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arXiv:cond-mat/0603190 · Series on advances in quantum many-body theory

Realization, Characterization, and Detection of Novel Superfluid Phases with Pairing between Unbalanced Fermion Species

Kun Yang

Published Nov 1, 2006• 3 citations
arXivHTMLPDF

Abstract

In this chapter we review recent experimental and theoretical work on various novel superfluid phases in fermion systems, that result from pairing fermions of different species with unequal densities. After briefly reviewing existing experimental work in superconductors subject to a strong magnetic field and trapped cold fermionic atom systems, we discuss how to characterize the possible pairing phases based on their symmetry properties, and the structure/topology of the Fermi surface(s) formed by the unpaired fermions due to the density imbalance. We also discuss possible experimental probes that can be used to directly detect the structure of the superfluid order parameter in superconductors and trapped cold atom systems, which may establish the presence of some of these phases unambiguously.

DOI
10.1142/9789812773043_0010

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In this chapter we review recent experimental and theoretical work on various novel superfluid phases in fermion systems, that result from pairing fermions of different species with unequal densities. After briefly reviewing existing experimental work in superconductors subject to a strong magnetic field and trapped cold fermionic atom systems, we discuss how to characterize the possible pairing phases based on their symmetry properties, and the structure/topology of the Fermi surface(s) formed by the unpaired fermions due to the density imbalance. We also discuss possible experimental probes that can be used to directly detect the structure of the superfluid order parameter in superconductors and trapped cold atom systems, which may establish the presence of some of these phases unambiguously.
In this chapter the recent theoretical work on phase transition in imbalanced fermion superfluids is reviewed. The imbalanced systems are those in which the two fermionic species candidate to form pairing have different Fermi surfaces or densities. We consider systems subjected to weak interactions. In this scenario two distinct phase transitions are predicted to occur. A thermodynamical phase transition, induced by the temperature (T), and a quantum phase transition as a function of the increasing chemical potentials asymmetry, that takes place at zero temperature. We also briefly discuss some recent experimental work at non-zero T with imbalanced Fermi gases in cold atomic traps.
Abstract This chapter reviews experimental studies of fermionic superfluidity in ultracold atomic gases. Scattering properties of ultracold atoms and Feshbach resonances are introduced. The basic theoretical framework is presented based on the Leggett ansatz that provides intuition into many of the observed phenomena. The various experimental observations related to fermion pair condensation and superfluidity are described. The thermodynamic measurements of strongly interacting Fermi gases are considered. Experiments on superfluidity in the presence of population imbalance are reviewed. These studies have led to the observation of the Clogston–Chandrasekhar (or Pauli) limit of fermionic superfluidity and to the identification of a novel attractive Fermi liquid of polaronic quasiparticles. Novel Fermi systems, such as Fermi gases in lower dimensions, optical lattices, dipolar Fermi gases, and spin–orbit coupled Fermi gases, are also touched on briefly.
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:
We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in the limit of weak coupling. We focus on the dependence of the pairing gap and the free energy on the variations in the number densities of the two species while the total density of the system is held fixed. As the density asymmetry is increased, the system exhibits a transition from a homogenous Bardeen-Cooper-Schrieffer (BCS) phase to phases with spontaneously broken global space symmetries. One such realization is the deformed Fermi surface superfluidity (DFS) which exploits the possibility of deforming the Fermi surfaces of the species into ellipsoidal form at zero total momentum of Cooper pairs. The critical asymmetries at which the transition from DFS to the unpaired state occurs are larger than those for the BCS phase. In this precritical region the DFS phase lowers the pairing energy of the asymmetric BCS state. We compare quantitatively the DFS phase to another realization of superconducting phases with broken translational symmetry: the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell phase, which is characterized by a nonvanishing center-of-mass momentum of the Cooper pairs. The possibility of the detection of the DFS phase in the time-of-flight experiments is discussed and quantified for the case of 6Li^{6}\mathrm{Li}6Li atoms trapped in two different hyperfine states.
We report the observation of pairing in a gas of atomic fermions with unequal numbers of two components. Beyond a critical polarization, the gas separates into a phase that is consistent with a superfluid paired core surrounded by a shell of normal unpaired fermions. The critical polarization diminishes with decreasing attractive interaction. For near-zero polarization, we measured the parameter beta = -0.54 +/- 0.05, describing the universal energy of a strongly interacting paired Fermi gas, and found good agreement with recent theory. These results are relevant to predictions of exotic new phases of quark matter and of strongly magnetized superconductors.
As a means of realizing oscillatory pairing between fermions, we study superfluid pairing between two fermion ``spin'' species that are confined to adjustable spin-dependent trapping potentials. Focusing on the one-dimensional limit, we find that with increasing separation between the spin-dependent traps, the fermions exhibit distinct phases, including a fully paired phase, a spin-imbalanced phase with oscillatory pairing, and an unpaired fully spin-polarized phase. We obtain the phase diagram of fermions in such a spin-split trap and discuss signatures of these phases in cold-atom experiments.