We address the problem of a single "spin-down" impurity atom interacting attractively with a spin-up Fermi gas in two dimensions (2D). We consider the case where the mass of the impurity is greater than or equal to the mass of a spin-up fermion. Using a variational approach, we resolve the questions raised by previous studies and we show that there is, in fact, a transition between polaron and molecule (dimer) ground states in 2D. For the molecule state, we use a variational wave function with a single particle-hole excitation on the Fermi sea and we find that its energy matches that of the exact solution in the limit of infinite impurity mass. Thus, we expect the variational approach to provide a reliable tool for investigating 2D systems.
We revisit the polaron-molecule transition in three-dimensional(3D) fermion systems using the well-established variational approach. The molecule is found to be intrinsically unstable against lowest-order particle-hole excitations, and it can only approximate the ground state of impurity system with finite total momentum in the strong coupling regime. The polaron-molecule transition can therefore be reinterpreted as a first-order transition between single impurity systems with different total momenta. Within certain interaction window near their transition, both states appear as local minima i…
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 each of these dressed bound states as a function of mass ratio $r=m_\uparrow/m_\downarrow$ and interaction strength. 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 (FFLO) molecule that has bound an additional majority atom. For sufficientl…
Using exact Bethe ansatz (BA) solutions, we show that a spin-down fermion immersed into a fully polarized spin-up Fermi sea with a weak attraction is dressed by the surrounding spin-up fermions to form the one-dimensional analog of a polaron. As the attraction becomes strong, the spin-down fermion binds with one spin-up fermion to form a tightly bound molecule. Throughout the whole interaction regime, a crossover from the polaron to a molecule state is fully demonstrated through exact results of the excitation spectrum, the effective mass, binding energy and kinetic energy. Furthermore, a clea…
A single down spin Fermion with an attractive, zero range interaction with a Fermi sea of up-spin Fermions forms a polaronic quasiparticle. The associated quasiparticle weight vanishes beyond a critical strength of the attractive interaction, where a many-body bound state is formed. From a variational wavefunction in the molecular limit, we determine the critical value for the polaron to molecule transition. The value agrees well with the diagrammatic Monte Carlo results of Prokof'ev and Svistunov and is consistent with recent rf-spectroscopy measurements of the quasiparticle weight by Schirot…
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 analys…
The problem of a single down spin particle interacting with a Fermi sea of up spin particles is of current interest in the field of cold atoms. The Hubbard model, appropriate to atoms in an optical lattice potential, is considered in parallel with a gas model. As the strength of an attractive short-range interaction is increased there is a crossover from "polaron" behaviour, in which the Fermi sea is weakly perturbed, to "molecule" behaviour in which the down spin particle is bound to a single up spin particle. It is shown that this is a smooth crossover, not a sharp transition as claimed by m…
Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bond molecule. Thus it is seen that the system undergos a cross-over from a mean field polaron-like nature into a mixture of excess fermion…
We study the impurity problem in a gas of $^{173}$Yb atoms near the recently discovered orbital Feshbach resonance. In an orbital Feshbach resonance, atoms in the electronic ground state $^1S_0$ interact with those in the long-lived excited $^3P_0$ state with magnetically tunable interactions. We consider an impurity atom with a given hyperfine spin in the $^3P_0$ state interacting with a single-component Fermi sea of atoms in the ground $^1S_0$ manifold. Close to the orbital Feshbach resonance, the impurity can induce collective particle-hole excitations out of the Fermi sea, which can be reg…
We study the spectrum of an impurity coupled to a Fermi sea (e.g., minority atom in an ultracold gas, exciton in a solid) by attraction strong enough to form a molecule/trion. We introduce a diagrammatic scheme which allows treating a finite mass impurity while reproducing the Fermi edge singularity in the immobile limit. For large binding energies the spectrum is characterized by a semi-coherent repulsive polaron and an incoherent molecule-hole continuum, which is the lowest-energy feature in the single-particle spectrum. The previously predicted attractive polaron seems not to exist for stro…
In this work, we explore the polaron and molecule physics by utilizing a unified variational ansatz with up to two particle-hole(p-h) excitations(V-2ph). We confirm the existence of a first-order transition in 3D and 2D Fermi polarons, and show that the nature of such transition lies in an energy competition between systems with different momenta ${\mathbf Q}=0$ and $|{\mathbf Q}|=k_F$, here ${\mathbf Q}$ is defined as the momentum of Fermi polaron system with respect to the Fermi sea of majority fermions (with Fermi momentum $k_F$). The literally proposed molecule ansatz is identified as an a…
We theoretically investigate attractive Fermi polarons in three dimensions at finite temperature and impurity concentration through the many-body T-matrix theory and high-temperature virial expansion. By using the analytically continued impurity Green's function, we calculate the direct rf spectroscopy of attractive polarons in the unitary regime. Taking the peak value of the rf spectroscopy as the polaron energy and the full width half maximum as the polaron lifetime, we determine the temperature range of validity for the quasi-particle description of Fermi polarons in the unitary limit.
We consider the highly spin-imbalanced limit of a two-component Fermi gas, where there is a small density of $\downarrow$ impurities attractively interacting with a sea of $\uparrow$ fermions. In the single-impurity limit at zero temperature, there exists the so-called polaron-molecule transition, where the impurity sharply changes its character by binding a $\uparrow$ fermion at sufficiently strong attraction. Using a recently developed variational approach, we calculate the thermodynamic properties of the impurity, and we show that the transition becomes a smooth crossover at finite temperat…
We show that spin-orbit coupling (SOC) gives rise to pairing instability in a highly polarized two-dimensional Fermi gas for arbitrary interaction strength. The pairing instability can lead to a Fulde-Ferrell-Larkin-Ovchinnikov-like molecular state, which undergoes a first-order transition into a pairing state with zero center-of-mass momentum as the parameters are tuned. These pairing states are metastable against a polaron state dressed by particle-hole fluctuations for small SOC. At large SOC, a polaron-molecule transition exists, which suggests a phase transition between the topological su…
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 side, 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 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 study itinerant ferromagnetism, a long standing problem in quantum mechanics.
A light impurity in a Fermi sea undergoes a transition from a polaron to a molecule for increasing interaction. We develop a new method to compute the spectral functions of the polaron and molecule in a unified framework based on the functional renormalization group with full self-energy feedback. We discuss the energy spectra and decay widths of the attractive and repulsive polaron branches as well as the molecular bound state and confirm the scaling of the excited state decay rate near the transition. The quasi-particle weight of the polaron shifts from the attractive to the repulsive branch…
We study an impurity atom in a two-dimensional Fermi gas using variational wave functions for (i) an impurity dressed by particle-hole excitations (polaron) and (ii) a dimer consisting of the impurity and a majority atom. In contrast to three dimensions, where similar calculations predict a sharp transition to a dimer state with increasing interspecies attraction, we show that the polaron ansatz always gives a lower energy. However, the exact solution for a heavy impurity reveals that both a two-body bound state and distortions of the Fermi sea are crucial. This reflects the importance of part…
Understanding the behavior of an impurity strongly interacting with a Fermi sea is a long-standing challenge in many-body physics. When the interactions are short-ranged, two vastly different ground states exist: a polaron quasiparticle and a molecule dressed by the majority atoms. In the single-impurity limit, it is predicted that at a critical interaction strength, a first-order transition occurs between these two states. Experiments, however, are always conducted in the finite temperature and impurity density regime. The fate of the polaron-to-molecule transition under these conditions, whe…
We determine the phase diagram of a polaron model with mixed breathing-mode and Su-Schrieffer-Heeger couplings and show that it has two sharp transitions, in contrast to pure models which exhibit one (for Su-Schrieffer-Heeger coupling) or no (for breathing-mode coupling) transition. Our results indicate that the physics of realistic mixed polaron models is much richer than that of simplified models. We then show that ultracold molecules trapped in optical lattices can be used to study precisely this mixed Hamiltonian, and that the relative contributions of the two couplings can be tuned with e…
We study the impurity problem in a Fermi gas of $^{173}$Yb atoms near an orbital Feshbach resonance, where a single moving particle in the $^3P_0$ state interacting with two background Fermi seas of particles in different nuclear states of the ground $^1S_0$ manifold. By employing wave function ansatzs for molecule and polaron states, we investigate various properties of the molecule, the attractive polaron, and the repulsive polaron states. We find that in comparison to the case of only one Fermi sea is populated, the presence of an additional Fermi sea acts as an energy shift between the two…
We generalize the application of small polaron theory to ultracold gases of Ref. [\onlinecite{jaksch_njp1}] to the case of Bose-Fermi mixtures, where both components are loaded into an optical lattice. In a suitable range of parameters, the mixture can be described within a Bogoliubov approach in the presence of fermionic (dynamic) impurities and an effective description in terms of polarons applies. In the dilute limit of the slow impurity regime, the hopping of fermionic particles is exponentially renormalized due to polaron formation, regardless of the sign of the Bose-Fermi interaction. Th…
The properties of impurities immersed in a large Fermi sea are naturally described in terms of dressed quasiparticles: attractive and repulsive polarons, and dressed molecules. Motivated by recent experiments on narrow Feshbach resonances, we analyze here how the quasiparticle properties are affected by a non-zero resonance range. We find two interesting analytic results. For large range, the ground state energy close to resonance is shown to become perturbative in the inverse range. In the limit of broad resonance instead, we provide a new Tan's relation linking the impurity ground state ener…
We study polaron excitations induced by an impurity interacting with a two-dimensional $p+ip$ Fermi superfluid. As the Fermi-Fermi pairing interaction is tuned, the background Fermi superfluid undergoes a topological phase transition. We show that such a transition is accompanied by a discontinuity in the second derivative of the polaron energy, regardless of the impurity-fermion interaction. We also identify a polaron to trimer crossover when the Fermi superfluid is in the strongly interacting, thus topologically trivial, regime. However, the trimer state is metastable against the molecular s…
We consider a single spin-down impurity atom interacting via an attractive, short-range potential with a spin-up Fermi sea in two dimensions (2D). Similarly to 3D, we show how the impurity can form a metastable state (the "repulsive polaron") with energy greater than that of the non-interacting impurity. Moreover, we find that the repulsive polaron can acquire a finite momentum for sufficiently weak attractive interactions. Even though the energy of the repulsive polaron can become sizeable, we argue that saturated ferromagnetism is unfavorable in 2D because of the polaron's finite lifetime an…
The Fermi-polaron problem of a mobile impurity interacting with fermionic medium emerges in various contexts, ranging from the foundations of Landau's Fermi-liquid theory to electron-exciton interaction in semiconductors, to unusual properties of high-temperature superconductors. While classically the medium provides only a dissipative environment to the impurity, quantum picture of polaronic dressing is more intricate and arises from the interplay of few- and many-body aspects of the problem. The conventional expectation for the dynamics of Fermi polarons is that it is dissipative in characte…
We theoretically investigate how quasi-particle properties of an attractive Fermi polaron are affected by nonzero temperature and finite impurity concentration. By applying both non-self-consistent and self-consistent many-body $T$-matrix theories, we calculate the polaron energy (including decay rate), effective mass, and residue, as functions of temperature and impurity concentration. The temperature and concentration dependences are weak on the BCS side with a negative impurity-medium scattering length. Toward the strong attraction regime across the unitary limit, we find sizable dependence…
In this article we study the interaction between an impurity and the gas of Bogoliubov excitations of a Fermi superfluid by mapping it on the polaron problem for an impurity in a BEC. The description of the Fermi superfluid across the BEC-BCS crossover regime is based on a recently developed effective field theory presented in [Eur. Phys. J. B 88, 122 (2015)] and provides us with the interaction-dependent dispersion relations for the Bogoliubov excitations. The behavior of the polaronic coupling constant $α$ and of the effective mass of the polaron is examined in a broad window of the BEC-BCS …
We present controlled numerical results for the ground state spectral function of the resonant Fermi polaron in three dimensions. We establish the existence of a "dark continuum"---a region of anomalously low spectral weight between the narrow polaron peak and the rest of the spectral continuum. The dark continuum develops when the s-wave scattering length is of the order of the inverse Fermi wavevector, $a\lesssim 1/k_{\rm F}$, i.e. in the absence of a small interaction-related parameter when the spectral weight is not expected to feature a near-perfect gap structure after the polaron peak.
We propose a new protocol to examine many-polaron properties in a cold atom experiment. Initially, polaronic clouds are prepared around the opposite edges of a majority gas cloud. After time evolution, the collision of two clouds exhibits various polaronic effects. To see how {\it collective} properties of many polarons with mediated interactions appear in the case in which the impurity and majority gases are composed of mass-balanced fermions with different spin components, we perform a nonlinear hydrodynamic simulation for collisional dynamics of two Fermi polaronic clouds. We found that the…
We investigate the zero-temperature quasiparticle properties of a mobile impurity immersed in a strongly interacting Fermi superfluid at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen--Cooper--Schrieffer (BCS) superfluid, by using a many-body $T$-matrix approach that excludes Efimov trimer bound states. Termed BEC-BCS crossover polaron, or crossover polaron in short, this quasiparticle couples to elementary excitations of a many-body background and therefore could provide a useful probe of the underlying strongly interacting Fermi superfluid. Due to the existence of a signifi…
The interplay between measurement and quantum correlations in many-body systems can lead to novel types of collective phenomena which are not accessible in isolated systems. In this work, we merge the Zeno-paradigm of quantum measurement theory with the concept of polarons in condensed-matter physics. The resulting quantum-Zeno Fermi-polaron is a quasi-particle which emerges for lossy impurities interacting with a quantum-degenerate bath of fermions. For loss rates of the order of the impurity-fermion binding energy the quasi-particle is short lived. However, we show that in the strongly dissi…
We apply the diagrammatic Monte Carlo approach to three-dimensional Fermi-polaron systems with mass-imbalance, where an impurity interacts resonantly with a noninteracting Fermi sea whose atoms have a different mass. This method allows to go beyond frequently used variational techniques by stochastically summing all relevant impurity Feynman diagrams up to a maximum expansion order limited by the sign problem. Polaron energy and quasiparticle residue can be accurately determined over a broad range of impurity masses. Furthermore, the spectral function of an imbalanced polaron demonstrates the …
We study the extremely polarized two-component Fermi gas with a mass imbalance in the strongly interacting regime. Specifically we focus on the experimentally available mixture of ${}^6$Li and ${}^{40}$K atoms. In this regime spin polarons, i.e., dressed minority atoms, form. We consider the spectral function for the minority atoms, from which the lifetime and the effective mass of the spin polaron can be determined. Moreover, we predict the radio-frequency (RF) spectrum and the momentum distribution for the spin polarons for experiments with ${}^6$Li and ${}^{40}$K atoms. Subsequently we stud…
The dynamics of a single impurity in an environment is a fundamental problem in many-body physics. In the solid state, a well-known case is an impurity coupled to a bosonic bath, for example lattice vibrations. Here the impurity together with its accompanying lattice distortion form a new entity, a polaron. This quasiparticle plays an important role in the spectral function of high-Tc superconductors as well as in colossal-magnetoresistance in manganites. For impurities in a fermionic bath, the attention so far has been mostly on heavy or immobile impurities which exhibit Anderson's orthogonal…
We study the polaron problem of an impurity immersed in a dissipative spin-orbit coupled Fermi gas via a non-self-consistent T-matrix method. We first propose an experimental scheme to realize a spin-orbit coupled Fermi bath with dissipation, and show that such a system can be described by a non-Hermitian Hamiltonian that contains an imaginary spin-flip term and an imaginary constant shift term. We find that the non-Hermiticity will change the single particle dispersion of the bath gas, and modify the properties of attractive and repulsive polarons such as energy, quasi-particle residue, effec…
We study the properties of the two-dimensional Fermi polaron model in which an impurity attractively interacts with a Fermi sea of particles in the zero-range limit. We use a diagrammatic Monte Carlo (DiagMC) method which allows us to sample a Feynman diagrammatic series to very high order. The convergence properties of the series and the role of multiple particle-hole excitations are discussed. We study the polaron and molecule energy as a function of the coupling strength, revealing a transition from a polaron to a molecule in the ground state. We find a value for the critical interaction st…
An impurity atom immersed in an ultracold atomic Fermi gas can form a quasiparticle, so-called Fermi polaron, due to impurity-fermion interaction. We consider a three-dimensional homogeneous dipolar Fermi gas as a medium, where the interatomic dipole-dipole interaction (DDI) makes the Fermi surface deformed into a spheroidal shape, and, using a Chevy-type variational method, investigate the ground-state properties of the Fermi polaron: the effective mass, the momentum distribution of a particle-hole (p-h) excitation, the drag parameter, and the medium density modification around the impurity. …
Quantum Monte Carlo techniques are employed to study the properties of polarons in an ultracold Fermi gas, at $T= 0,$ and in the unitary regime using both a zero-range model and a square-well potential. For a fixed density, the potential range is varied and results are extrapolated and compared against a zero-range model. A discussion regarding the choice of an interacting potential with a finite range is presented. We compute the polaron effective mass, the polaron binding energy, and the effective coupling between them. The latter is obtained using the Landau-Pomeranchuk's weakly interacting…
We measure radio-frequency spectra for a two-component mixture of a $^6$Li atomic Fermi gas in the quasi-two-dimensional regime. Near the Feshbach resonance, where the transverse Fermi energy is large compared to the confinement-induced dimer binding energies for the initial and final states, we find that the observed resonances do not correspond to transitions between confinement-induced dimers. The spectrum appears to be well-described by transitions between noninteracting polaron states in two dimensions.
We report on the experimental observation of multiorbital polarons in a two-dimensional Fermi gas of $^{173}\mathrm{Yb}$ atoms formed by mobile impurities in the metastable $^3\mathrm{P}_0$ orbital and a Fermi sea in the ground-state $^1\mathrm{S}_0$ orbital. We spectroscopically probe the energies of attractive and repulsive polarons close to an orbital Feshbach resonance and characterize their coherence by measuring the quasiparticle residue. For all probed interaction parameters, the repulsive polaron is a long-lived quasiparticle with a decay rate more than 2 orders of magnitude below its …
An extremely polarized mixture of an ultracold Fermi gas is expected to reduce to a Fermi polaron system, which consists of a single impurity immersed in the Fermi sea of majority atoms. By developing a many-body T -matrix theory, we investigate spectral properties of the polarized mixture in experimentally relevant regimes in which the system of finite impurity concentration at nonzero temperature is concerned. We explicitly demonstrate presence of polaron physics in the polarized limit and discuss effects of many polarons in an intermediate regime in a self-consistent manner. By analyzing th…
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.
We investigate the properties a mobile ion immersed in a Bose-Einstein condensate (BEC) using different theoretical approaches. A coherent state variational ansatz predicts that the ion spectral function exhibits several branches in addition to polaronic quasiparticle states, and we employ a diagrammatic analysis of the ion-atom scattering in the BEC to identify them as arising from the binding of an increasing number of bosons to the ion. We develop a simplified model describing the formation of these molecular ions showing that their spectral weight scales with the number of bound atoms. The…
We consider the Fermi polaron problem at zero temperature, where a single impurity interacts with non-interacting host fermions. We approach the problem starting with a Frohlich-like Hamiltonian where the impurity is described with canonical position and momentum operators. We apply the Lee-Low-Pine (LLP) transformation to change the fermionic Frohlich Hamiltonian into the fermionic LLP Hamiltonian which describes a many-body system containing host fermions only. We adapt the self-consistent Hartree-Fock (HF) approach, first proposed by Edwards, to the fermionic LLP Hamiltonian in which a pair…
We study the quantum phases of one-dimensional Bose-Fermi mixtures in optical lattices. Assuming repulsive interparticle interactions, equal mass, and unit total filling, we calculate the ground-state phase diagram by means of both Tomonaga-Luttinger liquid theory and time-evolving block decimation method. We demonstrate the existence of a counterflow superfluid (CFSF) phase of polaron pairs, which are composite particles consisting of two fermions and two bosonic holes, in a broad range of the parameter space. We find that this phase naturally emerges in $^{174}$Yb-$^{173}$Yb mixtures, realiz…
Efficient variational approach to the Fermi polaron problem in two dimensions, both in and out of equilibrium
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；ETH Zurich（苏黎世联邦理工学院）；Harvard University（哈佛大学）
We theoretically analyze inverse radiofrequency (rf) spectroscopy experiments in two-component Fermi gases. We consider a small number of impurity atoms interacting strongly with a bath of majority atoms. In two-dimensional geometries we find that the main features of the rf spectrum correspond to an attractive polaron and a metastable repulsive polaron. Our results suggest that the attractive polaron has been observed in a recent experiment [Phys. Rev. Lett. 106, 105301 (2011)].
We investigate the ground state properties of the gaseous mixture of a single species of bosons and fermions at zero temperature, where bosons are major in population over fermions, and form the Bose-Einstein condensate (BEC). The boson-boson and boson-fermion interactions are assumed to be weakly repulsive and attractive respectively, while the fermion-fermion interaction is absent due to the Pauli exclusion for the low energy $s$-wave scattering. We treat fermions as a gas of polarons dressed with Bogoliubov phonons, which is an elementary excitation of the BEC, and evaluate the ground state…
Polarons can serve as an ideal platform to identify few-body correlations in tackling complex many-body problems. In this work, we reveal various crystalline few-body correlations smoothly emergent from the mass-imbalanced Fermi polarons in two dimensions. A unified variational approach up to three particle-hole excitations allows us to extract the dominant dimer, trimer or tetramer correlation in a single framework. When the fermion-impurity mass ratio is beyond certain critical value, the Fermi polaron is found to undergo a smooth crossover, instead of a sharp transition, from the polaronic …
