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 dependences. In particular, with increasing temperature the effective mass quickly approaches the bare mass and the residue is significantly enhanced. At the temperature $T\sim0.1T_{F}$, where $T_{F}$ is the Fermi temperature of the background Fermi sea, the residual polaron-polaron interaction seems to become attractive. This leads to a notable down-shift in the polaron energy. We show that, by taking into account the temperature and impurity concentration effects, the measured polaron energy in the first Fermi polaron experiment {[}A. Schirotzek \textit{et al.}, Phys. Rev. Lett. \textbf{102}, 230402 (2009){]} can be better theoretically explained.
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…
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 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.
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…
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…
We give a detailed account of a stationary impurity in an ideal Bose-Einstein condensate, which we call the ideal Bose polaron, at both zero and non-zero temperatures and arbitrary strength of the impurity-boson coupling. The time evolution is solved exactly and it is found that, surprisingly, many of the features that have been predicted for the real BEC are already present in this simpler setting and can be understood analytically therein. We obtain explicit formulae for the time evolution of the condensate wave function at $T=0$ and of the one-particle density matrix at $T>0$. For negative …
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…
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…
When mobile impurities are introduced and coupled to a Fermi sea, new quasiparticles known as Fermi polarons are formed. There are two interesting, yet drastically different regimes of the Fermi polaron problem: (I) the attractive polaron (AP) branch, connected to pairing phenomena spanning the crossover from BCS superfluidity to the Bose-Einstein condensation of molecules; and (II) the repulsive branch (RP), which underlies the physics responsible for Stoner's itinerant ferromagnetism. Here, we study Fermi polarons in two dimensional systems, where many questions and debates regarding their n…
We study the properties of a single impurity in a dilute Bose gas, a Bose polaron, using the functional renormalization group. We use an ansatz for the effective action motivated by a derivative expansion, and we compute the energies of the attractive and repulsive branches of excitations in both two and three spatial dimensions. Three-body correlations play an important role in the attractive branch, and we account for those by including three-body couplings between two bath bosons and the impurity. Our calculations compare very favorably with state-of-the-art experimental measurements and nu…
The problem of an impurity particle moving through a bosonic medium plays a fundamental role in physics. However, the canonical scenario of a mobile impurity immersed in a Bose-Einstein condensate (BEC) has not yet been realized. Here, we use radio frequency spectroscopy of ultracold bosonic $^{39}$K atoms to experimentally demonstrate the existence of a well-defined quasiparticle state of an impurity interacting with a BEC. We measure the energy of the impurity both for attractive and repulsive interactions, and find excellent agreement with theories that incorporate three-body correlations, …
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…
Impurities in a Fermi sea, or Fermi polarons, experience a Casimir interaction induced by quantum fluctuations of the medium. When there is short-range attraction between impurities and fermions, also the induced interaction between two impurities is strongly attractive at short distance and oscillates in space for larger distances. We theoretically investigate the scattering properties and compute the scattering phase shifts and scattering lengths between two heavy impurities in an ideal Fermi gas at zero temperature. While the induced interaction between impurities is weakly attractive for w…
We study the properties of an impurity of mass $M$ moving through a spatially homogeneous three-dimensional fully polarized Fermi gas of particles of mass $m$. In the weakly attractive limit, where the effective coupling constant $g\to0^-$ and perturbation theory can be used, both for a broad and a narrow Feshbach resonance, we obtain an explicit analytical expression for the complex energy $ΔE(\KK)$ of the moving impurity up to order two included in $g$. This also gives access to its longitudinal and transverse effective masses $m_\parallel^*(\KK)$, $m_\perp^*(\KK)$, as functions of the impur…
We investigate the formation of a Bose polaron when a single impurity in a Bose-Einstein condensate is quenched from a non-interacting to an attractively interacting state in the vicinity of a Feshbach resonance. We use a beyond-Fröhlich Hamiltonian to describe both sides of the resonance and a coherent-state variational ansatz to compute the time evolution of boson density profiles in position space. We find that on the repulsive side of the Feshbach resonance, the Bose polaron performs long-lived oscillations, which is surprising given that the two-body problem has only one bound state coupl…
The study of polaron of an open quantum system plays an important role in both verifying the effectiveness of approximate many-body theory and predicting novel quantum phenomenone in open quantum systems. In a pioneering work, Piazza et al have proposed a Fermi-polaron scheme with a lossy impurity [54], which exhibits a novel long-lived attractive polaron branch in the quantum Zeno limit. However, we would also run into a counterpart problem that an impurity scatters with an open quantum bath exciting polarons, which is what we focus in on. In this work, we conclude the molecular state under t…
We investigate a polaronic excitation in a one-dimensional spin-1/2 Fermi gas with contact attractive interactions, using the complex Langevin method, which is a promising approach to evade a possible sign problem in quantum Monte Carlo simulations. We found that the complex Langevin method works correctly in a wide range of temperature, interaction strength, and population imbalance. The Fermi polaron energy extracted from the two-point imaginary Green's function is not sensitive to the temperature and the impurity concentration in the parameter region we considered. Our results show a good a…
We use a class of variational wave functions to study the properties of an impurity in a Bose-Einstein condensate, i.e. the "Bose polaron". The impurity interacts with the condensate through a contact interaction, which can be tuned by a Feshbach resonance. We find a stable attractive polaron branch that evolves continuously across the resonance to a tight-binding diatomic molecule deep in the positive scattering length side. A repulsive polaron branch with finite lifetime is also observed and it becomes unstable as the interaction strength increases. The effective mass of the attractive polar…
We use a high-temperature expansion to explore spin correlations around a single hole in a two- dimensional lattice filled with a hard-core two component bose gas. We find that the spins around the hole develop ferromagnetic order and quantify the degree of polarization at temperatures of order the hopping energy, finding a measurably nonzero polarization. We also discuss the effect of fixing the overall magnetization of the system for finite-sized systems.
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 theoretically investigate the quasiparticle (polaron) properties of an impurity immersing in a Bose-Einstein condensate with equal Rashba and Dresselhaus spin-orbit coupling at zero temperature. In the presence of spin-orbit coupling, all bosons can condense into a single plane-wave state with finite momentum, and the corresponding excitation spectrum shows an intriguing roton minimum. We find that the polaron properties are strongly modified by this roton minimum, where the ground state of attractive polaron acquires a nonzero momentum and anisotropic effective mass. Across the resonance o…
When an impurity is immersed in a Bose-Einstein condensate, impurity-boson interactions are expected to dress the impurity into a quasiparticle, the Bose polaron. We superimpose an ultracold atomic gas of $^{87}$Rb with a much lower density gas of fermionic $^{40}$K impurities. Through the use of a Feshbach resonance and RF spectroscopy, we characterize the energy, spectral width and lifetime of the resultant polaron on both the attractive and the repulsive branches in the strongly interacting regime. The width of the polaron in the attractive branch is narrow compared to its binding energy, e…
We investigate the properties of attractive polaron formed by a single impurity dressed with the particle-hole excitations in a three-dimensional (3D) doped (extrinsic) parabolic system. %at zero-temperature limit. Base on the single particle-hole variational ansatz, we study the pair propagator, self-energy, and the non-self-consistent medium $T$-matrix. The non-self-consistent $T$-matrix discussed in this paper contains only the open channel since we don't consider the shift of center-of-mass due to the resonance (e.g., induced by the magnetic field). Besides, since we focus on the low-densi…
We consider a polaronic model in which impurity fermions interact with background bosons in a dipolar condensate. The polaron in this model emerges as an impurity dressed with a cloud of phonons of the dipolar condensate, which, due to the competition between the attractive and repulsive part of the dipole-dipole interaction, obey an anisotropic dispersion spectrum. We study how this anisotropy affects the Cerenkov-like emission of Bogoliubov phonon modes, which can be directly verified by experiments in which a dipolar BEC moves against an obstacle. We also study the spectral function of impu…
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…
Institute for Quantum Optics and Quantum Information (IQOQI)（量子光学与量子信息研究所）；University of Innsbruck（因斯布鲁克大学）；International School for Advanced Studies (SISSA)（高级研究国际学校）；Monash University（莫纳什大学）；Aarhus University（奥胡斯大学）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
Since the Efimov effect was introduced in 1970, a detailed theoretical understanding of Efimov physics has been developed in the few-body context. However, it has proven to be challenging to describe the role Efimov-type correlations play in many-body systems such as quenched or collapsing Bose-Einstein condensates (BECs). To study the impact the Efimov effect can have in such scenarios, we consider a light impurity immersed in a weakly interacting BEC, forming a Bose polaron. In this case, the higher-order correlations are localized around the impurity, making it more feasible to develop a th…
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…
We study the relaxation dynamics of driven, two-dimensional semiconductors, where itinerant electrons dress optically pumped excitons to form two Fermi-polaron branches. Repulsive polarons excited around zero momentum quickly decay to the attractive branch at high momentum. Collisions with electrons subsequently lead to a slower relaxation of attractive polarons, which accumulate at the edge of the light-cone around zero momentum where the radiative loss dominates. The bosonic nature of exciton polarons enables stimulated scattering, which results in a lasing transition at higher pump power. T…
The Bose polaron has attracted theoretical and experimental interest because the mobile impurity is surrounded by a bath that undergoes a superfluid-to-normal phase transition. Although many theoretical works have studied this system in its ground state, only few analyze its behavior at finite temperature. We have studied the effect of temperature on a Bose polaron system performing ab-initio Path Integral Monte Carlo simulations. This method is able to approach the critical temperature without losing accuracy, in contrast with perturbative approximations. We have calculated the polaron energy…
An impurity immersed in a Bose-Einstein condensate is no longer accurately described by the Fröhlich Hamiltonian as the coupling between the impurity and the boson bath gets stronger. We study the dominant effects of the two-phonon terms beyond the Fröhlich model on the ground-state properties of the polaron using Feynman's variational path-integral approach. The previously reported discrepancy in the effective mass between the renormalization group approach and this theory is shown to be absent in the beyond-Fröhlich model on the positive side of the Feshbach resonance. Self-trapping, charact…
We investigate a single impurity interacting with a free two-dimensional atomic Fermi gas. The interaction between the impurity and the gas is characterized by an arbitrary attractive short-range potential, which, in two dimensions, always admits a two-particle bound state. We provide analytical expressions for the energy and the effective mass of the dressed impurity by including the two-body bound state, which is crucial for strong interactions, in the integral equation for the effective interaction. Using the same method we give also the results for the polaron parameters in one and three d…
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 …
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…
The temperature dependence of a mobile impurity in a dilute Bose gas, the Bose polaron, is investigated for wide a range of impurity-bath interactions. Using a diagrammatic resummation scheme designed to include scattering processes important at finite temperature $T$, we show that the phase transition of the environment to a Bose-Einstein condensate at the critical temperature $T_c$ leads to several non-trivial effects. The attractive polaron present at $T=0$ fragments into two quasiparticle states for finite temperature whenever $|a|\gtrsim a_B$, with $a$ and $a_B$ the impurity-boson and bos…
We study the problem of a single impurity of mass $M$ immersed in a Fermi sea of particles of mass $m$. The impurity and the fermions interact through a s-wave narrow Feshbach resonance, so that the Feshbach length $R_*$ naturally appears in the system. We use simple variational ansatz, limited to at most one pair of particle-hole excitations of the Fermi sea and we determine for the polaronic and dimeronic branches the phase diagram between absolute ground state, local minimum, thermodynamically unstable regions (with negative effective mass), and regions of complex energies (with negative im…
We study the effect of Efimov physics (in the few-body sector) to the spectral response of Bose polaron, a many-body system consisting of an impurity immersed in a bath of bosonic atoms. We find that the Efimov correlation can be greatly enhanced by increasing the mass ratio between the bosons and the impurity, which results in visible signatures in the rf spectrum of the polaron. Using a diagrammatic approach up to the third-order virial expansion, we show how the mass imbalance and the enhanced three-body effect modify the line shape and the width of the polaron spectrum. Moreover, we study …
We theoretically investigate the behavior of a moving impurity immersed in a sea of fermionic atoms that are confined in a quasi-periodic (bichromatic) optical lattice, within a standard variational approach. We consider both repulsive and attractive contact interactions for such a simplest many-body localization problem of Fermi polarons. The variational approach enables us to access relatively large systems and therefore may be used to understand many-body localization in the thermodynamic limit. The energy and wave-function of the polaron states are found to be strongly affected by the quas…
We investigate thermal evolution of radio-frequency (RF) spectra of a spin-imbalanced Fermi gas near a Feshbach resonance in which degenerate Fermi-polaron and classical Boltzmann-gas regimes emerge in the low-temperature and high-temperature limits, respectively. By using a self-consistent framework of strong-coupling diagrammatic approaches, both of the ejection and reserve RF spectra available in cold-atom experiments are analyzed. We find a variety of transfers from Fermi polarons to Boltzmann gas such that a thermal crossover expected in the weak-coupling regime is shifted to a sharp tran…
We use a non-perturbative renormalization group approach to develop a unified picture of the Bose polaron problem, where a mobile impurity is strongly interacting with a surrounding Bose-Einstein condensate (BEC). A detailed theoretical analysis of the phase diagram is presented and the polaron-to-molecule transition is discussed. For attractive polarons we argue that a description in terms of an effective Fröhlich Hamiltonian with renormalized parameters is possible. Its strong coupling regime is realized close to a Feshbach resonance, where we predict a sharp increase of the effective mass. …
