Superfluid Pairing Research Articles

Polaron spectroscopy of interacting Fermi systems: Insights from exact diagonalization

Immersing a mobile impurity into a many-body quantum system represents a theoretically intriguing and experimentally effective way of probing its properties. In this work, we study the polaron spectral function in various environments, within the framework of Fermi-Hubbard models. Inspired by possible realizations in cold atoms and semiconductor heterostructures, we consider different configurations for the background Fermi gas, including charge density waves, multiple Fermi seas and pair superfluids. While our calculations are performed using an exact-diagonalization approach, hence limiting our analysis to systems of few interacting Fermi particles, we identify robust spectral features supported by theoretical results. Our work provides a benchmark for computations based on mean-field approaches and reveal surprising features of polaron spectra, inspiring new theoretical investigations.

Pairing Superfluid–Insulator Transition Induced by Atom–Molecule Conversion in Bosonic Mixtures in Optical Lattice

Motivated by the recent experiment on bosonic mixtures of atoms and molecules, we investigate pairing superfluid–insulator (SI) transition for bosonic mixtures of atoms and molecules in a one-dimensional optical lattice, which is described by an extended Bose–Hubbard model with atom–molecule conservation (AMC). It is found that AMC can induce an extra pair–superfluid phase though the system does not demonstrate pair-hopping. In particular, the system may undergo several pairing SI or insulator–superfluid transitions as the detuning from the Feshbach resonance is varied from negative to positive, and the larger positive detuning can bifurcate the pair–superfluid phases into mixed superfluid phases consisting of single-atomic and pair-atomic superfluid. The calculation of the second-order Rényi entropy reveals that the discontinuity in its first-order derivative corresponds to the phase boundary of the pairing SI transition. This means that the residual entanglement in our mean-field treatment can be used to efficiently capture the signature of the pairing SI transition induced by AMC.

Direct observation of nonlocal fermion pairing in an attractive Fermi-Hubbard gas

The Hubbard model of attractively interacting fermions provides a paradigmatic setting for fermion pairing. It features a crossover between Bose-Einstein condensation of tightly bound pairs and Bardeen-Cooper-Schrieffer superfluidity of long-range Cooper pairs, and a “pseudo-gap” region where pairs form above the superfluid critical temperature. We directly observe the nonlocal nature of fermion pairing in a Hubbard lattice gas, using spin- and density-resolved imaging of ∼ 1000 fermionic potassium-40 atoms under a bilayer microscope. Complete fermion pairing is revealed by the vanishing of global spin fluctuations with increasing attraction. In the strongly correlated regime, the fermion pair size is found to be on the order of the average interparticle spacing. Our study informs theories of pseudo-gap behavior in strongly correlated fermion systems.

Electron–Phonon Superconductivity in Boron‐Based Chalcogenide (X= S, Se) Monolayers

AbstractElectron–phonon mediated superconductivity is deeply investigated in two boron based monolayer materials, namely, , a metal exhibiting the ability to superconduct, and a new metal, , presenting perfect kinetic stability. Calculations based on density functional perturbation theory combined with the maximally localized Wannier function also reveal that both materials exhibit anisotropic planar hexagonal structure like graphene. The key parameters involved in the superconductor behavior are all calculated. The electronic density in the Fermi surface is given to provide the environment for enhanced electron–phonon coupling. The longitudinal and transverse vibration modes of optical phonons mainly contribute to the electron–phonon coupling strength. Furthermore, the binding energy between the bosonic Cooper pair superfluid is quantified and determined. The critical temperature for the two materials is 20 and 10.5 K, respectively. The results obtained show the potential use of such materials for superconducting applications.

Mixtures of ultracold atomic gases in optical lattices with nonzero pair or counterflow hopping

We study the critical behavior of a mixture of two species of lattice bosons described by the extended Bose–Hubbard model. Our goal is to analyze in which conditions exotic orderings like pair superfluid or counterflow superfluid could be detected. We use a numerical method based on mean field approximation to calculate the phase diagram of the system, along with particle density, and order parameter profiles in selected multicritical points. We observe that the phase diagram becomes significantly renormalized in the presence of pair flow or counterflow. Furthermore, a critical particle density emerges, which isolates a new region of the phase diagram, in which the exotic order parameter exists for any value of single-particle hopping.

Resonant superfluidity in the Rabi-coupled spin-dependent Fermi-Hubbard model

We investigate the ground-state phase diagram of the one-dimensional attractive Fermi-Hubbard model with spin-dependent hoppings and an on-site Rabi coupling using the density matrix renormalization group method. In particular, we show that even in the limit of one component being immobile the pair superfluidity can be resonantly enhanced when the Rabi coupling is on the order of the interaction strength just before the system starts to strongly polarize. We derive an effective spin-1/2 XXZ model in order to understand the ground-state properties in the strong attraction limit.

Collective interlayer pairing and pair superfluidity in vertically stacked layers of dipolar excitons

Layered bosonic dipolar fluids have been suggested to host a condensate of interlayer molecular bound states. However, experimental observation has remained elusive. Motivated by two recent experimental works [C. Hubert et al., Phys. Rev. X9, 021026 (2019) and D. J. Choksy et al., Phys. Rev. B 103, 045126 (2021)], we theoretically study, using numerically exact quantum Monte Carlo calculations, the experimental signatures of collective interlayer pairing in vertically stacked indirect exciton (IX) layers. We find that IX energy shifts associated with each layer evolve nontrivially as a function of density imbalance following a nonmonotonic trend with a jump discontinuity at density balance, identified with the interlayer IX molecule gap. This behavior discriminates between the superfluidity of interlayer bound pairs and independent dipole condensation in distinct layers. Considering finite temperature and finite density imbalance conditions, we find a cascade of Berezinskii-Kosterlitz-Thouless (BKT) transitions, initially into a pair superfluid and only then, at lower temperatures, into complete superfluidity of both layers. Our results may provide a theoretical interpretation of existing experimental observations in GaAs double quantum well (DQW) bilayer structures. Furthermore, to optimize the visibility of pairing dynamics in future studies, we present an analysis suggesting realistic experimental settings in GaAs and transition metal dichalcogenide (TMD) bilayer DQW heterostructures where collective interlayer pairing and pair superfluidity can be clearly observed.

Two-dimensional paired topological superfluids of Rydberg Fermi gases

We systematically investigate the topological properties of spin polarized Rydberg-dressed fermionic atoms loaded in a bilayer optical lattice. Through tuning the Rydberg coupling strength and the interlayer tunneling amplitude, we identify different types of topological superfluid states generated from the interlayer pairing and relative pairing phase modulation of the coupled two-dimensional $p$-wave superfluids. These phases include gapped/gapless with/without time-reversal symmetry. One of the most interesting states is a gapless paired topological superfluid with both the time-reversal symmetry and particle-hole symmetry, which is a realization of a DIII gapless topological superconductor. The flexibility of experimental manipulation in such Rydberg-dressed fermionic systems therefore becomes a promising system for realizing interesting topological superfluids.

Coexistence of two kinds of superfluidity at finite temperatures in optical lattices

Bosonic lattice systems with extended interactions constitute a unique platform to study new phases of matter. This work presents an analysis of the Bose–Hubbard model with density-induced tunneling. The U(1) quantum rotor method in the path integral effective action formulation is used. This approach enables the discovery of a second kind of superfluidity in physical systems: pair superfluidity, thus adding to the phases of matter. It also sheds light on the properties of single-particle Bose–Einstein condensation (BEC) in optical lattice systems with higher inter-particle correlations. The derived effective phase Hamiltonian includes the residue of many-body correlations, providing information about phase transitions between the normal state and single-particle and pair superfluids at finite temperatures. The thermodynamical properties of the system are investigated. The impact of density-induced tunneling on single-particle BEC is also analyzed. The density-induced term supports single-particle coherence at high densities and low temperatures, improving the single BEC critical temperature. It is also responsible for dissipative effects, which are independent of the system’s thermal properties.

Mobile impurity probing a two-dimensional superfluid phase transition

The use of atomically sized quantum systems as highly sensitive measuring devices represents an exciting and quickly growing research field. Here, we explore the properties of a quasiparticle formed by a mobile impurity interacting with a two-dimensional fermionic superfluid. The energy of the quasiparticle is shown to be lowered by superfluid pairing as this increases the compressibility of the Fermi gas, thereby making it easier for the impurity to perturb its surroundings. We demonstrate that the fundamentally discontinuous nature of the superfluid to normal phase transition of a two-dimensional system, leads to a rapid increase in the quasiparticle energy around the critical temperature. The magnitude of this increase exhibits a nonmonotonic behavior as a function of the pairing strength with a sizable maximum in the cross-over region, where the spatial extend of the Cooper pairs is comparable to the interparticle spacing. Since the quasiparticle energy is measurable with present experimental techniques, our results illustrate how impurities entangled with their environment can serve as useful probes for non-trivial thermal and quantum correlations.

Exact Quasiparticle Properties of a Heavy Polaron in BCS Fermi Superfluids.

We present the Ramsey response and radio-frequency spectroscopy of a heavy impurity immersed in an interacting Fermi superfluid, using the exact functional determinant approach. We describe the Fermi superfluid through the conventional Bardeen-Cooper-Schrieffer theory and investigate the role of the pairing gap on quasiparticle properties revealed by the two spectroscopies. The energy cost for pair breaking prevents Anderson's orthogonality catastrophe that occurs in a noninteracting Fermi gas and allows the existence of polaron quasiparticles in the exactly solvable heavy impurity limit. Hence, we rigorously confirm the remarkable features such as dark continuum, molecule-hole continuum, and repulsive polaron. For a magnetic impurity scattering at finite temperature, we predict additional resonances related to the subgap Yu-Shiba-Rusinov bound state, whose positions can be used to measure the superfluid pairing gap. For a nonmagnetic scattering at zero temperature, we surprisingly find undamped repulsive polarons. These exact results might be readily observed in quantum gas experiments with Bose-Fermi mixtures that have a large-mass ratio.

Heavy polarons in ultracold atomic Fermi superfluids at the BEC-BCS crossover: Formalism and applications

We investigate the system of a heavy impurity embedded in a paired two-component Fermi gas at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen-Cooper-Schrieffer (BCS) superfluid via an extension of the functional determinant approach (FDA). FDA is an exact numerical approach applied to study manifestations of Anderson's orthogonality catastrophe (OC) in the system of a static impurity immersed in an ideal Fermi gas. Here, we extend the FDA to a strongly correlated superfluid background described by a BCS mean-field wave function. In contrast to the ideal Fermi gas case, the pairing gap in the BCS superfluid prevents the OC and leads to genuine polaron signals in the spectrum. Thus our exactly solvable model can provide a deeper understanding of polaron physics. In addition, we find that the polaron spectrum can be used to measure the superfluid pairing gap, and in the case of a magnetic impurity, the energy of the subgap Yu-Shiba-Rusinov (YSR) bound state. Our theoretical predictions can be examined with state-of-art cold-atom experiments.

Quantum simulation of interacting fermions

Fermions are basic building blocks in the standard model. Interactions among these elementary particles determine how they assemble and consequently form various states of matter in our nature. Simulating fermionic degrees of freedom is also a central problem in condensed matter physics and quantum chemistry, which is crucial to understanding high-temperature superconductivity, quantum magnetism and molecular structure and functionality. However, simulating interacting fermions by classical computing generically face the minus sign problem, encountering the exponential computation complexity. Ultracold atoms provide an ideal experimental platform for quantum simulation of interacting fermions. This highly-controllable system enables the realizing of nontrivial fermionic models, by which the physical properties of the models can be obtained by measurements in experiment. This deepens our understanding of related physical mechanisms and helps determine the key parameters. In recent years, there have been versatile experimental studies on quantum ground state physics, finite temperature thermal equilibrium, and quantum many-body dynamics, in fermionic quantum simulation systems. Quantum simulation offers an access to the physical problems that are intractable on the classical computer, including studying macroscopic quantum phenomena and microscopic physical mechanisms, which demonstrates the quantum advantages of controllable quantum systems. This paper briefly introduces the model of interacting fermions describing the quantum states of matter in such a system. Then we discuss various states of matter, which can arise in interacting fermionic quantum systems, including Cooper pair superfluids and density-wave orders. These exotic quantum states play important roles in describing high-temperature superconductivity and quantum magnetism, but their simulations on the classical computers have exponentially computational cost. Related researches on quantum simulation of interacting fermions in determining the phase diagrams and equation of states reflect the quantum advantage of such systems.

Superfluid density, Josephson relation and pairing fluctuations in a multi-component fermion superfluid

In this work, a Josephson relation is generalized to a multi-component fermion superfluid. Superfluid density is expressed through a two-particle Green function for pairing states. When the system has only one gapless collective excitation mode, the Josephson relation is simplified, which is given in terms of the superfluid order parameters and the trace of two-particle normal Green function. In addition, it is found that the matrix elements of two-particle Green function is directly related to the matrix elements of the pairing fluctuations of superfluid order parameters. Furthermore, in the presence of inversion symmetry, the superfluid density is given in terms of the pairing fluctuation matrix. The results of the superfluid density in Haldane model show that the generalized Josephson relation can be also applied to a multi-band fermion superfluid in lattice.

Nuclear superfluidity at finite temperature

The equation of motion for the two-fermion two-time correlation function in the pairing channel is considered at finite temperature. Within the Matsubara formalism, the Dyson-type Bethe-Salpeter equation (Dyson-BSE) with the frequency-dependent interaction kernel is obtained. Similarly to the case of zero temperature, it is decomposed into the static and dynamical components, where the former is given by the contraction of the bare interaction with the two-fermion density and the latter is represented by the double contraction of the four-fermion two-time correlation function, or propagator, with two interaction matrix elements. The dynamical kernel with the four-body propagator, being formally exact, requires approximations to avoid generating prohibitively complicated hierarchy of equations. We focus on the approximation where the dynamical interaction kernel is truncated on the level of two-body correlation functions, neglecting the irreducible three-body and higher-rank correlations. Such a truncation leads to the dynamical kernel with the coupling between correlated fermionic pairs, which can be interpreted as emergent bosonic quasibound states, or phonons, of normal and superfluid nature. The latter ones are, thus, the mediators of the dynamical superfluid pairing. In this framework, we obtained the closed system of equations for the fermionic particle-hole and particle-particle propagators. This allows us to study the temperature dependence of the pairing gap beyond the Bardeen-Cooper-Schrieffer approximation, that is implemented for medium-heavy nuclear systems. The cases of 68Ni and 44,46Ca are discussed in detail.

Toolbox for elementary fermions with a dipolar Fermi gas in a three-dimensional optical lattice

There has been growing interest in investigating properties of elementary particles predicted by the standard model. Examples of such studies include exploring their low-energy analogs in a condensed-matter system, where they arise as collective states or quasiparticles. Here we show that a toolbox for systematically engineering the emergent elementary fermions, i.e., Dirac, Weyl, and Majorana fermions, can be built in a single atomic system composed of a spinless magnetic dipolar Fermi gas in a three-dimensional optical lattice. The designed direction-dependent dipole-dipole interaction leads to both the basic building block, i.e., in-plane $p+ip$ superfluid pairing instability, and the manipulating tool, i.e., out-of-plane Peierls instability. It is shown that the Peierls instability provides a natural way of tuning the topological nature of $p+ip$ superfluids and can transform the fermion's nature between distinct emergent particles. Our scheme should contribute to the search for elementary particles through manipulating the topology.

Pairing and Pair Superfluid Density in One-Dimensional Two-Species Fermionic and Bosonic Hubbard Models.

We use unbiased computational methods to elucidate the onset and properties of pair superfluidity in two-species fermionic and bosonic systems with onsite interspecies attraction loaded in a uniform, i.e., with no confining potential, one-dimensional optical lattice. We compare results from quantum MonteCarlo (QMC) and density matrix renormalization group (DMRG), emphasizing the one-to-one correspondence between the Drude weight tensor, calculated with DMRG, and the various winding numbers extracted from the QMC. Our results show that, for any nonvanishing attractive interaction, pairs form and are the sole contributors to superfluidity; there are no individual contributions due to the separate species. For weak attraction, the pair size diverges exponentially, i.e., Bardeen-Cooper-Schrieffer (BCS) pairing, requiring huge systems to bring out the pair-only nature of the superfluid. This crucial property is largely overlooked in many studies, thereby misinterpreting the origin and nature of the superfluid. We compare and contrast this with the repulsive case and show that the behavior is very different, contradicting previous claims about drag superfluidity and the symmetry of properties for attractive and repulsive interactions. Finally, our results show that the situation is similar for soft-core bosons: superfluidity is due only to pairs, even for the smallest attractive interaction strength compatible with the largest system sizes that we could attain.

Low-Density Neutron Matter and the Unitary Limit

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.

Pairing in pure neutron matter

We review the long standing problem of superfluid pairing in pure neutron matter. For the $s$-wave pairing, we summarize the state of the art of many-body approaches including different $nn$ interactions, medium polarization, short-range correlations and BCS-BEC crossover effects, and compare them with quantum Monte Carlo results at low-densities. We also address pairing in the $p$-wave, which appears at higher densities and hence has large uncertainties due to the poorly constrained interactions, medium effects and many-body forces.

Superfluid states in α – T 3 lattice* *Project supported by the National Natural Science Foundation of China (Grant No. 11874127) and the startup grant from Guangzhou University.

The superfluid states of attractive Hubbard model in α–T 3 lattice are investigated. It is found that one usual needs three non-zero superfluid order parameters to describe the superfluid states due to three sublattices. When two hopping amplitudes are equal, the system has particle–hole symmetry. The flat band plays an important role in superfluid pairing near half filling. For example, when the filling factor falls into the flat band, the large density of states in the flat band favors superfluid pairing and the superfluid order parameters reach relatively large values. When the filling factor is in the gap between the flat band and upper band, the superfluid order parameters take small values due to the vanishing of density of states. The superfluid order parameters show nonmonotonic behaviors with the increase of filling factor. At last, we also investigate the edge states with open boundary conditions. It is shown that there exist some interesting edge states in the middle of quasi-particle bands.