Superfluidity and magnetism in multicomponent ultracold fermions

We study the interplay between superfluidity and magnetism in a multicomponent gas of ultracold fermions. Ward-Takahashi identities constrain possible mean-field states describing order parameters for both pairing and magnetization. The structure of global phase diagrams arises from competition among these states as functions of anisotropies in chemical potential, density, or interactions. They exhibit first and second order phase transition as well as multicritical points, metastability regions, and phase separation. We comment on experimental signatures in ultracold atoms.     

Pairing superfluidity in spin-orbit coupled ultracold Fermi gases

We review some recent progresses on the study of ultracold Fermi gases with synthetic spin-orbit coupling.In particular,we focus on the pairing superfluidity in these systems at zero temperature.Recent studies have shown that different forms of spin-orbit coupling in various spatial dimensions can lead to a wealth of novel pairing superfluidity.A common theme of these variations is the emergence of new pairing mechanisms which are direct results of spin-orbit-coupling-modified single-particle dispersion spectra.As different configurations can give rise to single-particle dispersion spectra with drastic differences in symmetry,spin dependence and low-energy density of states,spin-orbit coupling is potentially a powerful tool of quantum control,which,when combined with other available control schemes in ultracold atomic gases,will enable us to engineer novel states of matter.     

BCS theory for trapped ultracold fermions

We develop an extension of the well-known BCS-theory to systems with trapped fermionic atoms. The theory fully includes the quantized energy levels in the trap. The key ingredient is to model the attractive interaction between two atoms by a pseudo-potential which leads to a well defined scattering problem and consequently to a BCS-theory free of divergences. We present numerical results for the BCS critical temperature and the temperature dependence of the gap. They are used as a test of existing semi-classical approximations. Received 18 December 1998     

Tunable superfluidity and quantum magnetism with ultracold polar molecules

By selecting two dressed rotational states of ultracold polar molecules in an optical lattice, we obtain a highly tunable generalization of the t-J model, which we refer to as the t-J-V-W model. In addition to XXZ spin exchange, the model features density-density interactions and density-spin interactions; all interactions are dipolar. We show that full control of all interaction parameters in both magnitude and sign can be achieved independently of each other and of the tunneling. As a first step towards demonstrating the potential of the system, we apply the density matrix renormalization group method to obtain the 1D phase diagram of the simplest experimentally realizable case. Specifically, we show that the tunability and the long-range nature of the interactions in the t-J-V-W model enable enhanced superfluidity. Finally, we show that Bloch oscillations in a tilted lattice can be used to probe the phase diagram experimentally.     

Noise correlations in one-dimensional systems of ultracold fermions

Time of flight images reflect the momentum distribution of the atoms in the trap, but the spatial noise in the image holds information on more subtle correlations. Using bosonization, we study such correlations in generic 1D systems of ultracold fermions. We show how pairing as well as spin and charge density wave correlations may be identified and extracted from time of flight images. These incipient orders manifest themselves as power-law singularities in the noise correlations, that depend on the Luttinger parameters, which suggests a general experimental technique to obtain them.     

Counterflow superfluidity of two-species ultracold atoms in a commensurate optical lattice

In the Mott-insulator regime, two species of ultracold atoms in an optical lattice can exhibit the low-energy counterflow motion. We construct effective Hamiltonians for the three classes of the two-species (fermion-fermion, boson-boson, and boson-fermion-type) insulators and reveal the conditions when the resulting ground state supports super-counter-fluidity (SCF), with the alternative being phase segregation. We emphasize a crucial role of breaking the isotopic symmetry between the species for realizing the SCF phase.     

Energy spectrum and superfluidity of spin-2 ultracold bosons in optical lattices

This paper studies the superfluidity of ultracold spin-2 Bose atoms with weak interactions in optical lattices by calculating the excitation energy spectrum using the Bogoliubov approach. The energy spectra exhibit the characteristics of the superfluid-phase explicitly and it finds the nonvanishing critical speeds of superfluid. The obtained results display that the critical speeds of superfluid are different for five spin components and can be controlled by adjusting the lattice parameters in experiments. Finally it discusses the feasibilities of implementing and measuring superfluid.     

Prospects of detecting baryon and quark superfluidity from cooling neutron stars

Baryon and quark superfluidity in the cooling of neutron stars are investigated. Future observations will allow us to constrain combinations of the neutron or Lambda-hyperon pairing gaps and the star's mass. However, in a hybrid star with a mixed phase of hadrons and quarks, quark gaps larger than a few tenths of an MeV render quark matter virtually invisible for cooling. If the quark gap is smaller, quark superfluidity could be important, but its effects will be nearly impossible to distinguish from those of other baryonic constituents.     

Stability of superflow for ultracold fermions in optical lattices

We investigate the stability of superflow of paired fermions in an optical lattice. We show that there are two distinct dynamical instabilities which limit the superflow in this system. One dynamical instability occurs when the superfluid stiffness becomes negative; this evolves, with increasing pairing interaction, from the fermion pair breaking instability to the well-known dynamical instability of lattice bosons. The second, more interesting, dynamical instability is marked by the emergence of a transient atom density wave. Both dynamical instabilities can be experimentally accessed by tuning the pairing interaction and the fermion density.     

Three ultracold fermions in a two-dimensional anisotropic harmonic confinement

We calculate the energy spectrum of three identical fermionic ultracold atoms in two different internal states confined in a two-dimensional anisotropic harmonic trap. Using the solutions of the corresponding two-body problems obtained in our previous work (Chen et al 2020 Phys. Rev. A 101, 053624), we derive the explicit transcendental equation for the eigen-energies, from which the energy spectrum is derived. Our results can be used for the calculation of the 3rd Virial coefficients or the studies of few-body dynamics.     

Ultra high temperature superfluidity in ultracold atomic Fermi gases with mixed dimensionality

It has been an important goal to achieve higher or even room temperature superconductivity,since the discovery of high Tc superconductors in 1986,with a typical maximum transition temperature Tc of around 95 K at ambien pressure[1]or up to 164 K for the Hg-based cuprates under high pressure[2].The typical Tc/TF is only around 0.05 or less,where TF denotes the Fermi temperature.There have been a few other families of superconductors,including the iron-based[3],heavy fermion[4]and organic superconductors[5].Their maximum attainable Tc/TF has not been able to exceed that of the cuprates.Other notable superconductors include the recently discovered H2S with a record high Tc=203 K under an enormous high pressure of 90 GPa[6],and the monolayer FeSe/SrTiO3 superconductors with a gap opening temperature up to 100 K[7].     

Probing non-abelian statistics of Majorana fermions in ultracold atomic superfluid

We propose an experiment to directly probe the non-abelian statistics of Majorana fermions by braiding them in an s-wave superfluid of ultracold atoms. We show that different orders of braiding operations give orthogonal output states that can be distinguished through Raman spectroscopy. Realization of Majorana states in an s-wave superfluid requires strong spin-orbital coupling and a controllable Zeeman field in the perpendicular direction. We present a simple laser configuration to generate the artificial spin-orbital coupling and the required Zeeman field in the dark-state subspace.     

Detection of spatial correlations in an ultracold gas of fermions

Spatial correlations are observed in an ultracold gas of fermionic atoms close to a Feshbach resonance. The correlations are detected by inducing spin-changing rf transitions between pairs of atoms. We observe the process in the strongly interacting regime for attractive as well as for repulsive atom-atom interactions and both in the regime of high and low quantum degeneracy. The observations are compared with a two-particle model that provides theoretical predictions for the measured rf transition rates.     

Magnetic phase transitions in one-dimensional strongly attractive three-component ultracold fermions

We investigate the nature of trions, pairing, and quantum phase transitions in one-dimensional strongly attractive three-component ultracold fermions in external fields. Exact results for the ground-state energy, critical fields, magnetization and phase diagrams are obtained analytically from the Bethe ansatz solutions. Driven by Zeeman splitting, the system shows exotic phases of trions, bound pairs, a normal Fermi liquid, and four mixtures of these states. Particularly, a smooth phase transition from a trionic phase into a pairing phase occurs as the highest hyperfine level separates from the two lower energy levels. In contrast, there is a smooth phase transition from the trionic phase into a normal Fermi liquid as the lowest level separates from the two higher levels.     

Probing nearest-neighbor correlations of ultracold fermions in an optical lattice

We demonstrate a probe for nearest-neighbor correlations of fermionic quantum gases in optical lattices. It gives access to spin and density configurations of adjacent sites and relies on creating additional doubly occupied sites by perturbative lattice modulation. The measured correlations for different lattice temperatures are in good agreement with an ab initio calculation without any fitting parameters. This probe opens new prospects for studying the approach to magnetically ordered phases.     

Probing superfluidity of periodically trapped ultracold atoms in a cavity by transmission spectroscopy

We study a system of periodic Bose-condensed atoms coupled to cavity photons using the input-output formalism of [14]. We show for the first time that the cavity will either act as a through-pass Lorentzian filter when the superfluid fraction of the condensate is minimum, or completely reflect the input field when the superfluid fraction is maximum. We show that by monitoring the ratio between the transmitted field and the reflected field, one can estimate the superfluid fraction.     

Suppression of superfluidity upon overflow of trapped fermions: quantal and Thomas-Fermi studies

Two issues are treated in this work. (i) The generic fact that, if a fermionic superfluid in the BCS regime overflows from a narrow container into a much wider one, pairing is much suppressed at the overflow point. Physical examples where this feature may play an important role are discussed. (ii) A Thomas-Fermi approach to inhomogeneous superfluid Fermi systems is presented and shown to work well in cases where the local density approximation breaks down.     

Signature of Mott-insulator transition with ultracold fermions in a one-dimensional optical lattice

Using the exact Bethe ansatz solution of the Hubbard model and Luttinger liquid theory, we investigate the density profiles and collective modes of one-dimensional ultracold fermions confined in an optical lattice with a harmonic trapping potential. We determine a generic phase diagram in terms of a characteristic filling factor and a dimensionless coupling constant. The collective oscillations of the atomic mass density, a technique that is commonly used in experiments, provide a signature of the quantum phase transition from the metallic phase to the Mott-insulator phase. A detailed experimental implementation is proposed.     

Quantum simulation of the Hubbard model with ultracold fermions in optical lattices

Ultracold atomic gases provide a fantastic platform to implement quantum simulators and investigate a variety of models initially introduced in condensed matter physics or other areas. One of the most promising applications of quantum simulation is the study of strongly correlated Fermi gases, for which exact theoretical results are not always possible with state-of-the-art approaches. Here, we review recent progress of the quantum simulation of the emblematic Fermi–Hubbard model with ultracold atoms. After introducing the Fermi–Hubbard model in the context of condensed matter, its implementation in ultracold atom systems, and its phase diagram, we review landmark experimental achievements, from the early observation of the onset of quantum degeneracy and superfluidity to the demonstration of the Mott insulator regime and the emergence of long-range anti-ferromagnetic order. We conclude by discussing future challenges, including the possible observation of high-$T_{\mathrm{c}}$ superconductivity, transport properties, and the interplay of strong correlations and disorder or topology.     

Light-induced unconventional Landau levels of ultracold fermions in a trilayer honeycomb lattice

The spectrum of cold fermionic atoms is studied in a trilayer honeycomb optical lattice subjected to a perpendicular effective magnetic field,which is created with optical means. In the low energy approximation,the spectrum shows unconventional Landau levels,which are proportional to the 3/2 power of integer numbers. The zoro modes exist and the quasiparticles are chiral. It is also proposed to identify the unconventional Landau levels via probing the dynamic structure factor of the system with Bragg spectr...