The zero-temperature phase diagrams of imbalanced fermions in 3D optical lattices are investigated to evaluate the validity of the Fermi-Hubbard model. It is found that depending on the filling factor, s-wave scattering strength and lattice potential, the system may fall into the normal($N$) phase, magnetized superfluid(SF$_M$) or phase separation of $N$ and BCS state. By tuning these parameters, the superfluidity could be favorable by enhanced effective couplings or suppressed by the increased band gap. The phase profiles in the presence of a harmonic trap are also investigated under LDA, which show some exotic shell structures compared to those without the optical lattice.
We study the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the rotation symmetry is spontaneously broken, in population imbalanced fermion gases. The superfluid gases at near T=0 are investigated on the basis of the Bogoliubov-de Gennes (BdG) equation. We find that the angular FFLO state is stabilized in the gases confined in the toroidal trap, but not in the harmonic trap. We discuss the mechanism of the angular FFLO state based on the self-one-dimensionalization of the superfluid gas.
The Functional Renormalisation Group approach is applied the imbalanced many-fermion systems. The system is found to exhibit the first order phase transition from the superfluid to normal phase when the density (chemical potential) mismatch becomes larger then some critical values. The perspectives of using fermionic cold atoms to study nuclear/quark matter is briefly discussed.
A system of a few attractively interacting fermionic $^6$Li atoms in one-dimensional harmonic confinement is investigated. Non-trivial inter-particle correlations induced by interactions in a particle-imbalanced system are studied in the framework of the noise correlation. In this way, it is shown that evident signatures of strongly correlated fermionic pairs in the Fulde-Ferrell-Larkin-Ovchinnikov state are present in the system and they can be detected by measurements directly accessible within state-of-the-art techniques. The results convincingly show that the exotic pairing mechanism is a …
We investigate the attractive Hubbard model in infinite spatial dimensions at quarter filling. By combining dynamical mean-field theory with continuous-time quantum Monte Carlo simulations in the Nambu formalism, we directly deal with the superfluid phase in the population imbalanced system. We discuss the low energy properties in the polarized superfluid state and the pseudogap behavior in the vicinity of the critical temperature.
The collective excitations that minimize the Helmholtz free energy of a population-imbalanced mixture of a $^{6}$Li gas loaded in a quasi one-dimensional optical lattice are obtained. These excitations reveal a rotonic branch after solving the Bethe-Salpeter equation under a generalized random phase approximation based on a single-band Hubbard Hamiltonian. The phase diagram describing stability regions of Fulde-Farrell-Larkin-Ovchinnikov and Sarma phases is also analyzed.
We study the zero temperature phase diagram of an imbalanced bilayer of dipolar fermions. We consider perpendicularly aligned identical dipoles in two layers and investigate the effect of population imbalance on the ground state phase at different layer spacings and average densities. The attractive part of the interlayer interaction could lead to the BEC-BCS crossover and the Fermi surface mismatch between two layers results in interesting uniform and nonuniform superfluid phases, which we have investigated here using the BCS mean-field theory together with the superfluid-mass density criteri…
Polarons can serve as an ideal platform to identify few-body correlations in tackling complex many-body problems. In this work, we reveal various crystalline few-body correlations smoothly emergent from the mass-imbalanced Fermi polarons in two dimensions. A unified variational approach up to three particle-hole excitations allows us to extract the dominant dimer, trimer or tetramer correlation in a single framework. When the fermion-impurity mass ratio is beyond certain critical value, the Fermi polaron is found to undergo a smooth crossover, instead of a sharp transition, from the polaronic …
We investigate a population-imbalanced two-species fermionic system where the resonantly-paired fermions combine to form bosonic molecules via Feshbach interaction. We study the dynamics of the intrinsic quantum fluctuations of the system. It is shown that the natural fluctuations of the condensate fraction consists of a fixed number of periodic components : indicating that these oscillations do not die out, and are sustained in the mean field dynamics of the system. These frequency components bear distinct signatures of the nature of pairing present in the system. We describe how a time depen…
The ground-state properties of the two-flavored mixture of a few attractive fermions confined in a one-dimensional harmonic trap is studied. It is shown that for slightly imbalanced system the pairing between fermions of opposite spins has completely different features that in the balanced case. The fraction of correlated pairs is suppressed by the presence of additional particle and another uncorrelated two-body orbital dominates in the ground-state of the system.
We consider a gas of two species of fermions with population imbalance. Using the renormalization group in $d=1+ε$ dimensions, we show that for spinless fermions and $ε> 0$ a fixed point appears at finite attractive coupling where the quasiparticle residue vanishes, and identify this with the transition to Larkin--Ovchinnikov--Fulde--Ferrell order (inhomogeneous superconductivity). When the two species of fermions also carry spin degrees of freedom we find a fixed point indicating a transition to spin density wave order.
We probe the superconducting gap in the zero temperature ground state of an attractively interacting spin-imbalanced two-dimensional Fermi gas with Diffusion Monte Carlo. A condensate fraction at nonzero pair momentum evidences a spatially non-uniform superconducting order parameter. Comparison with exact diagonalisation studies confirms that the nonzero condensate fraction across a range of nonzero fermion pair momenta is consistent with non-exclusive pairing between majority and minority fermions, an extension beyond FFLO theory.
A comprehensive analysis of the exact unitary dynamics of two-component mass-imbalanced fermions in a one-dimensional double-well potential is accomplished by considering the total number of particles maximum up to six. The simultaneous effect of mass imbalance between the flavors and their mutual interactions on the dynamics is scrutinized through the exact diagonalization. In particular, we investigate the occupation dynamics of such systems being initially prepared in experimentally accessible states in which opposite components occupy opposite wells. Moreover, to capture the role of intera…
We determine the relative stability of different ground-state phases of spin-imbalanced popula- tions of attractive fermions in square lattices. The phases are systematically characterized by the symmetry of the order parameter and the real- and momentum-space structures using Hartree- Fock-Bogoliubov theory. We find several type of unidirectional Larkin-Ovchinikov-type phases. We discuss the effect of commensuration between the ordering wave vector and the density imbalance, and describe the mechanism of Fermi surface reconstruction and pairing for various orders. A robust supersolid phase is…
The imbalanced superfluid state of spin-1/2 fermions with s-wave pairing is numerically studied by solving the Bogoliubov-de-Gennes equation at zero temperature in an annular disk geometry with narrow radial width. Two distinct types of systems are considered. The first case may be relevant to heavy fermion superconductors, where magnetic field causes spin imbalance via Zeeman interaction and the system is studied in a grand canonical ensemble. As the magnetic field increases, the system is transformed from the uniform superfluid state to the Fulde-Ferrell-Larkin-Ovchinnikov state, and finally…
We investigate the superfluid transition temperature of quasi-two-dimensional imbalanced Fermi gases beyond the mean-field approximation, through the second-order (or induced) interaction effects. For a balanced Fermi system the transition temperature is suppressed by a factor $\approx 2.72$. For imbalanced Fermi systems, the polarization and transition temperature of the tricritical point are significantly reduced as the two-body binding energy $|ε_B|$ increases.
Many-body systems undergoing quantum phase transitions reveal substantial growth of non-classical correlations between different parties of the system. This behavior is manifested by characteristic divergences of the von Neumann entropy. Here we show, that very similar features may be observed in one-dimensional systems of a few strongly interacting atoms when the structural transitions between different spatial orderings are driven by a varying shape of an external potential. When the appropriate adaptation of the finite-size scaling approach is performed in the vicinity of the transition poi…
Dynamical properties of two-component mass-imbalanced few-fermion systems confined in a one-dimensional harmonic trap following a sudden quench of interactions are studied. It is assumed that initially the system is prepared in the non-interacting ground state and then, after a sudden quench of interactions, the unitary evolution is governed by interacting many-body Hamiltonian. By careful analysis of the evolution of the Loschmidt echo, density distributions of the components, and entanglement entropy between them, the role of mass imbalance and particle number imbalance on the system's evolu…
We propose and analyze a variational wave function for a population-imbalanced one-dimensional Fermi gas that allows for Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type pairing correlations among the two fermion species, while also accounting for the harmonic confining potential. In the strongly interacting regime, we find large spatial oscillations of the order parameter, indicative of an FFLO state. The obtained density profiles versus imbalance are consistent with recent experimental results as well as with theoretical calculations based on combining Bethe ansatz with the local density approxi…
We study the ground-state properties of a two-component fermionic mixture effectively confined in a one-dimensional harmonic trap. We consider scenarios when numbers of particles in components are the same but particles have different masses. We examine whether it is possible to detect signatures of an unconventional pairing between opposite-spin fermions in the presence of attractive interactions. For this purpose, we perform the exact diagonalization of the many-body Hamiltonian and study the two-particle reduced density matrix. In agreement with expectations, we confirm that the many-body g…
We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of both hopping and population imbalance by means of dynamical mean-field theory (DMFT). It is shown that these mixtures can have easy-axis antiferromagnetic, ferrimagnetic, charge-density wave, and canted-antiferromagnetic order or be unordered depending on parameters of the system. We study the resulting phase diagram in detail and investigate the stability of the different phases with respect to thermal fluctuations. We also perform a quantitative analysis…
We use the mean-field theory to analyze the ground-state phase diagrams of spin-orbit coupled mass-imbalanced Fermi gases throughout the BCS-BEC evolution, including both the population-balanced and -imbalanced systems. Our calculations show that the competition between the mass and population imbalance and the Rashba-type spin-orbit coupling (SOC) gives rise to very rich phase diagrams, involving normal, superfluid and phase separated regions. In addition, we find quantum phase transitions between the topologically trivial gapped superfluid and the nontrivial gapless superfluid phases, openin…
We use Quantum Monte Carlo (QMC) simulations to study the pairing mechanism in a one-dimensional fermionic system governed by the Hubbard model with attractive contact interaction and with imbalance between the two spin populations. This is done for the uniform system and also for the system confined in a harmonic trap to compare with experiments on confined ultra-cold atoms. In the uniform case we determine the phase diagram in the polarization-temperature plane and find that the "Fulde-Ferrell-Larkin-Ovchinnikov" (FFLO) phase is robust and persists to higher temperature for higher polarizati…
We obtain the phase diagram of spin-imbalanced interacting Fermi gases from measurements of density profiles of $^6$Li atoms in a harmonic trap. These results agree with, and extend, previous experimental measurements. Measurements of the critical polarization at which the balanced superfluid core vanishes generally agree with previous experimental results and with quantum Monte Carlo (QMC) calculations in the BCS and unitary regimes. We disagree with the QMC results in the BEC regime, however, where the measured critical polarizations are greater than theoretically predicted. We also measure …
We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of hopping imbalance. Our analysis is based on dynamical mean-field theory (DMFT) and its real-space generalization at finite temperature. We study the temperature dependence of the transition into the ordered state as a function of the interaction strength and the imbalance parameter in two and three spatial dimensions. We show that below the critical temperature for Néel order mass-imbalanced mixtures also exhibit a charge-density wave, which provides a dir…
We study imbalanced fermionic superfluids in an array of one-dimensional tubes at the incipient dimensional crossover regime, wherein particles can tunnel between neighboring tubes. In addition to single-particle tunneling (ST), we consider pair tunneling (PT) that incorporates the interaction effect during the tunneling process. We find that with an increase of PT strength, a system of low global polarization evolves from a structure with a central Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state to one with a central BCS-like fully-paired state. For the case of high global polarization, the cen…
We study two-species fermion gases with attractive interaction in two-dimensional optical lattices producing an array of elongated tube confinements. Focusing on the interplay of Cooper pairing, spin imbalance (or magnetization) and intertube tunneling, we find the pairing gap can exhibit oscillatory behavior both along and across the tubes, reminiscent of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We obtain a Bose-Hubbard-like phase diagram that shows that the magnetization of the system undergoes an incompressible-compressible transition as a function of magnetic field and intertube tu…
We show that Larkin-Ovchinnikov (LO) states with modulated superfluid order parameters have a considerably larger range of stability in a lattice than in the continuum. We obtain the phase diagram for the 3D cubic attractive Hubbard model with an unequal population of up and down fermions using the Bogoliubov-de Gennes fully self-consistent method. We find a strong modulation of the local polarization that should provide a distinct signature for detection of the LO phase. The shell structure in the presence of a trap generates singularities in the density at the phase boundaries and provide ad…
We study the nature of superfluid pairing in imbalanced Fermi mixtures in two spatial dimensions. We present evidence that the combined effect of Fermi surface mismatch and order parameter fluctuations of the superfluid condensate can lead to continuous quantum phase transitions from a normal Fermi mixture to an intermediate Sarma-Liu-Wilczek superfluid with two gapless Fermi surfaces -- even when mean-field theory (incorrectly) predicts a first order transition to a phase-separated "Bardeen-Cooper-Schrieffer plus excess fermions" ground state. We propose a mechanism for non-Fermi liquid behav…
We study s-wave superconductivity in the two dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC crossover. We use a decomposition of the interaction in terms of an auxiliary pairing field, retain the static mode, and sample the pairing field via Monte Carlo. The method requires iterative solution of the Bogoliubov-de-Gennes (BdG) equations for amplitude and phase fluctuating configurations of the pairing field. We establish the full thermal phase diagram …
We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite imbalance. The existence of a quantum multicritical point for the unitary gas at vanishing chemical potential $μ$ and effective magnetic field $h$, first discussed by Nikolić and Sachdev, gives rise to three different phase diagrams, depending on whether the inverse scattering length $1/a$ is negative, positive or zero. Within a Luttinger-Ward formalism, the phase diagram and pressure of the unitary gas is calculated as a function of the dimensionless scaling variables $T/μ$ and $h/μ$. The resu…
We study the effect of high population imbalance in the two dimensional attractive Hubbard model, in the coupling regime corresponding to BCS-BEC crossover, and focus on thermal effects on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. Using a method that retains all the classical thermal fluctuations on the FFLO state we estimate a very low $T_c$ and infer a strongly first order normal state to FFLO transition. The $T_c$ is an order of magnitude below the mean field estimate. We track the fermionic momentum distribution, the density of states, and the pairing structure factor deep into th…
The calculation of the ground state and thermodynamics of mass-imbalanced Fermi systems is a challenging many-body problem. Even in one spatial dimension, analytic solutions are limited to special configurations and numerical progress with standard Monte Carlo approaches is hindered by the sign problem. The focus of the present work is on the further development of methods to study imbalanced systems in a fully non-perturbative fashion. We report our calculations of the ground-state energy of mass-imbalanced fermions using two different approaches which are also very popular in the context of …
We study the rich properties of the imbalanced antiferromagnet in an optical lattice. We present its phase diagram, discuss spin waves and explore the emergence of topological excitations in two dimensions, known as merons, which are responsible for a Kosterlitz-Thouless transition that has never unambiguously been observed.
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 study the superfluid properties of two-dimensional spin-population-imbalanced Fermi gases to explore the interplay between the Berezinskii-Kosterlitz-Thouless (BKT) phase transition and the possible instability towards the Fulde-Ferrell (FF) state. By the mean-field approximation together with quantum fluctuations, we obtain phase diagrams as functions of temperature, chemical potential imbalance and binding energy. We find that the fluctuations change the mean-field phase diagram significantly. We also address possible effects of the phase separation and/or the anisotropic FF phase to the …
A single down spin Fermion with an attractive, zero range interaction with a Fermi sea of up-spin Fermions forms a polaronic quasiparticle. The associated quasiparticle weight vanishes beyond a critical strength of the attractive interaction, where a many-body bound state is formed. From a variational wavefunction in the molecular limit, we determine the critical value for the polaron to molecule transition. The value agrees well with the diagrammatic Monte Carlo results of Prokof'ev and Svistunov and is consistent with recent rf-spectroscopy measurements of the quasiparticle weight by Schirot…
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 explore the ground states in population-imbalanced attractive 1-D fermionic optical lattice filling $p$ orbitals over the lowest $s$ one by using the density-matrix-renormalization-group (DMRG) method. The DMRG calculations find the occurrence of spatially non-uniform off-diagonal long-range order. In contrast to Fulde-Ferrel Larkin-Ovchinikov pair as observed in the single-band Hubbard model. The spatial oscillation period of the pair correlation function is widely fixed to be $π$ irrespective of the mismatch between spin-split Fermi surfaces. The ground-state $π$ order corresponds to $η$-…
We study fermion pairing in a population-imbalanced mixture of $^{6}$Li atomic gas loaded in a three-dimensional lattice at very low temperatures. Using the number equation for each population, the gap equation and the equation for the Helmholtz free energy, we determine the gap, chemical potentials and pair-momentum as functions of polarization. These parameters define the stability regions for: a Fulde-Ferrell-Larkin-Ovchinnikov phase; a phase separation region where BCS and normal phases coexist; a Sarma phase when the pair-momentum vanishes, and the transition to the normal phase when the …
Building on recent solutions of the fermion sign problem for specific models we present two continuous-time quantum Monte Carlo methods for efficient simulation of mass-imbalanced Hubbard models on bipartite lattices at half-filling. For both methods we present the solutions to the fermion sign problem and the algorithms to achieve efficient simulations. As applications, we calculate the dependence of the spin correlation on the mass imbalance in a one-dimensional lattice and study the thermal and quantum phase transitions to an antiferromagnetic Ising long-range ordered state in two dimension…
Lattice field theory is a useful tool for studying strongly interacting theories in condensed matter physics. A prominent example is the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. With Monte Carlo methods this system can be studied from first principles. In the presence of an imbalance (unequal number of particles in the two components) a sign problem arises, which makes conventional algorithms inapplicable. We will show how to apply reweighting techniques to generalise the recently developed worm algorithm to the imbalanced case, and pr…
By using the numerically exact density-matrix renormalization group (DMRG) approach, we investigate the ground states of harmonically trapped one-dimensional (1D) fermions with population imbalance and find that the Larkin-Ovchinnikov (LO) state, which is a condensed state of fermion pairs with nonzero center-of-mass momentum, is realized for a wide range of parameters. The phase diagram comprising the two phases of i) an LO state at the trap center and a balanced condensate at the periphery and ii) an LO state at the trap center and a pure majority component at the periphery, is obtained. The…
We compute the phase diagram of strongly interacting fermions in one dimension at finite temperature, with mass and spin imbalance. By including the possibility of the existence of a spatially inhomogeneous ground state, we find regions where spatially varying superfluid phases are favored over homogeneous phases. We obtain estimates for critical values of the temperature, mass and spin imbalance, above which these phases disappear. Finally, we show that an intriguing relation exists between the general structure of the phase diagram and the binding energies of the underlying two-body bound-st…
We study the phase diagram of mass- and spin-imbalanced unitary Fermi gases, in search for the emergence of spatially inhomogeneous phases. To account for fluctuation effects beyond the mean-field approximation, we employ renormalization group techniques. We thus obtain estimates for critical values of the temperature, mass and spin imbalance, above which the system is in the normal phase. In the unpolarized, equal-mass limit, our result for the critical temperature is in accordance with state-of-the-art Monte Carlo calculations. In addition, we estimate the location of regions in the phase di…
We present an overview of recent developments in species-imbalanced ("polarized") Feshbach-resonant Fermi gases. We summarize the current status of thermodynamics of these systems in terms of a phase diagram as a function of the Feshbach resonance detuning, polarization and temperature. We review instabilities of the s-wave superfluidity across the BEC-BCS crossover to phase separation, FFLO states, polarized molecular superfluidity and the normal state, driven by the species imbalance. We discuss different models and approximations of this system and compare their predictions to current exper…
The spectra of low-lying pair excitations for an imbalanced two-component superfluid Fermi gas are analytically derived within the path-integral formalism taking into account Gaussian fluctuations about the saddle point. The spectra are obtained for nonzero temperatures, both with and without imbalance, and for arbitrary interaction strength. On the basis of the pair excitation spectrum, we have calculated the thermodynamic parameters of state of cold fermions and the first and second sound velocities. The parameters of pair excitations show a remarkable agreement with the Monte Carlo data and…
We obtain a phase diagram of the spin imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types FFLO phases, i.e. superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the centre-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the…
We study the attractive Hubbard model with spin imbalance on two lattices featuring a flat band: the Lieb and kagome lattices. We present mean-field phase diagrams featuring exotic superfluid phases, similar to the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, whose stability is confirmed by dynamical mean-field theory (DMFT). The nature of the pairing is found to be richer than just the Fermi surface shift responsible for the usual FFLO state. The presence of a flat band allows for changes in the particle momentum distributions at null energy cost. This facilitates formation of nontrivial su…
We study a two species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with on-site inter-species repulsive interaction. Such a model can be realized in a cold atom system with fermionic atoms in two different hyperfine states loaded on an optical lattice and with tunable inter-species interaction strength via external fields. For a two-dimensional square lattice, when at least one of the fermion species is close to half-filling, the system is highly affected by lattice effects. With the majority species near half-filling and varying densities fo…
The suppression of antiferromagnetic ordering in geometrically frustrated Hubbard models leads to a variety of exotic quantum phases including quantum spin liquids and chiral states. Here, we focus on the Hubbard model on one of the simplest frustrated lattice geometries, a triangular lattice. Motivated by the recent realization of ultracold fermionic atoms in triangular optical lattices, we study the properties of the triangular-lattice Hubbard model through a Numerical Linked-Cluster Expansion algorithm. We investigate the Mott insulator transition finding a critical interaction $U_c/t = 7.0…
Quantum many body phases, in competition or coexistence has always been a fascinating area of research in condensed matter physics. One of the most widely investigated scenario of phase competition is that between superconductivity and magnetism, which in spite of several decades of research continues to bring up new surprises till date. While superconductivity and magnetism are naively considered to be antagonists, there are several circumstances where these many body phases can be found to be cooperating, coexisting and even promoting each other. The results of such cooperative behavior are …
Functional renormalisation group approach is applied to a imbalanced many- fermion system with a short-range attractive force. Composite boson field is introduced to describe the pairing between different flavour fermions. A set of approximate flow equations for the effective couplings is derived and solved. We identify the critical values of mass and particle number density mismatch when the system undergoes a phase transition to a normal state and determine the phase diagram both at unitary regime and nearby.
We study a trapped two-dimensional spin-imbalanced Fermi gas over a range of temperatures. In the moderate temperature regime, associated with current experiments, we find reasonable semi-quantitative agreement with the measured density profiles as functions of varying spin imbalance and interaction strength. Our calculations show that, in contrast to the three-dimensional case, the phase separation which appears as a spin balanced core, can be associated with non-condensed fermion pairs. We present predictions at lower temperatures where a quasi-condensate will first appear, based on the pair…
