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arXiv:1006.4723 · Physical Review Letters

Comment on “Normal Phase of an Imbalanced Fermi Gas”

Zhenhua Yu, Sascha Zöllner, C. J. Pethick

Published Oct 27, 2010• 19 citations
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Abstract

Recently Mora and Chevy [Phys. Rev. Lett. 104, 230402 (2010), arXiv:1003.0213v2], in studying the energy of an atomic Fermi gas consisting of a majority species, 1, and a minority species, 2, showed that, due to interatomic interactions, the energy density E of the gas has a contribution of the form E^(2)= f n_2^2 /2, where n_i is the density of species i. They attribute this term to a `modification of the single polaron properties due to Pauli blocking'. In this Comment, we demonstrate that E^(2) may equivalently be understood in terms of the familiar interaction between minority atoms induced by the majority component.

DOI
10.1103/physrevlett.105.188901

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•Jan 1, 2013•38 citations
Recently Mora and Chevy [Phys. Rev. Lett. 104, 230402 (2010), arXiv:1003.0213v2], in studying the energy of an atomic Fermi gas consisting of a majority species, 1, and a minority species, 2, showed that, due to interatomic interactions, the energy density E of the gas has a contribution of the form E^(2)= f n_2^2 /2, where n_i is the density of species i. They attribute this term to a `modification of the single polaron properties due to Pauli blocking'. In this Comment, we demonstrate that E^(2) may equivalently be understood in terms of the familiar interaction between minority atoms induced by the majority component.
We consider an imbalanced mixture of two different ultracold Fermi gases, which are strongly interacting. Calling spin-down the minority component and spin-up the majority component, the limit of small relative density $x={n}_{\ensuremath{\downarrow}}/{n}_{\ensuremath{\uparrow}}$ is usually considered as a gas of noninteracting polarons. This allows us to calculate, in the expansion of the total energy of the system in powers of xxx, the terms proportional to xxx (corresponding to the binding energy of the polaron) and to x5/3{x}^{5/3}x5/3 (corresponding to the kinetic energy of the polaron Fermi sea). We investigate in this paper terms physically due to an interaction between polarons and which are proportional to x2{x}^{2}x2 and x7/3{x}^{7/3}x7/3. We find three such terms. The first one corresponds to the overlap between the clouds dressing two polarons. The two other ones are due to the modification of the single polaron binding energy caused by the nonzero density of polarons. The second term is due to the restriction of the polaron momentum by the Fermi sea formed by the other polarons. The last one results from the modification of the spin-up Fermi sea brought by the other polarons. The calculation of all these terms is made at the simplest level of a single particle-hole excitation. It is performed for all the possible interaction strengths within the stability range of the polaron. At unitarity the last two terms give a fairly weak contribution while the first one is strong and leads to a marked disagreement with Monte Carlo results. The possible origins of this discrepancy are discussed.
Recent experiments on imbalanced Fermi gases have raised interest in the physics of an impurity immersed in a Fermi sea, the so-called Fermi polaron. In this Letter, a simple theory is devised to describe dilute Fermi-polaron ensembles corresponding to the normal phase of an imbalanced Fermi gas. An exact formula is obtained for the dominant interaction between polarons, expressed solely in terms of a single-polaron parameter. The physics of this interaction is identified as a signature of the Pauli exclusion principle.
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.
The induced intraspecies interactions among the majority species, mediated by the minority species, is computed for a population-imbalanced two-component Fermi gas. Although the Feshbach-resonance mediated interspecies interaction is dominant for equal populations, leading to singlet sss-wave pairing, we find that, in the strongly imbalanced regime, the induced intraspecies interaction leads to ppp-wave pairing and superfluidity of the majority species. Thus, we predict that the observed spin-polaron Fermi-liquid state in this regime is unstable to ppp-wave superfluidity, in accordance with the results of Kohn and Luttinger, below a temperature that, near unitarity, we find to be within current experimental capabilities. We present possible experimental signatures of the ppp-wave state using radiofrequency spectroscopy as well as density-density correlations after free expansion.
We consider imbalanced Fermi gases with strong attractive interactions, for which Cooper-pair formation plays an important role. The two-component mix-tures consist either of identical fermionic atoms in two different hyperfine states, or of two different atomic species both occupying only a single hyperfine state. In both cases, the number of atoms for each component is allowed to be differ-ent, which leads to a spin imbalance, or spin polarization. Two different atomic species also lead to a mass imbalance. Imbalanced Fermi gases are relevant to condensed-matter physics, nuclear physics and astroparticle physics. They have been studied intensively in recent years, following their experimental realization in ultracold atomic Fermi gases. The experimental control in such a system allows for a systematic study of the equation of state and the phase diagram as a function of temperature, spin polarization and interaction strength. In this re-view, we discuss the progress in understanding strongly-interacting imbalanced Fermi gases, where a main goal is to describe the results of the highly controlled experiments. We start by discussing Feshbach resonances, after which we treat the imbalanced Fermi gas in mean-field theory to give an introduction to the relevant physics. We encounter several unusual superfluid phases, including phase-separation, gapless Sarma superfluidity, and supersolidity. To obtain a more quantitative description of the experiments, we review also more sophisti-cated techniques, such as diagrammatic methods and the renormalization-group theory. We end the review by discussing two theoretical approaches to treat the inhomogeneous imbalanced Fermi gas, namely the Landau-Ginzburg theory and the Bogoliubov-de Gennes approach. Key words: