Normal state of a polarized fermi gas at unitarity

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.

Radio-Frequency Response and Contact of Impurities in a Quantum Gas

We investigate the radio-frequency spectroscopy of impurities interacting with a quantum gas at finite temperature. In the limit of a single impurity, we show using Fermi's golden rule that introducing (or injecting) an impurity into the medium is equivalent to ejecting an impurity that is initially interacting with the medium, since the "injection" and "ejection" spectral responses are simply related to each other by an exponential function of frequency. Thus, the full spectral information for the quantum impurity is contained in the injection spectral response, which can be determined using a range of theoretical methods, including variational approaches. We use this property to compute the finite-temperature equation of state and Tan contact of the Fermi polaron. Our results for the contact of a mobile impurity are in excellent agreement with recent experiments and we find that the finite-temperature behavior is qualitatively different compared to the case of infinite impurity mass.

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.

Resonantly Interacting Fermi-Fermi Mixture of ^{161}Dy and ^{40}K

We report on the realization of a Fermi-Fermi mixture of ultracold atoms that combines mass imbalance, tunability, and collisional stability. In an optically trapped sample of ^{161}Dy and ^{40}K, we identify a broad Feshbach resonance centered at a magnetic field of 217 G. Hydrodynamic expansion profiles in the resonant interaction regime reveal a bimodal behavior resulting from mass imbalance. Lifetime studies on resonance show a suppression of inelastic few-body processes by orders of magnitude, which we interpret as a consequence of the fermionic nature of our system. The resonant mixture opens up intriguing perspectives for studies on novel states of strongly correlated fermions with mass imbalance.

Roton-Induced Bose Polaron in the Presence of Synthetic Spin-Orbit Coupling

We predict the existence of a roton-induced Bose polaron for an impurity immersed in a three-dimensional Bose-Einstein condensate with Raman-laser-induced spin-orbit coupling, where the condensate is in a finite-momentum plane-wave state with an intriguing roton minimum in its excitation spectrum. This novel polaron is formed by dressing the impurity with roton excitations, instead of phonon excitations as in a conventional (i.e., phonon-induced) Bose polaron, and acquires a significant center-of-mass momentum and highly anisotropic effective mass. We find that the roton-induced polaron evolves from a phonon-induced polaron, as the interaction between impurity and atoms increases across a Feshbach resonance. The evolution is not smooth, and a first-order phase transition from a phonon- to roton-induced polaron is observed at a critical interaction strength.

Few Versus Many-Body Physics of an Impurity Immersed in a Superfluid of Spin 1/2 Attractive Fermions

In this Letter we investigate the properties of an impurity immersed in a superfluid of strongly correlated spin 1/2 fermions and we calculate the beyond-mean-field corrections to the energy of a weakly interacting impurity. We show that these corrections are divergent and have to be regularized by properly accounting for three-body physics in the problem and that our approach naturally provides a unifying framework for Bose and Fermi polaron physics.

Variational Approach for Impurity Dynamics at Finite Temperature

We present a general variational principle for the dynamics of impurity particles immersed in a quantum-mechanical medium. By working within the Heisenberg picture and constructing approximate time-dependent impurity operators, we can take the medium to be in any mixed state, such as a thermal state. Our variational method is consistent with all conservation laws and, in certain cases, it is equivalent to a finite-temperature Green's function approach. As a demonstration of our method, we consider the dynamics of heavy impurities that have suddenly been introduced into a Fermi gas at finite temperature. Using approximate time-dependent impurity operators involving only one particle-hole excitation of the Fermi sea, we find that we can successfully model the results of recent Ramsey interference experiments on ^{40}K atoms in a ^{6}Li Fermi gas. We also show that our approximation agrees well with the exact solution for the Ramsey response of a fixed impurity at finite temperature. Our approach paves the way for the investigation of impurities with dynamical degrees of freedom in arbitrary quantum-mechanical mediums.

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.

Nonperturbative Extraction of the Effective Mass in Neutron Matter

We carry out nonperturbative calculations of the single-particle excitation spectrum in strongly interacting neutron matter. These are microscopic quantum Monte Carlo computations of many-neutron energies at different densities as well as several distinct excited states. As input, we employ both phenomenological and chiral two- and three-nucleon interactions. We use the single-particle spectrum to extract the effective mass in neutron matter. With a view to systematizing the error involved in this extraction, we carefully assess the impact of finite-size effects on the quasiparticle dispersion relation. We find an effective-mass ratio that drops from 1 as the density is increased. We conclude by connecting our results with the physics of ultracold gases as well as with energy-density functional theories of nuclei and neutron-star matter.

Boiling a Unitary Fermi Liquid

We study the thermal evolution of a highly spin-imbalanced, homogeneous Fermi gas with unitarity limited interactions, from a Fermi liquid of polarons at low temperatures to a classical Boltzmann gas at high temperatures. Radio-frequency spectroscopy gives access to the energy, lifetime, and short-range correlations of Fermi polarons at low temperatures T. In this regime, we observe a characteristic T^{2} dependence of the spectral width, corresponding to the quasiparticle decay rate expected for a Fermi liquid. At high T, the spectral width decreases again towards the scattering rate of the classical, unitary Boltzmann gas, ∝T^{-1/2}. In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy, indicating the breakdown of a quasiparticle description. Density measurements in a harmonic trap directly reveal the majority dressing cloud surrounding the minority spins and yield the compressibility along with the effective mass of Fermi polarons.

Finite-Temperature Equation of State of Polarized Fermions at Unitarity

We study in a nonperturbative fashion the thermodynamics of a unitary Fermi gas over a wide range of temperatures and spin polarizations. To this end, we use the complex Langevin method, a first principles approach for strongly coupled systems. Specifically, we show results for the density equation of state, the magnetization, and the magnetic susceptibility. At zero polarization, our results agree well with state-of-the-art results for the density equation of state and with experimental data. At finite polarization and low fugacity, our results are in excellent agreement with the third-order virial expansion. In the fully quantum mechanical regime close to the balanced limit, the critical temperature for superfluidity appears to depend only weakly on the spin polarization.

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.

Visualizing the Efimov Correlation in Bose Polarons

The Bose polaron is a quasiparticle of an impurity dressed by surrounding bosons. In few-body physics, it is known that two identical bosons and a third distinguishable particle can form a sequence of Efimov bound states in the vicinity of interspecies scattering resonance. On the other hand, in the Bose polaron system with an impurity atom embedded in many bosons, no signature of Efimov physics has been reported in the existing spectroscopy measurements to date. In this Letter, we propose that a large mass imbalance between a light impurity and heavy bosons can help produce visible signatures of Efimov physics in such a spectroscopy measurement. Using the diagrammatic approach in the virial expansion to include three-body effects from pair-wise interactions, we determine the impurity self-energy and its spectral function. Taking the ^{6}Li-^{133}Cs system as a concrete example, we find two visible Efimov branches in the polaron spectrum, as well as their hybridizations with the attractive polaron branch. We also discuss the general scenarios for observing the signature of Efimov physics in polaron systems. This work paves the way for experimentally exploring intriguing few-body correlations in a many-body system in the near future.

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.

Dissipative dynamics of a driven quantum spin coupled to a bath of ultracold fermions

We explore the dynamics and the steady state of a driven quantum spin coupled to a bath of fermions, which can be realized with a strongly imbalanced mixture of ultracold atoms using currently available experimental tools. Radio-frequency driving can be used to induce tunneling between the spin states. The Rabi oscillations are modified due to the coupling of the quantum spin to the environment, which causes frequency renormalization and damping. The spin-bath coupling can be widely tuned by adjusting the scattering length through a Feshbach resonance. When the scattering potential creates a bound state, by tuning the driving frequency it is possible to populate either the ground state, in which the bound state is filled, or a metastable state in which the bound state is empty. In the latter case, we predict an emergent inversion of the steady-state magnetization. Our work shows that different regimes of dissipative dynamics can be explored with a quantum spin coupled to a bath of ultracold fermions.

Impurity problem in a bilayer system of dipoles

We consider a bilayer geometry where a single impurity moves in a two-dimensional plane and is coupled, via dipolar interactions, to a two-dimensional system of fermions residing in the second layer. Dipoles in both layers point in the same direction oriented by an external field perpendicular to the plane of motion. We use quantum Monte Carlo methods to calculate the binding energy and the effective mass of the impurity at zero temperature as a function of the distance between layers as well as of the in-plane interaction strength. In the regime where the fermionic dipoles form a Wigner crystal, the physics of the impurity can be described in terms of a polaron coupled to the bath of lattice phonons. By reducing the distance between layers this polaron exhibits a crossover from a free-moving to a tightly bound regime where its effective mass is orders of magnitude larger than the bare mass.

Quasiparticle lifetime in ultracold fermionic mixtures with density and mass imbalance

We show that atomic Fermi mixtures with density and mass imbalance exhibit a rich diversity of scaling laws for the quasiparticle decay rate beyond the quadratic energy and temperature dependence of conventional Fermi liquids. For certain densities and mass ratios, the decay rate is linear, whereas in other cases, it exhibits a plateau. Remarkably, this plateau extends from the deeply degenerate to the high temperature classical regime of the light species. Many of these scaling laws are analogous to what is found in very different systems, including dirty metals, liquid metals, and high temperature plasmas. The Fermi mixtures can in this sense span a whole range of seemingly diverse and separate physical systems. Our results are derived in the weakly interacting limit, making them quantitatively reliable. The different regimes can be detected with radio-frequency spectroscopy.

Imaginary polarization as a way to surmount the sign problem in ab initio calculations of spin-imbalanced Fermi gases

From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.

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.

Metastability in spin-polarized Fermi gases

We study the role of particle transport and evaporation on the phase separation of an ultracold, spin-polarized atomic Fermi gas. We show that the previously observed deformation of the superfluid paired core is a result of evaporative depolarization of the superfluid due to a combination of enhanced evaporation at the center of the trap and the inhibition of spin transport at the normal-superfluid phase boundary. These factors contribute to a nonequilibrium jump in the chemical potentials at the phase boundary. Once formed, the deformed state is highly metastable, persisting for times of up to 2 s.

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.

Itinerant ferromagnetism of a repulsive atomic Fermi gas: a quantum monte carlo study

We investigate the phase diagram of a two-component repulsive Fermi gas at T=0 by means of quantum Monte Carlo simulations. Both purely repulsive and resonant attractive model potentials are considered in order to analyze the limits of the universal regime where the details of interatomic forces can be neglected. The equation of state of both balanced and unbalanced systems is calculated as a function of the interaction strength and the critical density for the onset of ferromagnetism is determined. The energy of the strongly polarized gas is calculated and parametrized in terms of the physical properties of repulsive polarons, which are relevant for the stability of the fully ferromagnetic state. Finally, we analyze the phase diagram in the interaction-polarization plane under the assumption that only phases with homogeneous magnetization can be produced.

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.

Lifshitz point in the phase diagram of resonantly interacting 6Li-40K mixtures

We consider a strongly interacting 6Li-40K mixture, which is imbalanced both in the masses and the densities of the two fermionic species. At present, it is the experimentalist's favorite for reaching the superfluid regime. We construct an effective thermodynamic potential that leads to excellent agreement with Monte Carlo results for the normal state. We use it to determine the universal phase diagram of the mixture in the unitarity limit, where we find, in contrast to the mass-balanced case, the presence of a Lifshitz point. This point is characterized by the effective mass of the Cooper pairs becoming negative, which signals an instability towards a supersolid phase.

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.

Superfluidity in a gas of strongly interacting fermions

After an introduction into 100 years of research on superfluidity and the concept of the BCS-BEC crossover, we describe recent experimental studies of a spin-polarized Fermi gas with strong interactions. Tomographically resolving the spatial structure of an inhomogeneous trapped sample, we have mapped out the superfluid phases in the parameter space of temperature, spin polarization, and interaction strength. Phase separation between the superfluid and the normal component occurs at low temperatures, showing spatial discontinuities in the spin polarization. The critical polarization of the normal gas increases with stronger coupling. Beyond a critical interaction strength all minority atoms pair with majority atoms, and the system can be effectively described as a boson-fermion mixture. Pairing correlations have been studied by rf spectroscopy, determining the fermion pair size and the pairing gap energy in a resonantly interacting superfluid.

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.

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.

Determination of the superfluid gap in atomic Fermi gases by quasiparticle spectroscopy

We present majority and minority radio frequency spectra of strongly interacting imbalanced Fermi gases of 6Li. We observed a smooth evolution in the nature of pairing correlations from pairing in the superfluid region to polaron binding in the highly polarized normal region. The imbalance induces quasiparticles in the superfluid region even at very low temperature. This leads to a local bimodal spectral response, which allowed us to determine the superfluid gap Delta and the Hartree energy U.

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.

Superfluid pairing gap in strong coupling

The zero-temperature pairing gap is a fundamental property of interacting Fermions, providing a crucial test of many-body theories in strong coupling. We analyze recent cold-atom experiments on imbalanced Fermi systems using Quantum Monte Carlo results for the superfluid and normal phases. Through this analysis we extract, for the first time, the experimental zero-temperature pairing gap in the fully paired superfluid state at unitarity where the two-body scattering length is infinite. We find that the zero-temperature pairing gap is greater than 0.4 times the Fermi energy E(F), with a preferred value of (0.45+/-0.05) E(F). The ratio of the pairing gap to the Fermi Energy is larger here than in any other Fermi system measured to date.

Exact solution for a trapped Fermi gas with population imbalance and BCS pairing

The problem of a two-component Fermi gas in a harmonic trap, with an imbalanced population and a pairing interaction of zero total momentum, is mapped onto the exactly solvable reduced BCS model. For a one-dimensional trap, the complete ground state diagram is determined with various topological features in ground state energy spectra. In addition to the conventional two-shell density profile of a paired core and polarized outer wings, a three-shell structure as well as a double-peak superfluid distribution are unveiled.

Renormalization group theory for the imbalanced Fermi gas

We formulate a Wilsonian renormalization group theory for the imbalanced Fermi gas. The theory is able to recover quantitatively well-established results in both the weak-coupling and the strong-coupling (unitarity) limits. We determine for the latter case the line of second-order phase transitions of the imbalanced Fermi gas and, in particular, the location of the tricritical point. We obtain good agreement with the recent experiments of Y. Shin et al. [Nature (London) 451, 689 (2008)10.1038/nature06473].

Destroying superfluidity by rotating a Fermi gas at unitarity

We study the effect of the rotation on a harmonically trapped Fermi gas at zero temperature under the assumption that vortices are not formed. We show that at unitarity the rotation produces a phase separation between a nonrotating superfluid (S) core and a rigidly rotating normal (N) gas. The interface between the two phases is characterized by a density discontinuity n(N)/n(S)=0.85, independent of the angular velocity. The depletion of the superfluid and the angular momentum of the rotating configuration are calculated as a function of the angular velocity. The conditions of stability are also discussed and the critical angular velocity for the onset of a spontaneous quadrupole deformation of the interface is evaluated.