T. Espinosa-Ortega, O. Kyriienko, I. A. Shelykh
We consider a mixture of two neutral cold Fermi gases with repulsive interactions. We show that in some region of the parameter space of the system the effective attraction between fermions of the same type can appear due to the exchange of collective excitations. This leads to the formation of BCS pairing in the case where bare inter-atomic interactions are repulsive.
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We investigate the phase diagram and the BCS-BEC crossover of a homogeneous three-component ultracold Fermi gas with a U(3) invariant attractive interaction. We show that the system at sufficiently low temperatures exhibits population imbalance, as well as fermionic pairing. We describe the crossover in this system, connecting the weakly interacting BCS regime of the partially population-imbalanced fermion pairing state and the BEC limit with three weakly interacting species of molecules, including pairing fluctuations within a t-matrix calculation of the particle self-energies.
Pairing near the boundary of a box-shaped trap in the BEC-BCS crossover
本研究针对盒形势阱中吸引相互作用费米子的配对问题，在半无限超流体极限下分析边缘配对特性，发现弱耦合BCS区的类Friedel振荡会随耦合向BEC区增强而被抑制。
This paper gives a survey of a diagrammatic approach for fermionic pairing fluctuations, which are relevant to the BCS-BEC crossover realized with ultracold Fermi gases. Emphasis will be given to the physical intuition about the relevant physical processes that can be associated with this approach. Specific results will be presented for thermodynamic and dynamical quantities, where a critical comparison with alternative diagrammatic approaches will also be attempted.
In this work we numerically investigate the fate of the Bardeen-Cooper-Schrieffer (BCS) pairing in the presence of quenched phase under Peierls substitution using time-dependent real space and momentum space Bogoliubov-de Gennes equation methods and Anderson pseudospin representation method. This kind of phase imprint can be realized by modulating electric field in ultracold atoms and illumining of THz optical pump pulse in solids with conventional and unconventional superconductors. In the case of weak phase imprint, the BCS pairing is stable; while in the strong phase imprint, instability to…
We analyze the BCS-BEC crossover transition of a balanced two component mixture of fermions interacting via a finite range potential, within a mean field approach. For the analysis we consider three finite range potentials cases describing the interaction between different Fermi species: a square well, an exponential and a Yukawa potential. The T = 0 thermodynamics analysis along the BCS-BEC crossover allow us to recognize the proper variables, for finite range interactions, that capture the transition from a thermodynamic non-universal behavior at unitarity, to its universal restoration. On t…
We investigate the phase diagram of two-component fermions in the BCS-BEC crossover. Using functional renormalization group equations we calculate the effect of quantum fluctuations on the fermionic self-energy parametrized by a wavefunction renormalization, an effective Fermi radius and the gap. This allows us to follow the modifications of the Fermi surface and the dispersion relation for fermionic excitations throughout the whole crossover region. We also determine the critical temperature of the second order phase transition to superfluidity. Our results are in agreement with BCS theory in…
We investigate pseudogap phenomena originating from pairing fluctuations in the BCS-BEC crossover regime of a two-dimensional Fermi gas in a harmonic trap. Including pairing fluctuations within a $T$-matrix theory and effects of a trap within the local density approximation, we calculate the local density of states (LDOS) at the superfluid phase transition temperature $T_{\rm c}$. In the weak-coupling regime, we show that the pseudogap already appears in LDOS around the trap center. The spatial region where the pseudogap can be seen in LDOS becomes wider for a strong pairing interaction. We al…
Rf spectra and pseudogap in ultracold Fermi gases across the BCS-BEC crossover from pairing fluctuation theory
本文通过计算超冷原子气体在BCS-BEC交叉点的谱函数和RF谱，探讨了伪隙的配对机制，采用粒子-空穴涨落理论，揭示了伪隙连续出现的机制。
We study a two-component Bose gas with a symmetric spin-orbit coupling, and find that two atoms can form a bound state with any intra- or inter-species scattering length. Consequently, in the dilute limit, the Bardeen-Cooper-Shrieffer (BCS) pairing state of bosons can be formed with weakly-attractive inter-species and repulsive intra-species interactions. The quasiparticle excitation energies are anisotropic due to spin-orbit coupling. This BCS paring state is energetically favored over Bose-Einstein condensation (BEC) of atoms at low densities. As the density increases, there is a first-order…
We study the superconducting properties of population-imbalanced ultracold Fermi mixtures in one-dimensional (1D) optical lattices that can be effectively described by the spin-imbalanced attractive Hubbard model (AHM) in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain the ground state phase diagrams including some unconventional superconducting phases such as the Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase, and the $η$ phase (an extremal case of the FFLO phase), both for the case of a fixed chemical potential and for a fixed number of particles. I…
Ultradilute quantum droplets are intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of ultradilute quantum droplets in three-, one- and two-dimensional two-component Bose-Bose mixtures, by generalizing the conventional Bogoliubov theory to include the bosonic pairing arising from the interspecies attraction. Our pairing theory is fully equivalent to a variational approach and hence gives an upper bound for the energy of quantum droplets. In three dimen…
We investigate the pairing symmetry of the superfluid state in repulsively interacting three-component (colors) fermionic atoms in optical lattices. When two of the three color-dependent repulsions are much larger than the other, pairing symmetry is an extended s wave, although the superfluid state appears adjacent to the paired Mott insulator in the phase diagram. As the difference between the three repulsions is decreased in square optical lattices, the extended s-wave pairing changes into a nodal s-wave pairing and then into a d-wave pairing. This change in pairing symmetry is attributed to…
By including the effect of a trap with characteristic energy given by the Fermi temperature $T_F$ in a two-body two-channel model for Feshbach resonances, we reproduce the experimental closed-channel fraction $Z$ across the BEC-BCS crossover and into the BCS regime of a $^6$Li atomic Fermi gas. We obtain the expected behavior $Z \propto \sqrt{T_F}$ at unitarity, together with the recently measured proportionality constant. Our results are also in agreement with recent measurements of the $Z$ dependency on $T_F$ on the BCS side, where a significant discrepancy between experiments and theory has…
Spin-triplet pairing instability in a two-dimensional repulsive Hubbard model
研究通过数值方法揭示二维反常相互作用Hubbard模型中自旋三重态p波配对不稳定性，发现其与铁磁自旋相关性密切相关。
We theoretically investigate normal-state properties of an ultracold Fermi gas with an orbital Feshbach resonance (OFR). Recently, OFR has attracted much attention as a promising pairing mechanism to realize a superfluid 173Yb Fermi gas. Including pairing fluctuations within a T-matrix approximation, and removing effects of an experimentally inaccessible deep bound state, we evaluate strong-coupling corrections to single-particle excitations. With increasing the strength of an OFR-induced tunable pairing interaction, the open channel is shown to exhibit the pseudogap phenomenon in the BCS-BEC …
Understanding novel pairings in attractive degenerate Fermi gases is crucial for exploring rich superfluid physics. In this report, we reveal unconventional pairings induced by spin-orbit coupling (SOC) in a one-dimensional optical lattice, using a state-of-the-art density-matrix renormalization group method. When both bands are partially occupied, we find a strong competition between the interband Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and intraband Bardeen-Cooper-Schrieffer (BCS) pairings. In particular, for the weak and moderate SOC strengths, these two pairings can coexist, giving rise to…
The theoretical description of the critical temperature Tc of a Fermi superfluid dates back to the work by Gor'kov and Melik-Barkhudarov (GMB), who addressed it for a weakly-coupled (dilute) superfluid in the BCS (weak-coupling) limit of the BCS-BEC crossover. The point made by GMB was that particle-particle (pairing) excitations, which are responsible for superfluidity to occur below Tc, and particle-hole excitations, which give rise to screening also in a normal system, get effectively disentangled from each other in the BCS limit, thus yielding a reduction by a factor 2.2 of the value of Tc…
We study pseudogap behaviors of ultracold Fermi gases in the BCS-BEC crossover region. We calculate the density of states (DOS), as well as the single-particle spectral weight, above the superfluid transition temperature $T_{\rm c}$ including pairing fluctuations within a $T$-matrix approximation. We find that DOS exhibits a pseudogap structure in the BCS-BEC crossover region, which is most remarkable near the unitarity limit. We determine the pseudogap temperature $T^*$ at which the pseudogap structure in DOS disappears. We also introduce another temperature $T^{**}$ at which the BCS-like dou…
Extensive research has been lavished on effects of spin-orbit couplings (SOC) in attractively interacting Fermi systems in both neutral cold atom systems and condensed matter systems. Recently, it was suggested that a SOC drives a new class of BCS to BEC crossover which is different than the conventional one without a SOC. Here, we explore what are the most relevant physical quantities to describe such a new BCS to BEC crossover and their experimental detections. We extend the concepts of the pairing length and "Cooper-pair size" in the absence of SOC to Fermi systems with SOC. We investigate …
We investigate the photoemission-type spectrum in a cold Fermi gas which was recently measured by JILA group [J. T. Stewart {\it et al}., Nature \textbf{454}, 744 (2008)]. This quantity gives us very useful information about single-particle properties in the BCS-BEC crossover. In this letter, including pairing fluctuations within a $T$-matrix theory, as well as effects of a harmonic trap within the local density approximation, we show that spatially inhomogeneous pairing fluctuations due to the trap potential is an important key to understand the observed spectrum. In the crossover region, whi…
We investigate the uniform spin susceptibility $χ_{\rm s}$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation, we show that $χ_{\rm s}$ exhibits non-monotonic temperature dependence in the normal state. In particular, $χ_{\rm s}$ is suppressed near the superfluid phase transition temperature $T_{\rm c}$ due to strong pairing fluctuations. To characterize this anomalous behavior, we introduce the spin-gap temperature $T_{\rm s}$ as the temp…
We analyse a p+ip-wave pairing BCS Hamiltonian, coupled to a single bosonic degree of freedom representing a molecular condensate, and investigate the nature of the BEC-BCS crossover for this system. For a suitable restriction on the coupling parameters, we show that the model is integrable and we derive the exact solution by the algebraic Bethe ansatz. In this manner we also obtain explicit formulae for correlation functions and compute these for several cases. We find that the crossover between the BEC state and the strong pairing p+ip phase is smooth for this model, with no intermediate qua…
We investigate strong pairing fluctuations and effects of a harmonic trap in the superfluid phase of an ultracold Fermi gas. Including amplitude and phase fluctuations of the inhomogeneous superfluid order parameter $Δ(r)$ in a trap within a combined $T$-matrix theory with the local density approximation, we examine local properties of single-particle excitations and a thermodynamic quantity in the BCS-BEC crossover region. Below the superfluid phase transition temperature $T_{\rm c}$, we show that inhomogeneous pairing fluctuations lead to a shell structure of the gas cloud in which the spati…
We in this paper investigate the phase diagram associated with the BCS-BEC crossover of a three-component ultracold superfluid-Fermi-gas of different chemical-potentials and equal masses in two dimensions. The gap order parameter and number densities are found analytically by using the functional path-integral method. The balance of paring will be broken in the free space due to the unequal chemical-potentials. We obtain the same particle number-density and condensed fraction in the BCS superfluid phase as that in a recent paper (Phys. Rev. A 83, 033630), while the Sarma phase of coexistence o…
It is generally believed that the BCS-BEC evolution in fermionic systems with s-wave pairing is a smooth crossover. However, for nonzero orbital-angular-momentum pairing such as p- or d-wave pairing, the system undergoes a quantum phase transition at the point where the chemical potential $μ$ vanishes. In this paper, we study the BCS-BEC quantum phase transition and the collective excitations associated with the order-parameter fluctuations in two-dimensional fermionic systems with p- and d-wave pairings. We show that the quantum phase transition in such systems can be generically traced back …
Experiments with ultracold atoms provide a highly controllable laboratory setting with many unique opportunities for precision exploration of quantum many-body phenomena. The nature of such systems, with strong interaction and quantum entanglement, makes reliable theoretical calculations challenging. Especially difficult are excitation and dynamical properties, which are often the most directly relevant to experiment. We carry out exact numerical calculations, by Monte Carlo sampling of imaginary-time propagation of Slater determinants, to compute the pairing gap in the two-dimensional Fermi g…
We study the superfluid critical temperature in a two-band attractive Fermi system with strong pairing fluctuations associated with both interband and intraband couplings. We focus specifically on a configuration where the intraband coupling is varied from weak to strong in a shallow band coupled to a weakly-interacting deeper band. The whole crossover from the Bardeen-Cooper-Schrieffer (BCS) condensation of largely overlapping Cooper pairs to the Bose-Einstein condensation (BEC) of tightly bound molecules is covered by our analysis, which is based on the extension of the Nozières-Schmitt-Rink…
Pairing transitions in a Binary Bose Gas
该研究针对二元玻色气体的稳定BCS配对态问题，分析了平均场稳定区含s波种内排斥与种间吸引作用的系统，揭示了温度变化下的多步相变过程并给出相图，为相关实验研究提供了理论参考。
We report on a comprehensive study of the phase structure of cold, dilute nuclear matter featuring a SD condensate at non-zero isospin asymmetry, within wide ranges of temperatures and densities. We find a rich phase diagram comprising three superfluid phases, namely a Larkin-Ovchinnikov-Fulde-Ferrell phase, the ordinary BCS phase, and a heterogeneous, phase-separated BCS phase, with associated crossovers from the latter two phases to a homogeneous or phase-separated Bose-Einstein condensate of deuterons. The phase diagram contains two tricritical points (one a Lifshitz point), which may degen…
Critical current throughout the BCS-BEC crossover with the inclusion of pairing fluctuations
本文系统分析费米子超流体在BCS-BEC渡越中的电流-动量特性，发现低温下回流电流阈值对应朗道临界动量，并统一描述破对与声子两种耗散机制，改进与实验数据的吻合。
The pairing of fermionic atoms in a mixture of atomic fermion and boson gases at zero temperature is investigated. The attractive interaction between fermions, that can be induced by density fluctuations of the bosonic background, can give rise to a superfluid phase in the Fermi component of the mixture. The atoms of both species are assumed to be in only one internal state, so that the pairing of fermions is effective only in odd-l channels. No assumption about the value of the ratio between the Fermi velocity and the sound velocity in the Bose gas is made in the derivation of the energy gap …
We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen--Cooper--Schrieffer--Bose--Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic $T$ matrix approach, we~report how thermodynamic quantities such as the critical temperature, chemical potential, {and~momentum distributions} undergo the crossover from the BCS to BEC regime by tuning the intraband coupling in the shallow band. We also generalize the definition of Tan's contact to a two band system and report the two contac…
We investigate the specific heat at constant volume $C_V$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature $T_{\rm c}$. Within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while $C_V(T\gesim T_{\rm c})$ in the unitary regime is remarkably enhanced by {\it metastable} preformed Cooper pairs or pairing fluctuations, it is well described b…
The dineutron correlations and the crossover from superfluidity of neutron Cooper pairs in the $^1S_0$ pairing channel to Bose-Einstein condensation (BEC) of dineutron pairs in both symmetric and neutron matter are studied within the relativistic Hartree-Bogoliubov theory, with the effective interaction PK1 of the relativistic mean-field approach in the particle-hole channel and the finite-range Gogny force in the particle-particle channel. The influence of the pairing strength on the behaviors of dineutron correlations is investigated. It is found that the neutron pairing gaps at the Fermi su…
We build a holographic model for the pairing fluctuation pseudogap phase in fermionic high temperature superconductivity/superfluidity based on the BCS-BEC crossover scenario. The pseudogap originates from incoherent Cooper pairing and has been observed in recent cold atom experiments. The strength of Cooper pairing and hence the BCS-BEC crossover is controlled by an effective 4-Fermi interaction and we argue that the double-trace deformation for charged scalar operator is a close analog in large N field theories. We employ the double-trace deformed Abelian Higgs model of holographic supercond…
We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a harmonic trap in the local density approximation (LDA), we calculate the local spin susceptibility $χ_{\rm t}(r,T)$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that pairing fluctuations cause non-monotonic temperature dependence of $χ_{\rm t}(r,T)$. Although this behavior looks similar to the spin-gap phenomenon associated with pairing f…
Recently, the possibility of inducing superconductivity for electrons in two dimensional materials has been proposed via cavity-mediated pairing. The cavity-mediated electron-electron interactions are long range, which has two main effects: firstly, within the standard BCS-type pairing mediated by adiabatic photons, the superconducting critical temperature depends polynomially on the coupling strength, instead of the exponential dependence characterizing the phonon-mediated pairing; secondly, as we show here, the effect of photon fluctuations is significantly enhanced. These mediate novel non-…
Fermion systems with flat bands can boost superconductivity by enhancing the density of states at the Fermi level. We use quasiexact numerical methods to show that repulsive interactions between spinless fermions in a one-dimensional (1D) flat-band system, the Creutz ladder, give a finite pairing energy that increases with repulsion, though charge quasi-order (QO) remains dominant. Adding an attractive component shifts the balance in favor of superconductivity and the interplay of two flat bands further yields a remarkable enhancement of superconductivity, well outside of known paradigms for 1…
The aim of this Ph.D. thesis was to investigate superconducting properties in the presence of Zeeman magnetic field in systems with local fermion pairing on the lattice. The study also concerned the evolution from the weak coupling (BCS-like) limit to the strong coupling limit of tightly bound local pairs (BEC) with increasing attraction, both in the ground state and at finite temperatures, within the spin-polarized extended Hubbard model. The analysis was also extended to the case of spin dependent hopping integrals (mass imbalance), with special attention paid to the BCS-BEC crossover physic…
BCS-BEC crossover in trapped one-dimensional Fermi-Hubbard chains: entanglement and correlation signatures from DMRG and effective-pairing theory
研究一维费米Hubbard链在谐振子约束下的BCS-BEC交叉，结合DMRG和有效模型分析相互作用与约束对交叉的影响，揭示绝缘区与超流关联共存的现象。
Similar to what has recently been achieved with Bose-Bose mixtures [Lamporesi et al., Phys. Rev. Lett. 104, 153202 (2010)], mixed-dimensional Fermi-Fermi mixtures can be created by applying a species-selective one-dimensional optical lattice to a two-species Fermi gas ($σ\equiv \{\uparrow, \downarrow \}$), such a way that only one of the species feel the lattice potential and is confined to a quasi-two-dimensional geometry, while having negligible effect on the other, that is leaving it three dimensional. We investigate the ground state phase diagram of superfluidity for such mixtures in the B…
We study the character change of the pionic condensation at finite isospin chemical potential μ_\mathrm{I} by adopting the linear sigma model as a non-local interaction between quarks. At low |μ_\mathrm{I}| the condensation is purely bosonic, then the Cooper pairing around the Fermi surface grows gradually as |μ_\mathrm{I}| increases. This q-\bar q pairing is weakly coupled in comparison with the case of the q-q pairing that leads to color superconductivity.
Strongly correlated Fermi systems with pairing interactions become superfluid below a critical temperature $T_c$. The extent to which such pairing correlations alter the behavior of the liquid at temperatures $T > T_c$ is a subtle issue that remains an area of debate, in particular regarding the appearance of the so-called pseudogap in the BCS-BEC crossover of unpolarized spin-$1/2$ nonrelativistic matter. To shed light on this, we extract several quantities of crucial importance at and around the unitary limit, namely: the odd-even staggering of the total energy, the spin susceptibility, the …
We study theoretically the superconductivity in doped Weyl semimetals with an inversion symmetry based on the Bogoliubov-de Gennes equations. In principle, the two superconducting states, i.e., the zero momentum BCS-like pairing and the finite momentum Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing are competing in this kind of systems. Our self-consistent calculation indicates that the BCS-type state may be the ground state. The competition between these two pairing states is studied in detail through normal state Fermi surface and the finite energy spectral functions. Generally, the Fermi s…
We present a theoretical study of the finite-temperature Kosterlitz-Thouless (KT) and vortex-antivortex lattice (VAL) melting transitions in two-dimensional Fermi gases with $p$- or $d$-wave pairing. For both pairings, when the interaction is tuned from weak to strong attractions, we observe a quantum phase transition from the Bardeen-Cooper-Schrieffer (BCS) superfluidity to the Bose-Einstein condensation (BEC) of difermions. The KT and VAL transition temperatures increase during this BCS-BEC transition and approach constant values in the deep BEC region. The BCS-BEC transition is characterize…
The subject of BCS - Bose Einstein condensation (BEC) crossover is particularly exciting because of its realization in ultracold Fermi gases and its possible relevance to high temperature superconductors. In the paper we review that body of theoretical work on this subject which represents a natural extension of the seminal papers by Leggett and by Nozieres and Schmitt-Rink (NSR). The former addressed only the ground state, now known as the "BCS-Leggett" wave-function and the key contributions of the latter pertain to calculations of the superfluid transition temperature $T_c$. These two paper…
Structures and proximity effects of inhomogeneous population-imbalanced Fermi gases with pairing interactions
研究不均匀人口不平衡费米气体在不同相共存时的结构和性质，通过Bogoliubov-de Gennes方程分析配对强度和自旋极化变化对FFLO相和BCS超流相的转换影响，揭示近邻效应和相间特性。
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