The study of ultracold atomic Fermi gases is a rapidly exploding subject which is defining new directions in condensed matter and atomic physics. Quite generally what makes these gases so important is their remarkable tunability and controllability. Using a Feshbach resonance one can tune the attractive two-body interactions from weak to strong and thereby make a smooth crossover from a BCS superfluid of Cooper pairs to a Bose-Einstein condensed superfluid. Furthermore, one can tune the population of the two spin states, allowing observation of exotic spin-polarized superfluids, such as the Fulde Ferrell Larkin Ovchinnikov (FFLO) phase. A wide array of powerful characterization tools, which often have direct condensed matter analogues, are available to the experimenter. In this Chapter, we present a general review of the status of these Fermi gases with the aim of communicating the excitement and great potential of the field.
Quantum phase slips are the primary excitations in one-dimensional superfluids and superconductors at low temperatures. They have been well characterized in most condensed-matter systems, and signatures of their existence has been recently observed in superfluids based on quantum gases too. In this review we briefly summarize the main results obtained on the investigation of phase slips from superconductors to quantum gases. In particular we focus our attention on recent experimental results of the dissipation in one-dimensional Bose superfluids flowing along a shallow periodic potential, whic…
We consider dynamic, i.e., frequency-dependent, correlations in non-condensed ultracold atomic Bose gases. In particular, we consider the single-particle correlation function and its power spectrum. We compute this power spectrum for a one-component Bose gas, and show how it depends on the interatomic interactions that lead to a finite single-particle relaxation time. As another example, we consider the power spectrum of spin-current fluctuations for a two-component Bose gas and show how it is determined by the spin-transport relaxation time.
We investigate the equilibrium phase-coherence properties of Bose-condensed particle systems, focusing on their shape dependence and finite-size scaling (FSS). We consider three-dimensional (3D) homogeneous systems confined to anisotropic L x L x L_a boxes, below the BEC transition temperature $T_c$. We show that the phase correlations develop peculiar anisotropic FSS for any $T<T_c$, in the large-$L$ limit keeping the ratio λ= L_a/L^2 fixed. This phenomenon is effectively described by the 3D spin-wave (SW) theory. Its universality is confirmed by quantum Monte Carlo simulations of the 3D Bose…
Considering a Bose-Einstein condensed gas confined in one dimension with periodic boundary conditions, we demonstrate that, very generally, solitary-wave and rotational excitations coincide. This exact equivalence allows us to establish connections between a number of effects that are present in these two problems, many of which have been studied using the mean-field approximation.
We investigate the properties of quantized vortices in a dipolar Bose-Einstein condensed gas by means of a generalised Gross-Pitaevskii equation. The size of the vortex core hugely increases by increasing the weight of the dipolar interaction and approaching the transition to the supersolid phase. The critical angular velocity for the existence of an energetically stable vortex decreases in the supersolid, due to the reduced value of the density in the interdroplet region. The angular momentum per particle associated with the vortex line is shown to be smaller than $\hbar$, reflecting the redu…
This article reviews some recent developments for new cooling technologies in the fields of condensed matter physics and cold gases, both from an experimental and theoretical point of view. The main idea is to make use of distinct many-body interactions of the system to be cooled which can be some cooling stage or the material of interest itself, as is the case in cold gases. For condensed matter systems, we discuss magnetic cooling schemes based on a large magnetocaloric effect as a result of a nearby quantum phase transition and consider effects of geometrical frustration. For ultracold gase…
We explore atom-laser-like transport processes of ultracold Bose-condensed atomic vapors in mesoscopic waveguide structures beyond the Gross-Pitaevskii mean-field theory. Based on a microscopic description of the transport process in the presence of a coherent source which models the outcoupling from a reservoir of perfectly Bose-Einstein condensed atoms, we derive a system of coupled quantum evolution equations that describe the dynamics of a dilute condensed Bose gas in the framework of the Hartree-Fock-Bogoliubov approximation. We apply this method to study the transport of dilute Bose gase…
This paper summarizes some of the relevant features exhibited by bi-nary mixtures of Bose-Einstein condensates in the presence of coherent coupling at zero temperature. The coupling, which is experimentally produced by proper photon transitions, can either involve negligible momentum transfer from the electromagnetic radiation (Rabi coupling) or large momentum transfer (Raman coupling) associated with spin-orbit effects.The nature of the quantum phases exhibited by coherently coupled mixtures is discussed in detail, including their paramagnetic, ferromagnetic, and, in the case of spin-orbit co…
The temporal evolution of a perturbation of the equilibrium distribution of a condensed Bose gas is investigated using the kinetic equation which describes collision between condensate and noncondensate atoms. The dynamics is studied in the low momentum limit where an analytical treatment is feasible. Explicit results are given for the behavior at large times in different temperature regimes.
Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic, long-range dipolar interactions play a prominent role at the many-body level. In this article we review recent theoretical studies concerning the physics of such systems. Starting from a general discussion on interaction design techniques and microscopic Hamiltonians, we provide a summary of recent work focused on many-body properties of dipolar systems, including: …
We review the physics of one-dimensional interacting bosonic systems. Beginning with results from exactly solvable models and computational approaches, we introduce the concept of bosonic Tomonaga-Luttinger Liquids relevant for one-dimension, and compare it with Bose-Einstein condensates existing in dimensions higher than one. We discuss the effects of various perturbations on the Tomonaga-Luttinger liquid state as well as extensions to multicomponent and out of equilibrium situations. Finally, we review the experimental systems that can be described in terms of models of interacting bosons in…
Recent experiments with ultra-cold atoms have demonstrated the possibility of realizing experimentally fermionic superfluids with imbalanced spin populations. We discuss how these developments have shed a new light on a half- century old open problem in condensed matter physics, and raised new interrogations of their own.
The Anderson-Bogoliubov branch of collective excitations in a condensed Fermi gas is treated using the effective bosonic action of Gaussian pair fluctuations. The spectra of collective excitations are treated for finite temperature and momentum throughout the BCS-BEC crossover. The obtained spectra explain, both qualitatively and quantitatively, recent experimental results on Goldstone modes in atomic Fermi superfluids.
We study the time evolution of two coupled many-body quantum systems one of which is assumed to be Bose condensed. Specifically, we consider two ultracold atomic clouds populating each two localized single-particle states, i.e. a two-component Bosonic Josephson junction. The cold atoms cloud can retain its coherence when coupled to the condensate and displays synchronization with the latter, differing from usual entrainment. We term this effect among the ultracold and the condensed clouds as {\it hybrid synchronization}. The onset of synchronization, which we observe in the evolution of averag…
We study the condensed phase of a Bose-Fermi mixture with a tunable pairing interaction between bosons and fermions with many-body diagrammatic methods and fixed-node diffusion Quantum Monte Carlo simulations. A universal behavior of the condensate fraction and bosonic momentum distribution with respect to the boson concentration is found to hold in an extended range of boson-fermion couplings and concentrations. For vanishing boson density, we prove that the bosonic condensate fraction reduces to the quasiparticle weight Z of the Fermi polaron studied in the context of polarized Fermi gases, …
A central challenge in modern condensed matter physics is developing the tools for understanding nontrivial yet unordered states of matter. One important idea to emerge in this context is that of a "pseudogap": the fact that under appropriate circumstances the normal state displays a suppression of the single particle spectral density near the Fermi level, reminiscent of the gaps seen in ordered states of matter. While these concepts arose in a solid state context, it is now being explored in cold gases. This article reviews the current experimental and theoretical understanding of the normal …
Spin-orbit coupling (SOC) is central to many physical phenomena, including fine structures of atomic spectra and quantum topological matters. Whereas SOC is in general fixed in a physical system, atom-laser interaction provides physicists a unique means to create and control synthetic SOC for ultracold atoms \cite{Dalibard}. Though significant experimental progresses have been made, a bottleneck in current studies is the lack of a two-dimensional (2D) synthetic SOC, which is crucial for realizing high-dimensional topological matters. Here, we report the experimental realization of 2D SOC in ul…
Exact calculation of the condensate fraction in multi-dimensional inhomogeneous interacting Bose systems which do not possess continuous symmetries is a difficult computational problem. We have developed an iterative procedure which allows to calculate the condensate fraction as well as the corresponding eigenfunction of the one-body density matrix. We successfully validate this procedure in diffusion Monte Carlo simulations of a Bose gas in an optical lattice at zero temperature. We also discuss relation between different criteria used for testing coherence in cold Bose systems, such as fract…
Spin-orbit coupling plays an increasingly important role in the modern condensed matter physics. For instance, it gives birth to topological insulators and topological superconductors. Quantum simulation of spin-orbit coupling using ultracold Fermi gases will offer opportunities to study these new phenomena in a more controllable setting. Here we report the first experimental study of a spin-orbit coupled Fermi gas. We observe spin dephasing in spin dynamics and momentum distribution asymmetry in the equilibrium state as hallmarks of spin-orbit coupling. We also observe evidences of Lifshitz t…
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 study energy and particle transport for one-dimensional strongly interacting bosons through a single channel connecting two atomic reservoirs. We show the emergence of particle- and energy- current separation, leading to the violation of the Wiedemann-Franz law. As a consequence, we predict different time scales for the equilibration of temperature and particle imbalances between the reservoirs. Going beyond the linear spectrum approximation, we show the emergence of ther- moelectric effects, which could be controlled by either tuning interactions or the temperature. Our results describe in…
We report on previously unobserved inter-system degeneracies in two-component equal-mass Fermi gases with interspecies zero-range interactions under isotropic harmonic confinement. Over the past 10 years, two-component Fermi gases consisting of $n_1$ spin-up and $n_2$ spin-down atoms with interspecies zero-range interactions have become a paradigm for modeling condensed matter systems, nuclear matter and neutron matter. We show that the eigen energies of the $(n_1+1,n_2-1)$ system are degenerate with the eigen energies of the $(n_1,n_2)$ system for any s-wave scattering length $a_s$, including…
Recently it has been proposed that three-component Fermi gases may exhibit a new type of crossover physics in which an unpaired Fermi sea of atoms smoothly evolves into that of trimers in addition to the ordinary BCS-BEC crossover of condensed pairs. Here we study its corresponding polaron problem in which a single impurity atom of one component interacts with condensed pairs of the other two components with equal populations. By developing a variational approach in the vicinity of a narrow Feshbach resonance, we show that the impurity atom smoothly changes its character from atom to trimer wi…
The notion of fluctuation indices, characterizing thermodynamic stability of statistical systems, is advanced. These indices are especially useful for investigating the stability of nonuniform and trapped atomic assemblies. The fluctuation indices are calculated for several systems with Bose-Einstein condensate. It is shown that: the ideal uniform Bose-condensed gas is thermodynamically unstable; trapped ideal gases are stable for the confining dimension larger than two; trapped gases, under the confining dimension two, are weakly unstable; harmonically trapped gas is stable only for the spati…
We study the BCS-Bose Einstein Condensation (BEC) crossover of a three dimensional spin polarized Fermi gas with Rashba spin-orbital-coupling (SOC). At finite temperature, the effects of non-condensed pairs due to the thermal excitation are considered based on the $G_0G$ pair fluctuation theory. These fluctuations generate a pseudogap even persistent above $T_c$. Within this framework, the Sarma state or the spin polarized superfluid state and polarized pseudogap state are explored in detail. The resulting $T_c$ curves show that the enhancement of pairing due to the SOC roughly cancels out the…
One exciting progress in recent cold atom experiments is the development of high resolution, in situ imaging techniques for atomic quantum gases [1-3]. These new powerful tools provide detailed information on the distribution of atoms in a trap with resolution approaching the level of single atom and even single lattice site, and complement the well developed time-of-flight method that probes the system in momentum space. In a condensed matter analogy, this technique is equivalent to locating electrons of a material in a snap shot. In situ imaging has offered a new powerful tool to study atomi…
The pair-condensed unpolarized spin-$1/2$ Fermi gases have a collective excitation branch in their pair-breaking continuum (V.A. Andrianov, V.N. Popov, 1976). We study it at zero temperature, with the eigenenergy equation deduced from the linearized time-dependent BCS theory and extended analytically to the lower half complex plane through its branch cut, calculating both the dispersion relation and the spectral weights (quasiparticle residues) of the branch. In the case of BCS superconductors, so called because the effect of the ion lattice is replaced by a short-range electron-electron inter…
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…
Interacting Fermi systems in the strongly correlated regime play a fundamental role in many areas of physics and are of particular interest to the condensed matter community. Though weakly inter- acting fermions are understood, strongly correlated fermions are difficult to describe theoretically as there is no small interaction parameter to expand about. Existing strong coupling theories rely heavily on the so-called many-body T-matrix approximation that sums ladder-type Feynman diagrams. Here, by acknowledging the fact that the effective interparticle interaction (i.e., the vertex function) b…
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 implementat…
The dynamics of internal spin, electronic orbital, and nuclear motion states of atoms and molecules have preoccupied the atomic and molecular physics community for decades. Increasingly, such dynamics are being examined within many-body systems composed of atomic and molecular gases. Our findings sometimes bear close relation to phenomena observed in condensed-matter systems, while on other occasions they represent truly new areas of investigation. I discuss several examples of spin dynamics that occur within spinor Bose-Einstein gases, highlighting the advantages of spin-sensitive imaging for…
We present a theory of the emission of fermion pairs from a superfluid Fermi gas induced by a photon absorption. In the solid state physics, this type of process is called double photo-emission (DPE). The spectrum of the induced two-particle current (or DPE current) provides a direct insight into the pair-correlation of condensate fermion pairs. We develop a general formalism for two-particle current induced by DPE by treating the coupling of two Fermi gases with the time-dependent perturbation theory. This formalism is used to calculate energy distributions of DPE current from the superfluid …
We examine possible low-temperature phases of a repulsively Rydberg-dressed Fermi gas in a three-dimensional free space. It is shown that the collective density excitations develop a roton minimum, which is softened at a wavevector smaller than the Fermi wavevector when the particle density is above a critical value. The mean field calculation shows that unlike the insulating charge density waves states often observed in conventional condensed matters, a self-assembled metallic density wave state emerges at low temperatures. In particular, the density wave state supports a Fermi surface and a …
When attempting to understand the role of disorder in condensed-matter physics, one faces severe experimental and theoretical difficulties and many questions are still open. Two of the most challenging ones, which have been debated for decades, concern the effect of disorder on superconductivity and quantum magnetism. Recent progress in ultracold atomic gases paves the way towards realization of versatile quantum simulators which will be useful to solve these questions. In addition, ultracold gases offer original situations and viewpoints, which open new perspectives to the field of disordered…
A trapped Bose-Einstein condensate, being strongly perturbed, exhibits several spatial structures. First, there appear quantum vortices. Increasing the amount of the injected energy leads to the formation of vortex tangles representing quantum vortex turbulence. Continuing energy injection makes the system so strongly perturbed that vortices become destroyed and there develops another kind of spatial structures with essentially heterogeneous spatial density. These structures consist of high-density droplets, or grains, surrounded by the regions of low density. The droplets are randomly distrib…
The non-Abelian gauge fields play a key role in achieving novel quantum phenomena in condensed-matter and high-energy physics. Recently, the synthetic non-Abelian gauge fields have been created in the neutral degenerate Fermi gases, and moreover, generate many exotic effects. All the previous predictions can be well understood by the microscopic Bardeen-Cooper-Schrieffer theory. In this work, we establish an SU(2) Ginzburg-Landau theory for degenerate Fermi gases with the synthetic non-Abelian gauge fields. We firstly address a fundamental problem how the non-Abelian gauge fields, imposing ori…
We study quantum information flow in a model comprising of an impurity qubit immersed in a Bose-Einstein condensed reservoir. We demonstrate how information flux between the qubit and the condensate can be manipulated by engineering the ultracold reservoir within experimentally realistic limits. We place a particular emphasis on non-Markovian dynamics, characterized by a reversed flow of information from the background gas to the qubit and identify a controllable crossover between Markovian and non-Markovian dynamics in the parameter space of the model.
We study the superfluid state of atomic Fermi gases using a BCS-BEC crossover theory. Our approach emphasizes non-condensed fermion pairs which strongly hybridize with their (Feshbach-induced) molecular boson counterparts. These pairs lead to pseudogap effects above $T_c$ and non-BCS characteristics below. We discuss how these effects influence the experimental signatures of superfluidity.
Spin-orbit coupling links a particle's velocity to its quantum mechanical spin, and is essential in numerous condensed matter phenomena, including topological insulators and Majorana fermions. In solid-state materials, spin-orbit coupling originates from the movement of electrons in a crystal's intrinsic electric field, which is uniquely prescribed. In contrast, for ultracold atomic systems, the engineered "material parameters" are tuneable: a variety of synthetic spin-orbit couplings can be engineered on demand using laser fields. Here we outline the current experimental and theoretical statu…
Three-dimensional topological gapless matters with gapless degeneracies protected by a topological invariant defined over a closed manifold in momentum space have attracted considerable interest in various fields ranging from condensed matter materials to ultracold atomic gases. As a highly controllable and disorder free system, ultracold atomic gases provide a versatile platform to simulate topological gapless matters. Here, the current progress in studies of topological gapless phenomena in three-dimensional cold atom systems is summarized in the review. It is mainly focused on Weyl points, …
The process of exciting the gas of trapped bosons from an equilibrium initial state to strongly nonequilibrium states is described as a procedure of symmetry restoration caused by external perturbations. Initially, the trapped gas is cooled down to such low temperatures, when practically all atoms are in Bose-Einstein condensed state, which implies the broken global gauge symmetry. Excitations are realized either by imposing external alternating fields, modulating the trapping potential and shaking the cloud of trapped atoms, or it can be done by varying atomic interactions by means of Feshbac…
We address the important question of how to characterize the normal state of fermionic superfluids under the influence of a strong effective magnetic field, implemented through rapid rotation or novel artificial field techniques. We consider the effects of crossing from BCS to BEC and the role of non-condensed pairs, or pseudogap effects. Using a simple extension of Gor'kov theory we demonstrate how these pairs organize above the transition $T_c$ into precursors of a vortex configuration, which are associated with distortions of the ideal Abrikosov lattice. This non-uniform normal state appear…
Cold atomic gases have proven capable of emulating a number of fundamental condensed matter phenomena including Bose-Einstein condensation, the Mott transition, Fulde-Ferrell-Larkin-Ovchinnikov pairing and the quantum Hall effect. Cooling to a low enough temperature to explore magnetism and exotic superconductivity in lattices of fermionic atoms remains a challenge. We propose a method to produce a low temperature gas by preparing it in a disordered potential and following a constant entropy trajectory to deliver the gas into a non-disordered state which exhibits these incompletely understood …
We study the rotational properties of a two-component Bose-Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or "collective" excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion re…
Recent experimental progresses allow for exploring some important physical quantities of ultracold Fermi gases, such as the compressibility, spin susceptibility, viscosity, optical conductivity and spin diffusivity. Theoretically, these quantities can be evaluated from suitable linear response theories. For BCS superfluid, it has been found that the gauge invariant linear response theories can be fully consistent with some stringent consistency constraints. When the theory is generalized to stronger-than-BCS regime, one may meet serious difficulties to satisfy the gauge invariance conditions. …
Ultracold two-component Fermi gases with a tunable population imbalance have provided an excellent opportunity for studying the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, which have been of great interest in condensed matter physics. However, the FFLO states have not been observed experimentally in Fermi gases in three dimensions (3D), possibly due to their small phase space volume and extremely low temperature required for an equal-mass Fermi gas. Here we explore possible effects of mass imbalance, mainly in a $^6$Li--$^{40}$K mixture, on the one-plane-wave FFLO phases for a 3D ho…
We show that the optical spin conductivity being a small AC response of a bulk spin current and elusive in condensed matter systems can be measured in ultracold atoms. We demonstrate that this conductivity contains rich information on quantum states by analyzing experimentally achievable systems such as a spin-1/2 superfluid Fermi gas, a spin-1 Bose-Einstein condensate, and a Tomonaga-Luttinger liquid. The obtained conductivity spectra being absent in the Drude conductivity reflect quasiparticle excitations and non-Fermi liquid properties. Accessible physical quantities include the superfluid …
