We study the effect of the induced interaction on the superfluidtransition temperature of a spin-polarized Fermi gas. In the BCS limit, the polarization is very small in the superfluid state, and the effect of the induced interaction is almost the same as in the spin-balanced case. The temperature Tt and the polarization Pt of the tricritical point are both reduced from mean-field results by a factor about 2.22. This reduction is also significant beyond the BCS limit. In the unitary limit, we find (Pt,Tt/TF)=(0.42,0.16), in comparison with mean-field and experimental results.
In this work we analyze the dynamical behavior of the collision between two clouds of fermionic atoms with opposite spin polarization. By means of the time-evolving block decimation (TEBD) numerical method, we simulate the collision of two one-dimensional clouds in a lattice. There is a symmetry in the collision behaviour between the attractive and repulsive interactions. We analyze the pair formation dynamics in the collision region, providing a quantitative analysis of the pair formation mechanism in terms of a simple two-site model.
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.
We calculate the single particle spectral density of a normal (non-superfluid) two component gas of fermions in the BCS-BEC crossover within a T-matrix approximation. We review how non-condensed pairs lead to a spectral density reminiscent of the ordered state, and explore how a gap-like feature in the spectrum evolves as one changes the polarization of the gas. As the gas is polarized we find that this pseudogap becomes more diffuse and moves away from the Fermi level, reflecting the fact that fewer pairs are present but that they still play an important role in the excitations.
We study the three-fermion problem within a 1D model of a Feshbach resonance in order to gain insight into how the FFLO-like state at small negative scattering lengths evolves into a Bose-Fermi mixture at small positive scattering lengths. The FFLO state possesses an oscillating superfluid correlation function, while in a Bose-Fermi mixture correlations are monotonic. We find that this behavior is is already present at the 3-body level. We present an exact study of the 3-body problem, and gain extra insights by considering worldlines of a path integral Monte-Carlo calculation.
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…
We demonstrate the existence of a new type of spatially localized excitations in the unitary Fermi gas: spin polarized droplets with a peculiar internal structure involving the abrupt change of the pairing phase at the surface of the droplet. It resembles the structure of the Josephson-$π$ junction occurring when a slice of a ferromagnet is sandwiched between two superconductors. The stability of the impurity is enhanced by the mutual interplay between the polarization effects and the pairing field, resulting in an exceptionally long-lived state. The prospects for its realization in experiment…
We calculate the pair susceptibility of an attractive spin-polarized Fermi gas in the normal phase, as a function of the pair momentum. Close to unitarity, we find a strong enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing fluctuations over an extended region of the temperature-polarization phase diagram, which manifests itself as a pronounced peak in the pair-momentum distribution at a finite pair momentum. This peak should be amenable to experimental observation at achievable temperatures in a box-like trapping potential, as a fingerprint of FFLO pairing. Our calculations rest o…
Using the asymptotic Bethe Ansatz, we obtain an exact solution of the many-body problem for 1D spin-polarized fermions with resonant p-wave interactions, taking into account the effects of both scattering volume and effective range. Under typical experimental conditions, accounting for the effective range, the properties of the system are significantly modified due to the existence of "shape" resonances. The excitation spectrum of the considered model has unexpected features, such as the inverted position of the particle- and hole-like branches at small momenta, and roton-like minima. We find …
In the present paper we investigate the Tonks-Girardeau gas confined in a harmonic trap at finite temperature with thermal Bose-Fermi mapping method. The pair distribution, density distribution, reduced one-body density matrix, the occupations number of natural orbitals, and momentum distribution are evaluated. In the whole temperature regime the pair distribution and density distribution exhibit the same properties as those of polarized free Fermions because both of them depend on the modulus of wavefunction rather than wavefunction. While the reduced one-body density matrix, the natural orbi…
The method of many-particle quantum hydrodynamics has been recently developed, particularly this method has been used for an electrically polarized Bose-Einstein condensate. In this paper, we present the development of this method for an electrically polarized three dimensional Fermi gas. We derive corresponding dynamical equations: equation polarization and equation of polarization current evolution as well as the Euler and continuity equations. We study dispersion dependencies of collective excitations in a polarized Fermi gas and consider interference of an equilibrium polarization on dispe…
We study the exact dynamics of a one-dimensional spin-polarized gas of fermions in a double-well potential at zero and finite temperature. Despite the system is made of non-interacting fermions, its dynamics can be quite complex, showing strongly aperiodic spatio-temporal patterns during the tunneling. The extension of these results to the case of mixtures of spin-polarized fermions in interaction with self-trapped Bose-Einstein condensates (BECs) at zero temperature is considered as well. In this case we show that the fermionic dynamics remains qualitatively similar to the one observed in abs…
We study ultracold fermionic atoms trapped in a three dimensional optical lattice by combining the real-space dynamical mean-field approach with continuous-time quantum Monte Carlo simulations. For a spin-unpolarized system we show results the density and pair potential profile in the trap for a range of temperatures. We discuss how a polarized superfluid state is spatially realized in the spin-polarized system with harmonic confinement at low temperatures and present the local particle density, local magnetization, and pair potential.
Motivated by a recent experiment at MIT, we consider the collision of two clouds of spin-polarized atomic Fermi gases close to a Feshbach resonance. We explain why two dilute gas clouds, with underlying attractive interactions between their constituents, bounce off each other in the strongly interacting regime. Our hydrodynamic analysis, in excellent agreement with experiment, gives strong evidence for a metastable many-body state with effective repulsive interactions.
The spectrum of collective excitations of degenerate partially polarized spin-1/2 fermions is considered. The spin-up fermions and the spin-down fermions are considered as different fluids. Corresponding two-fluid hydrodynamics consistent with a non-linear Pauli equation is suggested. An equation of state for the spin current caused by the distribution of particles on different energy levels is suggested for the degenerate regime, where the spin current is caused by the Pauli blocking. Spectrum of three waves is found as a solution of the hydrodynamic equations: two sound waves and one spin wa…
We study inelastic two-body relaxation in a spin-polarized ultracold Fermi gas in the presence of a p-wave Feshbach resonance. It is shown that in reduced dimensionalities, especially in the quasi-one-dimensional case, the enhancement of the inelastic rate constant on approach to the resonance is strongly suppressed compared to three dimensions. This may open promising paths for obtaining novel many-body states.
We investigate the ground state of the two-dimensional polarized Fermi gas with spin-orbit coupling and construct the phase diagram at zero temperature. We find there exist phase separation when the binding energy is low. As the binding energy increasing, the topological nontrivial superfluid phase coexist with topologically trivial superfluid phase which is topological phase separation. The spin-orbit coupling interaction enhance the triplet pairing and destabilize the phase separation against superfluid phase.
Recent experiments with ultra-cold atoms have demonstrated the possibility of realizing experimentally fermionic superfluids with imbalanced spin populations. We discuss how these developments have shed a new light on a half- century old open problem in condensed matter physics, and raised new interrogations of their own.
We present a superfluid theory of a polarized dipolar Fermi gas. For two dipolar molecules each of which consists of two atoms with positive charge and negative charge, we derive an effective dipole-dipole pairing interaction. Using this pairing interaction, we show that the resulting BCS gap equation is not suffered from the well-known ultraviolet divergence, so that one can quantitatively predict superfluid properties of a dipolar Fermi gas. Using this cutoff-free superfluid theory, we examine the symmetry of the superfluid order parameter at T=0. We also discuss the deformation of the Fermi…
We study the BCS-Bose Einstein Condensation (BEC) crossover of a three dimensional spin polarized Fermi gas with Rashba spin-orbital-coupling (SOC). At finite temperature, the effects of non-condensed pairs due to the thermal excitation are considered based on the $G_0G$ pair fluctuation theory. These fluctuations generate a pseudogap even persistent above $T_c$. Within this framework, the Sarma state or the spin polarized superfluid state and polarized pseudogap state are explored in detail. The resulting $T_c$ curves show that the enhancement of pairing due to the SOC roughly cancels out the…
This paper a kinetic Boltzmann equation having a general type of collision kernel and modelling spin-dependent Fermi gases at low temperatures modelled by a kinetic equation of Boltzmann type. The distribution functions have values in the space of positive hermitean 2x2 complex matrices. Global existence of bounded weak solutions is proved in L1 to the initial value problem in a periodic box.
We study low temperature thermodynamic properties of a polarized Fermi gas trapped in a quartic anharmonic potential. We use a semi classical approximation and a low temperature series expansion method to derive analytical expressions for various thermodynamic quantities. These quantities include the total energy, particle number, and heat capacity for both positive and negative anharmonic confinements.
We consider a quasi-one-dimensional model of a two-component Fermi gas at zero temperature on one, two and three-leg attractive-U Hubbard ladders. We construct the grand canonical phase diagram of a two-component spin-polarized gas. We find that the structure of the phase diagram of the attractive-U Hubbard model for two and three leg ladders significantly differs q from the structure of the phase diagram of a single chain. We argue that the single chain model is a special case, and that multichain ladders display qualitative features of the 1D-to-3D crossover, observed in experiments with tra…
In this paper we analytically investigate the ground-state properties of a two-dimensional polarized degenerate Fermi gas in a high-finesse optical cavity, which is governed by a generalized Fermi-Dicke model with tunable parameters. By solving the photon-number dependent Bogoliubov-de-Gennes equation, we find rich quantum phases and phase diagrams, which depend crucially on the fermion-photon coupling strength, the fermion-fermion interaction strength, and the atomic resonant frequency (effective Zeeman field). In particular, without the fermion-fermion interaction and with a weak atomic reso…
We study a two-component Fermi gas that is so strongly polarized that it remains normal fluid at zero temperature. We calculate the occupation numbers within the particle-particle random-phase approximation, which is similar to the Nozieres-Schmitt-Rink approach. We show that the Luttinger theorem is fulfilled in this approach. We also study the change of the chemical potentials which allows us to extract, in the limit of extreme polarization, the polaron energy.
We study by Monte Carlo methods the thermodynamics of a spin polarized gas of non-relativistic fermions in 1+1 dimensions. The main result of this work is that our action suffers no significant sign problem for any spin polarization in the region relevant for dilute degenerate fermi gases. This lack of sign problem allows us to study attractive spin polarized fermions non-perturbatively at spin polarizations not previously explored. For some parameters values we verify results previously obtained by methods which include an uncontrolled step like complex Langevin and/or analytical continuation…
We study the tunneling of a spin polarized Fermi gas in a three-dimensional double well potential, focusing on the time dynamics starting from an initial state in which there is an imbalance in the number of particles in the two wells. Although fermions in different doublets of the double well tunnel with different frequencies, we point out that (incoherent) oscillations of a large number of particles can arise, as a consequence of the presence of transverse degrees of freedom. Estimates of the doublet structure and of the occupation of transverse eigenstates for a realistic experimental setup…
We systematically develop a density functional description for the equilibrium properties of a two-dimensional, harmonically trapped, spin-polarized dipolar Fermi gas based on the Thomas-Fermi von Weizsäcker approximation. We pay particular attention to the construction of the two-dimensional kinetic energy functional, where corrections beyond the local density approximation must be motivated with care. We also present an intuitive derivation of the interaction energy functional associated with the dipolar interactions, and provide physical insight into why it can be represented as a local fun…
We study the phase separation of a spin polarized Fermi gas with spin-orbit coupling near a wide Feshbach resonance. As a result of the competition between spin-orbit coupling and population imbalance, the phase diagram for a uniform gas develops a rich structure of phase separation involving gapless superfluid states which are topologically non-trivial. We find that these novel gapless phases can be stabilized by intermediate spin-orbit coupling strengths. We then demonstrate the phase separation induced by an external trapping potential and discuss the optimal parameter region for the experi…
We show that spin-orbit coupling (SOC) gives rise to pairing instability in a highly polarized two-dimensional Fermi gas for arbitrary interaction strength. The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-like molecular state, which undergoes a first-order transition into a pairing state with zero center-of-mass momentum as the parameters are tuned. These pairing states are metastable against a polaron state dressed by particle-hole fluctuations for small SOC. At large SOC, a polaron-molecule transition exists, which suggests a phase transition between the topological su…
We report the results of the computation of the order $(k_{\rm F}a_0)^2$ correction, where $k_{\rm F}=3π^2ρ$ is the Fermi wave vector and $a_0$ the $s$-wave scattering length of the repulsive interaction, to the ground-state energy of a mixture of oppositely polarized $N_a$ spin $1/2$ fermions $a$ of masses $m_a$ and $N_b$ spin $1/2$ fermions $b$ of masses $m_b$ ($ρ=N/V$, $N=N_a+N_b$). It is shown that the results of the paper \cite{FraPil} in which the same correction has been computed entirely numerically, using a more traditional approach, can be easily and semianalytically reproduced using…
Most recently, path integral molecular dynamics (PIMD) has been successfully applied to perform simulations of identical bosons and fermions by B. Hirshberg et al.. In this work, we demonstrate that PIMD can be developed to calculate Green's function and extract momentum distribution for spin-polarized fermions. In particular, we show that the momentum distribution calculated by PIMD has potential application to numerous quantum systems, such as cold atom simulation of Mott insulator in Fermi-Hubbard model.
We consider a mixture of a spin-polarized Fermi gas and a dipolar Bose-Einstein condensate in which s-wave scattering between fermions and the quasiparticles of the dipolar condensate can result in an effective attractive Fermi-Fermi interaction anisotropic in nature and tunable by the dipolar interaction. We show that such an interaction can significantly increase the prospect of realizing a superfluid with a gap parameter characterized with a coherent superposition of all odd partial waves. We formulate, in the spirit of the Hartree-Fock-Bogoliubov mean-field approach, a theory which allows …
We consider a polarized Fermi gas in the BCS-BEC crossover region above the critical temperature within a T matrix formalism. By treating the mean-field like shift of the quasiparticle energies in a self-consistent manner, we avoid the known pathological behavior of the standard Nozieres-Schmitt-Rink approach in the polarized case, i.e., the polarization has the right sign and the spin polarizability is positive. The momentum distributions of the correlated system are computed and it is shown that, in the zero-temperature limit, they satisfy the Luttinger theorem. Results for the phase diagram…
Usually, hydrodynamic equations are restricted by the continuity and Euler equations. However, the account of the higher moments of the distribution function gives better description of the kinetic properties. Therefore, the pressure tensor evolution equation (PTEE) is derived for spin polarized degenerate fermions. Moreover, it is found that the pressure tensor enters the interaction term generalizing the p-wave interaction in the Euler equation. Hence, the PTEE allows to give a more accurate description of the interaction in Euler equation. Next, the interaction is calculated for the PTEE. T…
We analyze the collision of three identical spin-polarized fermions at zero collision energy, assuming arbitrary finite-range potentials, and define the corresponding three-body scattering hypervolume $D_F$. The scattering hypervolume $D$ was first defined for identical bosons in 2008 by one of us. It is the three-body analog of the two-body scattering length. We solve the three-body Schrödinger equation asymptotically when the three fermions are far apart or one pair and the third fermion are far apart, deriving two asymptotic expansions of the wave function. Unlike the case of bosons for whi…
We study the transverse spin dynamics of trapped polarized Fermi gases in the high temperature limit. In the non-interacting collisionless regime, a magnetic field gradient induces collective spin wave oscillations. In the strongly interacting collisional regime, the dynamics are governed by spin diffusion. These two limits have been extensively studied both experimentally and theoretically, but the crossover between them has received less attention. In this paper, we use a quantum Boltzmann equation to study transverse spin dynamics and show how the excitations evolve from dispersive to diffu…
Using density functional theory in a time dependent approach we determine the frequencies of the compressional modes of the normal phase of a Fermi gas at unitarity as a function of its polarization. Our energy functional accounts for the typical elastic deformations exhibited by Landau theory of Fermi liquids. The comparison with the available experiments is biased by important collisional effects affecting both the {\it in phase} and the {\it out of phase} oscillations even at the lowest temperatures. New experiments in the collisionless regime would provide a crucial test of the applicabili…
Recently, a seminal STIRAP experiment allowed the creation of 40K-87Rb molecules in the rovibrational ground state [K.-K. Ni et al., Science 322, 231 (2008)]. In order to describe such a polarized dipolar Fermi gas in the hydrodynamic regime, we work out a variational time-dependent Hartree-Fock approach. With this we calculate dynamical properties of such a system as, for instance, the frequencies of the low-lying excitations and the time-of-flight expansion. We find that the dipole-dipole interaction induces anisotropic breathing oscillations in momentum space. In addition, after release fro…
We address the phase of a highly polarized Fermi gas across a narrow Feshbach resonance starting from the problem of a single down spin fermion immersed in a Fermi sea of up spins. Both polaron and pairing states are considered using the variational wave function approach, and we find that the polaron to pairing transition will take place at the BCS side of the resonance, strongly in contrast to a wide resonance where the transition is located at the BEC side. For pairing phase, we find out the critical strength of repulsive interaction between pairs above which the mixture of pairs and fermio…
We theoretically study the pairing behavior of the unitary Fermi gas in the normal phase. Our analysis is based on the static spin susceptibility, which characterizes the response to an external magnetic field. We obtain this quantity by means of the complex Langevin approach and compare our calculations to available literature data in the spin-balanced case. Furthermore, we present results for polarized systems, where we complement and expand our analysis at high temperature with high-order virial expansion results. The implications of our findings for the phase diagram of the spin-polarized …
I discuss the advantages and disadvantages of several procedures, some known and some new, for constructing stationary states within the mean field approximation for a system with pairing correlations and unequal numbers spin-up and spin-down fermions, using the two chemical potentials framework. One procedure in particular appears to have significant physics advantages over previously suggested in the literature computational frameworks. Moreover, this framework is applicable to study strongly polarized superfluid fermion systems with arbitrarily large polarizations and with arbitrary total p…
The transport properties of one-dimensional Fermi gases at low-temperatures are often described by the Luttinger liquid (LL) model. However, to study dissipation one needs to examine interactions beyond the LL model. In this work we provide a simple model which allows for a direct microscopic calculation of the bulk viscosity, namely the one dimensional spin polarized p-wave Fermi gas. We calculate the bulk viscosity in both the high- and low-temperature limits. We find that the bulk viscosity is finite and consistent with the requirement of scale symmetry, in spite of the inherent integrabili…
We study the BCS gap equation for a Fermi gas with unequal population of spin-up and spin-down states. For $\cosh(δ_μ/T) \leq 2$, with $T$ the temperature and $δ_μ$ the chemical potential difference, the question of existence of non-trivial solutions can be reduced to spectral properties of a linear operator, similar to the unpolarized case studied previously in \cite{FHNS,HHSS,HS}. For $\cosh(δ_μ/T) > 2$ the phase diagram is more complicated, however. We derive upper and lower bounds for the critical temperature, and study their behavior in the small coupling limit.
Repulsive Bose-Einstein condensate, where the short-range interaction is included up to the third order by the interaction radius, demonstrates existence of a bright soliton in a narrow interval of parameters. This soliton is studied here for the boson-fermion mixture, where spin-1/2 fermions are consider in the regime of full spin polarization. Influence of fermions via the boson-fermion interaction is considered up to the third order by the interaction radius. Fermions themselves are considered by hydrodynamic model including the pressure evolution equation. Interaction between fermions is c…
We non-perturbatively study pairing in the high-temperature regime of polarized unitary two-component Fermi gases by extracting the pair-momentum distribution and shot-noise correlations. Whereas the pair-momentum distribution allows us to analyze the propagation of pairs composed of one spin-up and one spin-down fermion, shot-noise correlations provide us with a tomographic insight into pairing correlations around the Fermi surfaces associated with the two species. Assuming that the dominant pairing patterns right above the superfluid transition also govern the formation of condensates in the…
We analyze the nature of quantum phase transition to a superfluid state of flexible chains in a gas of polar bosonic molecules confined in a stack of $N$ identical 1d ("cigar" type) optical lattice layers and polarized perpendicularly to the layers. Monte Carlo simulations within the $J$-current model show that, in the absence of the inter-tube tunneling, the transition to the $N$-layered superfluid is in the Berezinskii-Kosterlitz-Thouless universality class in the one-particle density matrix channel. The inter-layer tunneling changes it to the $q=N$ 2d Potts universality. The low energy fiel…
We study the extremely polarized two-component Fermi gas with a mass imbalance in the strongly interacting regime. Specifically we focus on the experimentally available mixture of ${}^6$Li and ${}^{40}$K atoms. In this regime spin polarons, i.e., dressed minority atoms, form. We consider the spectral function for the minority atoms, from which the lifetime and the effective mass of the spin polaron can be determined. Moreover, we predict the radio-frequency (RF) spectrum and the momentum distribution for the spin polarons for experiments with ${}^6$Li and ${}^{40}$K atoms. Subsequently we stud…
We show the spin-orbital coupling induced by an artificial light-induced gauge field can fully restore superfluidity suppressed by population imbalance in a two-dimensional (2D) Fermi gas, leading to unconventional superfluid states either with topological Majorana fermion excitations or showing a novel mixture of triplet pairing with spin-up (down) components respectively in the $p_{x}\pm ip_{y}$ pairing channels. We self-consistently calculate the zero temperature phase diagram at the BCS\ side of Feshbach resonance and show that the phase transitions between different superfluid states can …
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 analys…
By applying the recently proposed antisymmetric superfluid local density approximation (ASLDA) to strongly interacting polarized atomic gases at unitarity in very elongated traps, we find families of Larkin-Ovchinnikov (LO) type of solutions with prominent transversal oscillation of pairing potential. These LO states coexist with a superfluid state having a smooth pairing potential. We suggest that the LO phase could be accessible experimentally by increasing adiabatically the trap aspect ratio. We show that the local asymmetry effects contained in ASLDA do not support a deformed superfluid co…
We present an analytical treatment of a single \down atom within a Fermi sea of \up atoms, when the interaction is strong enough to produce a bound state, dressed by the Fermi sea. Our method makes use of a diagrammatic analysis, with the involved diagrams taking only into account at most two particle-hole pairs excitations. The agreement with existing Monte-Carlo results is excellent. In the BEC limit our equation reduces exactly to the Skorniakov and Ter-Martirosian equation. We present results when \up and \down atoms have different masses, which is of interest for experiments in progress.
We study quantum degenerate Fermi gases of ${^6}$Li atoms at high densities ($10^{15}$ cm$^{-3}$) and observe elastic and inelastic $p$-wave collisions far away from any Feshbach resonance. $P$-wave evaporation reaches temperatures of $T/T_F=0.42$ partially limited by the slow transfer of energy from high to low velocities through $p$-wave collisions. Via cross-dimensional thermalization, the $p$-wave background scattering volume is determined to be $\lvert V_p \rvert =(39^{+1.3}_{-1.6}a_0)^3$. $P$-wave dipolar relaxation creates a metastable mixture of the lowest and highest hyperfine states.
We present a nonperturbative computation of the equation of state of polarized, attractively interacting, nonrelativistic fermions in one spatial dimension at finite temperature. We show results for the density, spin magnetization, magnetic susceptibility, and Tan's contact. We compare with the second-order virial expansion, a next-to-leading-order lattice perturbation theory calculation, and interpret our results in terms of pairing correlations. Our lattice Monte Carlo calculations implement an imaginary chemical potential difference to avoid the sign problem. The thermodynamic results on th…
