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arXiv:1003.0213 · Physical Review Letters

Normal Phase of an Imbalanced Fermi Gas

Christophe Mora, Frédéric Chevy

Published Jun 8, 2010• 48 citations
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Abstract

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.

DOI
10.1103/physrevlett.104.230402

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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.

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•Jan 1, 2009•0 citations
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.
We consider the highly spin-imbalanced limit of a two-component Fermi gas, where there is a small density of $\ensuremath{\downarrow}$ impurities attractively interacting with a sea of $\ensuremath{\uparrow}$ fermions. In the single-impurity limit at zero temperature, there exists the so-called polaron-molecule transition, where the impurity sharply changes its character by binding a $\ensuremath{\uparrow}$ fermion at sufficiently strong attraction. Using a recently developed variational approach, we calculate the thermodynamic properties of the impurity, and we show that the transition becomes a smooth crossover at finite temperature due to the thermal occupation of excited states in the impurity spectral function. However, remnants of the single-impurity transition are apparent in the momentum-resolved spectral function, which can in principle be probed with Raman spectroscopy. We furthermore show that the Tan contact exhibits a characteristic nonmonotonic dependence on temperature that provides a signature of the zero-temperature polaron-molecule transition. For a finite impurity density, we argue that descriptions purely based on the behavior of the Fermi polaron are invalid near the polaron-molecule transition, since correlations between impurities cannot be ignored. In particular, we show that the spin-imbalanced system undergoes phase separation at low temperatures due to the strong attraction between $\ensuremath{\uparrow}\ensuremath{\downarrow}$ molecules induced by the Fermi sea. Thus, we find that the impurity spectrum and the induced impurity-impurity interactions are key to understanding the phase diagram of the spin-imbalanced Fermi gas.
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.
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.
In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions--the so-called Fermi polaron problem. On one hand, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides a quantitatively reliable insight into the phase diagram of strongly interacting population-imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to the study of itinerant ferromagnetism, a long-standing problem in quantum mechanics.
This thesis presents a theoretical study of strongly-interacting Fermi systems with population imbalance, which is motivated by some differences in cold atoms experiments. We calculate the energy of a single fermion interacting resonantly with a Fermi sea of different species fermions in anisotropic traps, and show that finite particle numbers and the trap geometry impact the phase structure and the critical polarization, the limit of resonance superfluidity in traps. Our findings contribute to understanding some experimental discrepancies as finite-size and confinement effects. For an imbalanced gas in the uniform system, we calculate the energy of adding an impurity, and construct the equation of state of the partially-polarized normal Fermi liquid. Finally, we study the properties of a spin-down polaron in a trapped gas containing arbitrary numbers of spin-up and spin-down fermions, and derive a self-consistent equation for the polaron energy.