We obtain a variety of predictions for the properties of population-imbalanced (or polarized) fermionic superfluids near their tricritical point. In the vicinity of the high-symmetry tricritical point, observable quantities such as the cloud shape, heat capacity, and local polarization should exhibit distinct behavior arising from the tricritical scaling laws, as well as logarithmic corrections to scaling reflecting the marginal nature of interactions.
We investigate a two-component atomic Fermi gas with population imbalance in the presence of Rashba-type spin-orbit coupling (SOC). As a competition between SOC and population imbalance, the finite-temperature phase diagram reveals a large varieties of new features, including the expanding of the superfluid state regime and the shrinking of both the phase separation and the normal regimes. For sufficiently strong SOC, the phase separation region disappears, giving way to the superfluid state. We find that the tricritical point moves toward regime of low temperature, high magnetic field, and hi…
We propose a mean-field, phenomenological Ginzburg-Landau free energy functional with two competing order parameters for a two-component, spin-polarized Fermi gas. This free energy supports a tricritical point which is different from the conventional one and this change offers a correct understanding of the experimental phase diagram of imbalanced Fermi systems (Shin et al, Nature, 2008). The specific heat also happens to be different than in standard theory.
We study resonantly-paired s-wave superfluidity in a degenerate gas of two species (hyperfine states labeled by $\uparrow,\downarrow$) of fermionic atoms when the numbers $N_{\uparrow}$ and $N_{\downarrow}$ of the two species are {\it unequal}, i.e., the system is "polarized". We find that the continuous crossover from the Bose-Einstein condensate (BEC) limit of tightly-bound diatomic molecules to the Bardeen-Cooper-Schrieffer (BCS) limit of weakly correlated Cooper pairs, studied extensively at equal populations, is interrupted by a variety of distinct phenomena under an imposed population di…
We study a two-component Fermi system with attractive interactions and different populations of the two species in a cubic lattice. For an intermediate coupling we find a uniformly polarized superfluid which is stable down to very low temperatures. The momentum distribution of this phase closely resembles that of the Sarma phase, characterized by two Fermi surfaces. This phase is shown to be stabilized by a potential energy gain, as in a BCS superfluid, in contrast to the unpolarized BEC which is stabilized by kinetic energy. We present general arguments suggesting that preformed pairs in the …
The interior of a neutron star is expected to be occupied by a neutron $^3P_2$ superfluid, which is the condensate of spin-triplet $p$-wave Cooper pairs of neutrons with total angular momentum $J=2$. Here we investigate the thermodynamic stability of $^3P_2$ superfluids in a neutron-star interior under a strong magnetic field. Using the theory incorporating the finite size correction of neutron Fermi surface, we show that the spin-polarized phases of $^3P_2$ superfluids, the magnetized biaxial nematic phase and the ferromagnetic phase, appear in high temperatures and high magnetic fields. Thes…
We calculate the excitation spectra of a spin-polarized Hubbard chain away from half-filling, using a high-precision momentum-resolved time-dependent Density Matrix Renormalization Group method. Focusing on the U<0 case, we present in some detail the single-fermion, pair, density and spin spectra, and discuss how spin-charge separation is altered for this system. The pair spectra show a quasi-condensate at a nonzero momentum proportional to the polarization, as expected for this Fulde-Ferrel-Larkin-Ovchinnikov-like superfluid.
We explore analytically the nature of the transition to the Fulde-Ferrel-Larkin-Ovchinnikov superfluid phases in the vicinity of the tricritical point, where these phases begin to appear. We make use of an expansion of the free energy up to an overall sixth order, both in order parameter amplitude and in wavevector. We first explore the minimization of this free energy within a subspace, made of arbitrary superpositions of plane waves with wavevectors of different orientations but same modulus. We show that the standard second order FFLO phase transition is unstable and that a first order tran…
Motivated by recent experiments in trapped Fermi gas with spin population imbalance, we discuss the effects of the quantum and thermal fluctuations of the interface between a fully paired superfluid core and a fully polarized Fermi gas. We demonstrate that even if there is no true partially polarized thermodynamic phase in bulk, the interface fluctuation can give rise to a partially polarized transition regime in trap. Our theory yields a definite prediction for the functional forms of the spatial profile of spin polarization and pairing gap, and we show that the spin-resolved density profiles…
Based on the integrable Gaudin model and local density approximation, we discuss the phase structure of one-dimensional trapped Fermi gases with imbalanced spin populations for arbitrary attractive interactions. A phase separation state, with a polarized superfluid core immersed in an unpolarized superfluid shell, emerges below a critical spin polarization. Above it, a coexistence of polarized superfluid matter and a fully polarized normal gas is favored. These two exotic states could be realized experimentally in highly elongated atomic traps, and diagnosed by measuring the lowest density com…
It is shown theoretically that ferromagnetic superconductors, UGe$_2$, URhGe, and UCoGe can be described in terms of the A-phase like triplet pairing similar to superfluid $^3$He in a unified way, including peculiar reentrant, S-shape, or L-shape $H_{\rm c2}$ curves. The associated double transition inevitable between the A$_1$ and A$_2$-phases in the $H$-$T$ plane is predicted, both of which are characterized by non-unitary state with broken time reversal symmetry and the half-gap. UTe$_2$, which has been discovered quite recently to be a spin-polarized superconductor, is analyzed successivel…
We calculate the zero temperature phase diagram of a polarized two-component Fermi gas in an array of weakly-coupled parallel one-dimensional (1D) 'tubes' produced by a two-dimensional optical lattice. Increasing the lattice strength drives a crossover from three-dimensional (3D) to 1D behavior, stabilizing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulated superfluid phase. We argue that the most promising regime for observing the FFLO phase is in the quasi-1D regime, where the atomic motion is largely 1D but there is weak tunneling in the other directions that stabilizes long range order.…
We argue that, for the recent experiments with imbalanced fermion gases, a temperature difference may occur between the normal (N) and the gapped superfluid (SF) phase. Using the mean-field formalism, we study particle scattering off the N-SF interface from the deep BCS to the unitary regime. We show that the thermal conductivity across the interface drops exponentially fast with increasing $h/k_B T$, where $h$ is the chemical potential imbalance. This implies a blocking of thermal equilibration between the N and the SF phase. We also provide a possible mechanism for the creation of gap oscill…
We investigate the superfluid properties of d-wave pairing symmetry within the Extended Hubbard Model (EHM) in a magnetic field. We analyze the temperature and magnetic field dependencies of the order parameter. We find that in the two-dimensional case, the spatially homogeneous spin polarized superfluidity ($SC(P\neq0)$) is stable in the weak coupling limit, at T=0, as opposed to the s-wave pairing symmetry case in 2D. We construct the ground state phase diagrams both for fixed chemical potential ($μ$) and electron concentration ($n$). Furthermore, we obtain the temperature vs. magnetic field…
We report on a study of the superfluid state of spin-polarized atomic Li6 confined in a magnetic trap. Density profiles of this degenerate Fermi gas, and the spatial distribution of the BCS order parameter are calculated in the local density approximation. The critical temperature is determined as a function of the number of particles in the trap. Furthermore we consider the mechanical stability of an interacting two-component Fermi gas, both in the case of attractive and repulsive interatomic interactions. For spin-polarized Li6 we also calculate the decay rate of the gas, and show that withi…
We study the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs (LP's) with increasing attraction, in the presence of the Zeeman magnetic field ($h$) for $d=2$, within the spin-polarized attractive Hubbard model. The broken symmetry Hartree approximation {as well as the} strong coupling expansion are used. We also apply the Kosterlitz-Thouless (KT) scenario to determine the phase coherence temperatures. For spin independent hopping integrals ($t^{\uparrow}=t^{\downarrow}$), we find no stable homogeneous polarized superfluid (SC$_M$) stat…
Recent experiments on imbalanced fermion gases have proved the existence of a sharp interface between a superfluid and a normal phase. We show that, at the lowest experimental temperatures, a temperature difference between N and SF phase can appear as a consequence of the blocking of energy transfer across the interface. Such blocking is a consequence of the existence of a SF gap, which causes low-energy normal particles to be reflected from the N-SF interface. Our quantitative analysis is based on the Hartree-Fock-Bogoliubov-de Gennes formalism, which allows us to give analytical expressions …
We study equal mass population imbalanced two-component atomic Fermi gas with unequal trap frequencies $(ω_{\uparrow} \neq ω_{\downarrow})$ at zero temperature using the local density approximation (LDA). We consider the strongly attracting Bose-Einstein condensation (BEC) limit where polarized (gapless) superfluid is stable. The system exhibits shell structure: unpolarized SF$\to$polarized SF$\to$normal N. Compared to trap symmetric case, when the majority component is tightly confined the gapless superfluid shell grows in size leading to reduced threshold polarization to form polarized (gapl…
We point out an error in recent work by Pao, Wu, and Yip [Phys. Rev.B {\bf 73}, 132506 (2006)], that stems from their use of a necessary but not sufficient condition [positive compressibility (magnetic susceptibility) and superfluid stiffness] for the stability of the ground state of a polarized Fermi gas. As a result, for a range of detunings their proposed ground-state solution is a local maximum rather than a minimum of the ground state energy, which thereby invalidates their proposed phase diagram for resonantly interacting fermions under an imposed population difference.
We study the role of particle transport and evaporation on the phase separation of an ultracold, spin-polarized atomic Fermi gas. We show that the previously observed deformation of the superfluid paired core is a result of evaporative depolarization of the superfluid due to a combination of enhanced evaporation at the center of the trap and the inhibition of spin transport at the normal-superfluid phase boundary. These factors contribute to a nonequilibrium jump in the chemical potentials at the phase boundary. Once formed, the deformed state is highly metastable, persisting for times of up t…
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 $t$-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 optical properties of optimally-doped Bi_2Sr_2CaCu_2O_{8+δ} (Bi2212) have been measured normal to the edge planes [ac plane, bc plane, and (1\bar{1}0) plane], for light polarized parallel to nodal and anti-nodal (gap) directions, respectively. While the superfluid contribution can be obtained from the optical conductivities in the (1\bar{1}0)-plane, it is unobservable in the ac and bc-planes. This apparent asymmetry implies that the edge region of high-T_c cuprates is unusual and further supports a d-wave symmetry of the superconducting order parameter.
The superfluid phase diagrams of a two-dimensional cold polarized Fermi gas in the BCS-BEC crossover are systematically and analytically investigated. In the BCS-Leggett mean field theory, the transition from unpolarized superfluid phase to normal phase is always of first order. For a homogeneous system, the two critical Zeeman fields and the critical population imbalance are analytically determined in the whole coupling parameter region, and the superfluid-normal mixed phase is shown to be the ground state between the two critical fields. The density profile in the presence of a harmonic trap…
Properties of strongly interacting, two-component finite Fermi systems are discussed within the recently developed coordinate-space Hartree-Fock-Bogoliubov (HFB) code {\hfbax}. Two illustrative examples are presented: (i) weakly bound deformed Mg isotopes, and (ii) spin-polarized atomic condensates in a strongly deformed harmonic trap.
We derive the underlying finite temperature theory which describes Fermi gas superfluidity with population imbalance in a homogeneous system. We compute the pair formation temperature and superfluid transition temperature $T_c$ and superfluid density in a manner consistent with the standard ground state equations, and thereby present a complete phase diagram. Finite temperature stabilizes superfluidity, as manifested by two solutions for $T_c$, or by low $T$ instabilities. At unitarity the polarized state is an ``intermediate temperature superfluid".
Recently, a homogeneous superfluid state with a single gapless Fermi surface was predicted to be the ground state of an ultracold Fermi gas with spin population imbalance in the regime of molecular Bose-Einstein condensation. We study vortices in this novel state using a symmetry-based effective field theory, which captures the low-energy physics of gapless fermions and superfluid phase fluctuations. This theory is applicable to all spin-imbalanced ultracold Fermi gases in the superfluid regime, regardless of whether the original fermion pairing interaction is weak or strong. We find a remarka…
A new excitation mode has been predicted to exist in the unitary Fermi gas. It has a form of a spin-polarized impurity, which was dubbed as ferron. It is characterized by a closed nodal surface of the pairing field surrounding a partially spin-polarized superfluid region, where the phase differs by $π$. In this paper, we discuss the effect of temperature on the generation of the ferron and the adiabaticity of the spin-polarizing potential together with ferron's ground state properties.
The real-space densities of a polarized strongly-interacting two-component Fermi gas of $^6$Li atoms reveal two low temperature regimes, both with a fully-paired core. At the lowest temperatures, the unpolarized core deforms with increasing polarization. Sharp boundaries between the core and the excess unpaired atoms are consistent with a phase separation driven by a first-order phase transition. In contrast, at higher temperatures the core does not deform but remains unpolarized up to a critical polarization. The boundaries are not sharp in this case, indicating a partially-polarized shell be…
The superfluid properties of the attractive Hubbard model in a Zeeman magnetic field, and in the weak coupling regime have been investigated. The temperature and magnetic field dependencies of the order parameter have been analyzed. Furthermore, the temperature vs. magnetic field and temperature vs. spin polarization phase diagrams for the 2D and 3D lattices have been obtained. For some parameters a reentrant transition has been found.
