space effects and Fermi statistics, and that it vanishes much faster than the energy difference between the two states, thereby confirming the first order nature of the polaron-molecule transition. In the regime where each state is metastable, we find quasiparticle lifetimes which are much longer than what is expected for a usual Fermi liquid. Our analysis indicates that the decay rates are sufficiently slow to be experimentally observable.
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.
We investigate the phase diagram of asymmetric two-component Fermi gases at zero temperature as a function of polarization and interaction strength. The equations of state of the uniform superfluid and normal phase are determined using quantum Monte Carlo simulations. We find three different mixed states, where the superfluid and the normal phase coexist in equilibrium, corresponding to phase separation between (a) the polarized superfluid and the fully polarized normal gas, (b) the polarized superfluid and the partially polarized normal gas, and (c) the unpolarized superfluid and the partially polarized normal gas.
Recent experiments on imbalanced Fermi gases in ultracold atomic systems have raised interest in the physics of an impurity immersed in a Fermi sea, the so-called Fermi polaron. In particular, the internal energy of a Fermi polaron gives the threshold for a fully polarized normal phase. When partially polarized, the normal phase can be described quantitatively as a Fermi liquid of dilute polarons. We discuss a simple theory devised to describe dilute Fermi-polaron ensembles and show that an exact formula can be obtained for the dominant interaction between polarons. It is expressed solely in terms of a single polaron parameter. The physics of this interaction is identified as a signature of the Pauli exclusion principle. The comparison of this theory with experimental results shows a remarkable agreement up to the vicinity of the transition to the superfluid phase.
We study the Fermi gas at unitarity and at T=0 by assuming that, at high polarizations, it is a normal Fermi liquid composed of weakly interacting quasiparticles associated with the minority spin atoms. With a quantum Monte Carlo approach we calculate their effective mass and binding energy, as well as the full equation of state of the normal phase as a function of the concentration x=n downward arrow/n upward arrow of minority atoms. We predict a first order phase transition from normal to superfluid at x(c)=0.44 corresponding, in the presence of harmonic trapping, to a critical polarization P(c)=(N upward arrow - N downward arrow/(N upward arrow + N downward arrow)=77%. We calculate the radii and the density profiles in the trap and predict that the frequency of the spin dipole mode will be increased by a factor of 1.23 due to interactions.
Understanding the behavior of an impurity strongly interacting with a Fermi sea is a long-standing challenge in many-body physics. When the interactions are short-ranged, two vastly different ground states exist: a polaron quasiparticle and a molecule dressed by the majority atoms. In the single-impurity limit, it is predicted that at a critical interaction strength, a first-order transition occurs between these two states. Experiments, however, are always conducted in the finite temperature and impurity density regime. The fate of the polaron-to-molecule transition under these conditions, where the statistics of quantum impurities and thermal effects become relevant, is still unknown. Here, we address this question experimentally and theoretically. Our experiments are performed with a spin-imbalanced ultracold Fermi gas with tunable interactions. Utilizing a novel Raman spectroscopy combined with a high-sensitivity fluorescence detection technique, we isolate the quasiparticle contribution and extract the polaron energy, spectral weight, and the contact parameter. As the interaction strength is increased, we observe a continuous variation of all observables, in particular a smooth reduction of the quasiparticle weight as it goes to zero beyond the transition point. Our observation is in good agreement with a theoretical model where polaron and molecule quasiparticle states are thermally occupied according to their quantum statistics. At the experimental conditions, polaron states are hence populated even at interactions where the molecule is the ground state and vice versa. The emerging physical picture is thus that of a smooth transition between polarons and molecules and a coexistence of both in the region around the expected transition.