Phase separation in a polarized Fermi gas at zero temperature

Repulsive Fermi and Bose Polarons in Quantum Gases

Polaron quasiparticles are formed when a mobile impurity is coupled to the elementary excitations of a many-particle background. In the field of ultracold atoms, the study of the associated impurity problem has attracted a growing interest over the last fifteen years. Polaron quasiparticle properties are essential to our understanding of a variety of paradigmatic quantum many-body systems realized in ultracold atomic gases and in the solid state, from imbalanced Bose–Fermi and Fermi–Fermi mixtures to fermionic Hubbard models. In this topical review, we focus on the so-called repulsive polaron branch, which emerges as an excited many-body state in systems with underlying attractive interactions such as ultracold atomic mixtures, and is characterized by an effective repulsion between the impurity and the surrounding medium. We give a brief account of the current theoretical and experimental understanding of repulsive polaron properties, for impurities embedded in both fermionic and bosonic media, and we highlight open issues deserving future investigations.

The 1S0 Pairing Gap in Neutron Matter

We report ab initio calculations of the S wave pairing gap in neutron matter calculated using realistic nuclear Hamiltonians that include two- and three-body interactions. We use a trial state, properly optimized to capture the essential pairing correlations, from which we extract ground state properties by means of auxiliary field diffusion Monte Carlo simulations. We extrapolate our results to the thermodynamic limit by studying the finite-size effects in the symmetry-restored projected Bardeen-Cooper-Schrieffer (PBCS) theory and compare our results to other ab initio studies done in the past. Our quantum Monte Carlo results for the pairing gap show a modest suppression with respect to the mean-field BCS values. These results can be connected to cold atom experiments, via the unitarity regime where fermionic superfluidity assumes a unified description, and they are important in the prediction of thermal properties and the cooling of neutron stars.

Polaron Problems in Ultracold Atoms: Role of a Fermi Sea across Different Spatial Dimensions and Quantum Fluctuations of a Bose Medium

The notion of a polaron, originally introduced in the context of electrons in ionic lattices, helps us to understand how a quantum impurity behaves when being immersed in and interacting with a many-body background. We discuss the impact of the impurities on the medium particles by considering feedback effects from polarons that can be realized in ultracold quantum gas experiments. In particular, we exemplify the modifications of the medium in the presence of either Fermi or Bose polarons. Regarding Fermi polarons we present a corresponding many-body diagrammatic approach operating at finite temperatures and discuss how mediated two- and three-body interactions are implemented within this framework. Utilizing this approach, we analyze the behavior of the spectral function of Fermi polarons at finite temperature by varying impurity-medium interactions as well as spatial dimensions from three to one. Interestingly, we reveal that the spectral function of the medium atoms could be a useful quantity for analyzing the transition/crossover from attractive polarons to molecules in three-dimensions. As for the Bose polaron, we showcase the depletion of the background Bose-Einstein condensate in the vicinity of the impurity atom. Such spatial modulations would be important for future investigations regarding the quantification of interpolaron correlations in Bose polaron problems.

Dynamical Variational Approach to Bose Polarons at Finite Temperatures

We discuss the interaction of a mobile quantum impurity with a Bose-Einstein condensate of atoms at finite temperature. To describe the resulting Bose polaron formation we develop a dynamical variational approach applicable to an initial thermal gas of Bogoliubov phonons. We study the polaron formation after switching on the interaction, e.g., by a radio-frequency (rf) pulse from a noninteracting to an interacting state. To treat also the strongly interacting regime, interaction terms beyond the Fröhlich model are taken into account. We calculate the real-time impurity Green's function and discuss its temperature dependence. Furthermore we determine the rf absorption spectrum and find good agreement with recent experimental observations. We predict temperature-induced shifts and a substantial broadening of spectral lines. The analysis of the real-time Green's function reveals a crossover to a linear temperature dependence of the thermal decay rate of Bose polarons as unitary interactions are approached.

Phase separations induced by a trapping potential in one-dimensional fermionic systems as a source of core-shell structures

Ultracold fermionic gases in optical lattices give a great opportunity for creating different types of novel states. One of them is phase separation induced by a trapping potential between different types of superfluid phases. The core-shell structures, occurring in systems with a trapping potential, are a good example of such separations. The types and the sequences of phases which emerge in such structures can depend on spin-imbalance, shape of the trap and on-site interaction strength. In this work, we investigate the properties of such structures within an attractive Fermi gas loaded in the optical lattice, in the presence of the trapping potential and their relations to the phase diagram of the homogeneous system. Moreover, we show how external and internal parameters of the system and parameters of the trap influence their properties. In particular, we show a possible occurrence of the core-shell structure in a system with a harmonic trap, containing the BCS and FFLO states. Additionally, we find a spatial separation of two superfuild states in the system, one in the BCS limit as well as the other one in the tightly bound local pairs (BEC) regime.

Time-Resolved Observation of Competing Attractive and Repulsive Short-Range Correlations in Strongly Interacting Fermi Gases

We exploit a time-resolved pump-probe spectroscopic technique to study the out-of-equilibrium dynamics of an ultracold two-component Fermi gas, selectively quenched to strong repulsion along the upper branch of a broad Feshbach resonance. For critical interactions, we find the rapid growth of short-range anticorrelations between repulsive fermions to initially overcome concurrent pairing processes. At longer evolution times, these two competing mechanisms appear to macroscopically coexist in a short-range correlated state of fermions and pairs, unforeseen thus far. Our work provides fundamental insights into the fate of a repulsive Fermi gas, and offers new perspectives towards the exploration of complex dynamical regimes of fermionic matter.

Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress

In this report we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides accurate analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate of the fermionic system and prove that within the considered model the fastest rate of long-time decoherence is given by [Formula: see text]. We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects can prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between different exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures [Formula: see text] where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid [Formula: see text]He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology.

Repulsive Fermi Polarons in a Resonant Mixture of Ultracold ^{6}Li Atoms

We employ radio-frequency spectroscopy to investigate a polarized spin mixture of ultracold ^{6}Li atoms close to a broad Feshbach scattering resonance. Focusing on the regime of strong repulsive interactions, we observe well-defined coherent quasiparticles even for unitarity-limited interactions. We characterize the many-body system by extracting the key properties of repulsive Fermi polarons: the energy E_{+}, the effective mass m^{*}, the residue Z, and the decay rate Γ. Above a critical interaction, E_{+} is found to exceed the Fermi energy of the bath, while m^{*} diverges and even turns negative, thereby indicating that the repulsive Fermi liquid state becomes energetically and thermodynamically unstable.

Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases

In this review, we discuss the properties of a few impurity atoms immersed in a gas of ultracold fermions--the so-called Fermi polaron problem. On one hand, this many-body system is appealing because it can be described almost exactly with simple diagrammatic and/or variational theoretical approaches. On the other, it provides a quantitatively reliable insight into the phase diagram of strongly interacting population-imbalanced quantum mixtures. In particular, we show that the polaron problem can be applied to the study of itinerant ferromagnetism, a long-standing problem in quantum mechanics.

Quantum Monte Carlo study of a resonant Bose-Fermi mixture

We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion component. We focus on the case where the boson density n(B) is smaller than the fermion density n(F), for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing n(B).

p-Wave polaron

We consider a single impurity immersed in a Fermi sea close to an interspecies p-wave Feshbach resonance. We calculate its dispersion and spectral response to a radio frequency pulse. In a magnetic field, dipolar interactions split the resonance and two novel features with respect to the s-wave case appear: a third polaron branch in the excitation spectrum, in addition to the usual attractive and repulsive ones; and an anisotropic dispersion of the impurity characterized by different effective masses perpendicular and parallel to the magnetic field. The anisotropy can be tuned as a function of the field strength and the two effective masses may have opposite signs, or become smaller than the bare mass.

Fermi-liquid behavior of the normal phase of a strongly interacting gas of cold atoms

We measure the magnetic susceptibility of a Fermi gas with tunable interactions in the low-temperature limit and compare it to quantum Monte Carlo calculations. Experiment and theory are in excellent agreement and fully compatible with the Landau theory of Fermi liquids. We show that these measurements shed new light on the nature of the excitations of the normal phase of a strongly interacting Fermi gas.

Trimers, molecules, and polarons in mass-imbalanced atomic Fermi gases

We consider the ground state of a single "spin-down" impurity atom interacting attractively with a "spin-up" atomic Fermi gas. By constructing variational wave functions for polarons, molecules, and trimers, we perform a detailed study of the transitions between these dressed bound states as a function of mass ratio r=m↑/m↓ and interaction strength. Crucially, we find that the presence of a Fermi sea enhances the stability of the p-wave trimer, which can be viewed as a Fulde-Ferrell-Larkin-Ovchinnikov molecule that has bound an additional majority atom. For sufficiently large r, we find that the transitions lie outside the region of phase separation of the imbalanced Fermi gas and should thus be observable in experiment, unlike the well-studied equal-mass case.

Exotic superfluid states of lattice fermions in elongated traps

We present real-space dynamical mean-field theory calculations for attractively interacting fermions in three-dimensional lattices with elongated traps. The critical polarization is found to be 0.8, regardless of the trap elongation. Below the critical polarization, we find unconventional superfluid structures where the polarized superfluid and Fulde-Ferrell-Larkin-Ovchinnikov-type states emerge across the entire core region.

Fermi-Bose mixtures near broad interspecies Feshbach resonances

In this Letter we study dressed bound states in Fermi-Bose mixtures near broad interspecies resonances, and implications on many-body correlations. We present the evidence for a first order phase transition between a mixture of Fermi gas and condensate, and a fully paired mixture where extended fermionic molecules occupy a single pairing channel instead of forming a molecular Fermi surface. We further investigate the effect of Fermi surface dynamics and pair fluctuations and discuss the validity of our results.

Decay of polarons and molecules in a strongly polarized Fermi gas

The ground state of an impurity immersed in a Fermi sea changes from a polaron to a molecule as the interaction strength is increased. We show here that the coupling between these two states is strongly suppressed due to a combination of phase-space effects and Fermi statistics, and that it vanishes much faster than the energy difference between the two states, thereby confirming the first order nature of the polaron-molecule transition. In the regime where each state is metastable, we find quasiparticle lifetimes which are much longer than what is expected for a usual Fermi liquid. Our analysis indicates that the decay rates are sufficiently slow to be experimentally observable.

Normal phase of an imbalanced Fermi gas

Recent experiments on imbalanced Fermi gases have raised interest in the physics of an impurity immersed in a Fermi sea, the so-called Fermi polaron. In this Letter, a simple theory is devised to describe dilute Fermi-polaron ensembles corresponding to the normal phase of an imbalanced Fermi gas. An exact formula is obtained for the dominant interaction between polarons, expressed solely in terms of a single-polaron parameter. The physics of this interaction is identified as a signature of the Pauli exclusion principle.

Collective oscillations of an imbalanced Fermi gas: axial compression modes and polaron effective mass

We investigate the low-lying compression modes of a unitary Fermi gas with imbalanced spin populations. For low polarization, the strong coupling between the two spin components leads to a hydrodynamic behavior of the cloud. For large population imbalance we observe a decoupling of the oscillations of the two spin components, giving access to the effective mass of the Fermi polaron, a quasiparticle composed of an impurity dressed by particle-hole pair excitations in a surrounding Fermi sea. We find m*/m = 1.17(10), in agreement with the most recent theoretical predictions.

Heavy-light fermion mixtures at unitarity

We investigate fermion pairing in the unitary regime for a mass ratio corresponding to a ;{6}Li-;{40}K mixture using quantum Monte Carlo methods. The ground-state energy and the average light- and heavy-particle excitation spectrum for the unpolarized superfluid state are nearly independent of the mass ratio. In the majority light system, the polarized superfluid is close to the energy of a phase separated mixture of nearly fully polarized normal and unpolarized superfluid. For a majority of heavy particles, we find an energy minimum for a normal state with a ratio of approximately 3ratio1 heavy to light particles. A slight increase in attraction to k_{F}a approximately 2.5 yields a ground state energy of nearly zero for this ratio. A cold unpolarized system in a harmonic trap at unitarity should phase separate into three regions, with a shell of unpolarized superfluid in the middle.

Finite-size and confinement effects in spin-polarized trapped Fermi gases

We calculate the energy of a single fermion interacting resonantly with a Fermi sea of different-species fermions in anisotropic traps, and show that finite particle numbers and the trap geometry impact the phase structure and the critical polarization. Our findings contribute to understanding some experimental discrepancies in spin-polarized Fermi gases as finite-size and confinement effects.

Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms

We have observed Fermi polarons, dressed spin-down impurities in a spin-up Fermi sea of ultracold atoms. The polaron manifests itself as a narrow peak in the impurities' rf spectrum that emerges from a broad incoherent background. We determine the polaron energy and the quasiparticle residue for various interaction strengths around a Feshbach resonance. At a critical interaction, we observe the transition from polaronic to molecular binding. Here, the imbalanced Fermi liquid undergoes a phase transition into a Bose liquid, coexisting with a Fermi sea.

Density and spin response function of a normal Fermi gas at unitarity

Using the Landau theory of Fermi liquids, we calculate the dynamic response of both a polarized and an unpolarized normal Fermi gas at zero temperature in the strongly interacting regime of large scattering length. We show that at small excitation energies the in phase (density) response is enhanced with respect to the ideal gas prediction due to the increased compressibility. Vice versa, the out of phase (spin) response is quenched as a consequence of the tendency of the system to pair opposite spins. The long wavelength behavior of the static structure factor is explicitly calculated. The results are compared with the predictions in the collisional and superfluid regimes. The emergence of a spin zero sound solution in the unpolarized normal phase is explicitly discussed.

Pair correlations of a spin-imbalanced Fermi gas on two-leg ladders

We study the pair correlations of a spin-imbalanced two-leg ladder with attractive interactions, using the density matrix renormalization group method. We identify regions in the phase diagram spanned by the chemical potential and the magnetic field that can harbor Fulde-Ferrell-Larkin-Ovchinnikov- (FFLO-)like physics. Results for the pair structure factor, exhibiting multiple pairing wave vectors, substantiate the presence of FFLO-like correlations. We further discuss phase separation scenarios induced by a harmonic trap, which differ from the case of isolated chains.

Probing spatial spin correlations of ultracold gases by quantum noise spectroscopy

Spin noise spectroscopy with a single laser beam is demonstrated theoretically to provide a direct probe of the spatial correlations of cold fermionic gases. We show how the generic many-body phenomena of antibunching, pairing, antiferromagnetic, and algebraic spin liquid correlations can be revealed by measuring the spin noise as a function of laser width, temperature, and frequency.

Polarized superfluidity in the attractive hubbard model with population imbalance

We study a two-component Fermi system with attractive interactions and different populations of the two species in a cubic lattice. For an intermediate coupling, we find a uniformly polarized superfluid which is stable down to very low temperatures. The momentum distribution of this phase closely resembles that of the Sarma phase, characterized by two Fermi surfaces. This phase is shown to be stabilized by a potential energy gain, as in a BCS superfluid, in contrast with the unpolarized Bose-Einstein condensate which is stabilized by kinetic energy. We present general arguments suggesting that preformed pairs in the unpolarized superfluid favor the stabilization of a polarized superfluid phase.

Unitary Fermi supersolid: the Larkin-Ovchinnikov phase

We present strong theoretical evidence that a Larkin-Ovchinnikov (LOFF/FFLO) pairing phase is favored over the homogeneous superfluid and normal phases in three-dimensional unitary Fermi systems. Using a density functional theory (DFT) based on the latest quantum Monte Carlo calculations and experimental results, we show that this phase is competitive over a large region of the phase diagram. The oscillations in the number densities and pairing field have a substantial amplitude, and a period some 3 to 10 times the average interparticle separation. Within the DFT, the transition to a normal polarized Fermi liquid at large polarizations is smooth, while the transition to a fully paired superfluid is abrupt.

Realization of a strongly interacting Bose-Fermi mixture from a two-component Fermi gas

We show the emergence of a strongly interacting Bose-Fermi mixture from a two-component Fermi mixture with population imbalance. By analyzing in situ density profiles of 6Li atoms in the BCS-BEC crossover regime, we identify a critical interaction strength, beyond which all minority atoms pair up with majority atoms and form a Bose condensate. This is the regime where the system can be effectively described as a boson-fermion mixture. We determine the dimer-fermion and dimer-dimer scattering lengths and beyond-mean-field contributions. Our study realizes a gedanken experiment of bosons immersed in a Fermi sea of one of their constituents, revealing the composite nature of the bosons.

Normal state of highly polarized Fermi gases: full many-body treatment

We consider a single atom within a Fermi sea of atoms. We elucidate by a full many-body analysis the quite mysterious agreement between Monte Carlo results and approximate calculations taking only into account single particle-hole excitations. It results from a nearly perfect destructive interference of the contributions of states with more than one particle-hole pair. This is linked to the remarkable efficiency of the expansion in powers of hole wave vectors, the lowest order leading to perfect interference. Going up to two particle-hole pairs gives an essentially perfect agreement with known exact results. Hence our treatment amounts to an exact solution of this problem.

Collisional properties of a polarized Fermi gas with resonant interactions

Highly polarized mixtures of atomic Fermi gases constitute a novel Fermi liquid. We demonstrate how information on thermodynamic properties may be used to calculate quasiparticle scattering amplitudes even when the interaction is resonant and apply the results to evaluate the damping of the spin dipole mode. We estimate that under current experimental conditions the mode would be intermediate between the hydrodynamic and collisionless limits.