We present a variational calculation of the energy of an impurity immersed a double Fermi sea of non-interacting Fermions. We show that in the strong-coupling regime, the system undergoes a first order transition between polaronic and trimer states. Our result suggests that the smooth crossover predicted in previous literature for a superfluid background is the consequence of Cooper pairing and is absent in a normal system.
In this article we investigate the properties of an impurity immersed in a superfluid of strongly correlated spin 1/2 fermions. For resonant interactions, we first relate the stability diagram of dimer and trimer states to the three-body problem for an impurity interacting with a pair of fermions. Then 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.
We report on controlled doping of an ultracold Rb gas with single neutral Cs impurity atoms. Elastic two-body collisions lead to a rapid thermalization of the impurity inside the Rb gas, representing the first realization of an ultracold gas doped with a precisely known number of impurity atoms interacting via s-wave collisions. Inelastic interactions are restricted to a single three-body recombination channel in a highly controlled and pure setting, which allows to determine the Rb-Rb-Cs three-body loss rate with unprecedented precision. Our results pave the way for a coherently interacting h…
In this article we calculate the energy of an impurity weakly coupled to a spin 1/2 fermionic superfluid. We show that the divergences resulting from three-body physics can only be cured using a proper description of the excitations of the many-body background. We highlight the crucial role played by interactions between quasiparticles which are overlooked within BCS (Bardeen-Cooper-Schrieffer) mean-field theory of fermionic superfluidity. By contrast, we prove that their addition using the Random Phase Approximation (RPA) allows us to regularize the energy of the impurity. Finally, we show th…
We unravel the correlated tunneling dynamics of an impurity trapped in a double well and interacting repulsively with a majority species of lattice trapped bosons. Upon quenching the tilt of the double well it is found that the quench-induced tunneling dynamics depends crucially on the interspecies interaction strength and the presence of entanglement inherent in the system. In particular, for weak couplings the impurity performs a rather irregular tunneling process in the double well. Increasing the interspecies coupling it is possible to control the response of the impurity which undergoes a…
The counterflow dynamics of two correlated impurities in a double-well coupled to an one-dimensional bosonic medium is explored. We determine the ground state phase diagram of the system according to the impurity-medium entanglement and the impurities two-body correlations. Specifically, bound impurity structures reminiscent of bipolarons for strong attractive couplings as well as configurations with two clustered or separated impurities in the repulsive case are identified. The interval of existence of these phases depends strongly on the impurity-impurity interactions and external confinemen…
We study the dissipative dynamics of neutral atoms in anisotropic harmonic potentials, immersed in a reservoir species that is not trapped by the harmonic potential. Considering initial motional excitation of the atoms along one direction, we explore the resulting spontaneous emission of reservoir excitations, across a range of trap parameters from strong to weak radial confinement. In different limits these processes are useful as a basis for analogies to laser cooling, or as a means to introduce controlled dissipation to many-body dynamics. For realistic experimental parameters, we analyse t…
In this paper, we study the problem of an impurity with infinite mass and the Casimir force between two impurities immersed in a Bose-Einstein condensate. Our calculation results shows that the Casimir force decays exponentially in distance at large distance.
We unravel the nonequilibrium correlated quantum quench dynamics of an impurity traveling through a harmonically confined Bose-Einstein condensate in one-dimension. For weak repulsive interspecies interactions the impurity oscillates within the bosonic gas. At strong repulsions and depending on its prequench position the impurity moves towards an edge of the bosonic medium and subsequently equilibrates. This equilibration being present independently of the initial velocity, the position and the mass of the impurity is inherently related to the generation of entanglement in the many-body system…
We consider a mobile impurity immersed in a Bose gas at finite temperature. Using perturbation theory valid for weak coupling between the impurity and the bosons, we derive analytical results for the energy and damping of the impurity for low and high temperatures, as well as for temperatures close to the critical temperature $T_c$ for Bose-Einstein condensation. These results show that the properties of the impurity vary strongly with temperature. In particular, the energy exhibits a non-monotonic behavior close to $T_c$, and the damping rises sharply close to $T_c$. We argue that this behavi…
We proposed the non-perturbative scheme for calculation of the impurity spectrum in the Bose system at zero temperature. The method is based on the path-integral formulation and describes an impurity as a zero-density ideal Fermi gas interacting with Bose system for which the action is written in terms of density fluctuations. On the example of the $^3$He atom immersed in the liquid helium-4 a good consistency with experimental data and results of Monte Carlo simulations is shown.
We investigate transport dynamics of a single low-energy ionic impurity in a Bose-Einstein condensate. The impurity is implanted into the condensate starting from a single Rydberg excitation, which is ionized by a sequence of fast electric field pulses aiming to minimize the ion's initial kinetic energy. Using a small electric bias field, we study the subsequent collisional dynamics of the impurity subject to an external force. The fast ion-atom collision rate, stemming from the dense degenerate host gas and the large ion-atom scattering cross section, allows us to study a regime of frequent c…
In this paper we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length $a$. Working up to order $a^3$, associated to the creation of two particle-hole pairs, reveals the first…
We develop a systematic perturbation theory for the quasiparticle properties of a single impurity immersed in a Bose-Einstein condensate. Analytical results are derived for the impurity energy, the effective mass, and residue to third order in the impurity-boson scattering length. The energy is shown to depend logarithmically on the scattering length to third order, whereas the residue and effective mass are given by analytical power series. When the boson-boson scattering length equals the boson-impurity scattering length, the energy has the same structure as that of a weakly interacting Bose…
We unravel the ground state properties and the non-equilibrium quantum dynamics of two bosonic impurities immersed in an one-dimensional fermionic environment by applying a quench of the impurity-medium interaction strength. In the ground state, the impurities and the Fermi sea are phase-separated for strong impurity-medium repulsions while they experience a localization tendency around the trap center for large attractions. We demonstrate the presence of attractive induced interactions mediated by the host for impurity-medium couplings of either sign and analyze the competition between induce…
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 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 an impurity immersed in the mixture of Bose ultracold gases in the regime where a quantum droplet exists. The quasi-one-dimensional geometry is considered. We find an effective attractive potential that acts by the quantum droplet onto the impurity. The bound states of the impurity in this potential are investigated. These impurity bound states can provide potential probes for the presence of quantum fluctuations effects on the droplet properties. In the case of strong impurity-BEC coupling, we study the properties of the nonlinear local modes on the impurity induced by the quantum fl…
We have created a triply quantum degenerate mixture of bosonic $^{41}$K and two fermionic species $^{40}$K and $^6$Li. The boson is shown to be an efficient coolant for the two fermions, spurring hopes for the observation of fermionic superfluids with imbalanced masses. We observe multiple heteronuclear Feshbach resonances, in particular a wide s-wave resonance for the combination $^{41}$K-$^{40}$K, opening up studies of strongly interacting {\it isotopic} Bose-Fermi mixtures. For large imbalance, we enter the polaronic regime of dressed impurities immersed in a bosonic or fermionic bath.
We consider a trapped atomic ensemble of interacting bosons in the presence of a single trapped ion in a quasi one dimensional geometry. Our study is carried out by means of the newly developed multilayer-multiconfiguration time-dependent Hartree method for bosons, a numerical exact approach to simulate quantum many-body dynamics. In particular, we are interested in the scenario by which the ion is so strongly trapped that its motion can be effectively neglected. This enables us to focus on the atomic ensemble only. With the development of a model potential for the atom-ion interaction, we are…
We consider an impurity immersed in a small Fermi gas under highly-elongated harmonic confinement. The impurity interacts with the atoms of the Fermi gas through an isotropic short-range potential with three-dimensional free-space s-wave scattering length $a_{3\text{d}}$. We investigate the energies of the molecular branch, i.e., the energies of the state that corresponds to a gas consisting of a weakly-bound diatomic molecule and "unpaired" atoms, as a function of the s-wave scattering length $a_{3\text{d}}$ and the ratio $η$ between the angular trapping frequencies in the tight and weak conf…
We consider a fixed impurity immersed in a Fermi gas at finite temperature. We take the impurity to have two internal spin states, where the $\uparrow$ state is assumed to interact with the medium such that it exhibits the orthogonality catastrophe, while the $\downarrow$ state is a bare noninteracting particle. Introducing a Rabi coupling between the impurity states therefore allows us to investigate the coupling between a discrete spectral peak and the Fermi-edge singularity, i.e., between states with and without a quasiparticle residue. Combining an exact treatment of the uncoupled impurity…
The properties of impurity immersed in the dilute $D$-dimensional Bose gas at temperatures close to the second-order phase transition point are considered. Particularly by means of the $1/N$-expansion we calculated the leading-order polaron energy and the damping rate in the limit of vanishing boson-boson interaction. It is show that the perturbative effective mass and the quasiparticle residue diverge logarithmically in the long-length limit signalling the non-analytic behavior of impurity spectrum and a non-pole structure of a polaron Green's function in the infrared region, respectively.
We present a method for amplifying a single or scattered impurities immersed in a background gas of ultra cold atoms so that they can be optically imaged and spatially resolved. Our approach relies on a Raman transfer between two stable atomic hyperfine states that is conditioned on the presence of an impurity atom. The amplification is based on the strong interaction among atoms excited to Rydberg states. We perform a detailed analytical study of the performance of the proposed scheme with particular emphasis on the influence of many-body effects.
We investigate the large-time asymptotical behavior of a mobile impurity immersed in a degenerate Tonks-Girardeau gas. We derive a correct weak-coupling kinetic equation valid for arbitrary ratio of masses of gas and impurity particles. When gas particles are either lighter or heavier than the impurity we find that our theory is equivalent to the Boltzmann theory with the collision integral calculated via the Fermi Golden Rule. On the contrary, in the equal-mass case, Fermi Golden Rule treatment gives false results due to not accounting for multiple coherent scattering events. The latter are t…
By means of Quantum Monte Carlo methods we calculate the binding energy of an impurity immersed in a Bose-Einstein condensate at T = 0. The focus is on the attractive branch of the Bose polaron and on the role played by the mass imbalance between the impurity and the surrounding particles. For an impurity resonantly coupled to the bath, we investigate the dependence of the binding energy on the mass ratio and on the interaction strength within the medium. In particular, we determine the equation of state in the case of a static (infinite mass) impurity, where three-body correlations are irrele…
The full momentum dependence of spectrum of a point-like impurity immersed in a dilute one-dimensional Bose gas is calculated on the mean-field level. In particular we elaborate, to the finite-momentum Bose polaron, the path-integral approach whose semi-classical approximation leads to the conventional mean-field treatment of the problem while quantum corrections can be easily accounted by standard loop expansion techniques. The extracted low-energy parameters of impurity spectrum, namely, the binding energy and the effective mass of particle, are shown to be in qualitative agreement with the …
Motivated by experiments with cold atoms, we investigate a mobile impurity immersed in a Fermi sea in three dimensions at zero temperature by means of the functional renormalization group. We first perform the derivative expansion of the effective action to calculate the ground state energy and Tan's contact across the polaron-molecule transition for several mass imbalances. Next we study quasiparticle properties of the impurity by using a real-time method recently developed in nuclear physics, which allows one to go beyond the derivative expansion. We obtain the spectral function of the polar…
By analyzing breathing mode of a Bose-Einstein condensate repulsively interacting with a polarized fermionic cloud, we further the understanding of a Bose-Fermi mixture recently realized by Lous et al. [\textit{Phys. Rev. Lett.} \textbf{120}, 243403]. We show that a hydrodynamic description of a domain wall between bosonic and fermionic atoms reproduces experimental data of Huang et al. [\textit{Phys. Rev. A} \textbf{99}, 041602(R)]. Two different types of interaction renormalization are explored, based on lowest order constrained variational and perturbation techniques. In order to replicate …
We present a theory of radio-frequency spectroscopy of impurities interacting with a quantum gas at finite temperature. By working in the canonical ensemble of a single impurity, we show that the impurity spectral response is directly connected to the finite-temperature equation of state (free energy) of the impurity. We consider two different response protocols: "injection", where the impurity is introduced into the medium from an initially non-interacting state; and "ejection", where the impurity is ejected from an initially interacting state with the medium. We show that there is a simple m…
We have calculated the zero-temperature binding energy of a single impurity atom immersed in a Bose-Einstein condensate of ultracold atoms that are trapped in an axially symmetric harmonic potential, where the impurity interacts with bosonic atoms in the condensate via a low-energy s-wave scattering. In this case, bosons are excited around the impurity to form a quasiparticle, namely, a BEC polaron. We have developed a variational method, {\it a la} Lee-Low-Pines (LLP) theory for electron-phonon systems, for description of the polaron with a conserved angular momentum around the symmetric axis…
We develop a method to extract the dissipation for a heavy moving impurity immersed in superfluid Fermi gases. The drag force is derived analytically. As a reward, we are able to extract the dynamical structure factor, from which density excitations of the system is carefully examined. We show that dissipations through drag force is associated with two types of excitations, one being single-particle and the other being collective. We map out the critical velocity for dissipation across the BEC-BCS crossover, consistent with existing experiments. For a magnetic impurity, we show that the dissip…
We study an impurity atom trapped by an anharmonic potential, immersed within a cold atomic Fermi gas with attractive interactions that realizes the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). Considering the qubit comprising the lowest two vibrational energy eigenstates of the impurity, we demonstrate that its dynamics probes the equilibrium density fluctuations encoded in the dynamic structure factor of the superfluid. Observing the impurity's evolution is thus shown to facilitate nondestructive measurements of the superfluid order paramet…
By using a non-self-consistent many-body $T$-matrix theory, we calculate the finite-temperature Raman spectroscopy of a mobile impurity immersed in a Fermi bath in three dimensions. The dependences of the Raman spectrum on the transferred momentum, temperature, and impurity-bath interaction are discussed in detail. We confirm that the peak in the Raman spectrum shows a weaker dependence on the impurity concentration than that in the radio-frequency spectroscopy, due to the nonzero transferred momentum, as anticipated. We compare our theoretical prediction with the recent measurement by Gal Nes…
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. …
We unravel the correlated quantum quench dynamics of a single impurity immersed in a bosonic environment confined in an one-dimensional double-well potential. A particular emphasis is placed on the structure of the time-evolved many-body wave function by relying on a Schmidt decomposition whose coefficients directly quantify the number of configurations that are macroscopically populated. For a non-interacting bosonic bath and weak postquench impurity-bath interactions, we observe the dynamical formation of a two-fold fragmented many-body state which is related to intra-band excitation process…
We consider a quantum impurity immersed in a dipolar Bose Einstein condensate and study the properties of the emerging polaron. We calculate the energy, effective mass and quasi-particle residue of the dipolar polaron and investigate their behaviour with respect to the strength of zero-range contact and a long-range dipolar interactions among the condensate atoms and with the impurity. While quantum fluctuations in the case of pure contact interactions typically lead to an increase of the polaron energy, dipole-dipole interactions are shown to cause a sign reversal. The described signatures of…
Knowing when a physical system has reached sufficient size for its macroscopic properties to be well described by many-body theory is difficult. We investigate the crossover from few to many-body physics by studying quasi one-dimensional systems of ultracold atoms consisting of a single impurity interacting with an increasing number of identical fermions. We measure the interaction energy of such a system as a function of the number of majority atoms for different strengths of the interparticle interaction. As we increase the number of majority atoms one by one we observe the fast convergence …
We consider the dynamics of an impurity atom immersed in an ideal Fermi gas at zero temperature. We focus on the coherent quantum evolution of the impurity following a quench to strong impurity-fermion interactions, where the interactions are assumed to be short range like in cold-atom experiments. To approximately model the many-body time evolution, we use a truncated basis method, where at most two particle-hole excitations of the Fermi sea are included. When the system is initially non-interacting, we show that our method exactly captures the short-time dynamics following the quench, and we…
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…
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 treat the nonequilibrium motion of a single impurity atom in a low-temperature single-species Fermi sea, interacting via a contact interaction. In the nonequilibrium regime, the impurity does a superdiffusive geometric random walk where the typical distance traveled grows with time as $\sim t^{d/(d+1)}$ for the $d$-dimensional system with $d\geq 2$. For nonzero temperature $T$, this crosses over to diffusive motion at long times with diffusivity $D\sim T^{-(d-1)/2}$. These results apply also to a nonzero concentration of impurity atoms as long as they remain dilute and nondegenerate.
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 te…
Single-atomic impurities immersed in a dilute Bose gas in the spherically symmetric harmonic trap potentials are studied at zero temperature. In order to find the ground state of the polarons, we present a conditional variational method with fixed expectation values of the total angular momentum operators, $\hat{J}^2$ and $\hat{J}_z$, of the system, using a cranking gauge-transformation for bosons to move them in the frame co-rotating with the impurity. In the formulation, the expectation value $\langle \hat{J^2}\rangle$ is shown to be shared in impurity and bosons, but the value $\langle \hat…
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…
We theoretically study the static and dynamic behavior of a BEC immersed in a large Fermi sea of ultracold atoms under conditions of tunable interspecies interaction. The degenerate Bose-Fermi mixture is kept in an elongated trap, typical for a single-beam optical dipole trap. We focus on the case of repulsive Bose-Fermi interaction and develop mean-field models to simulate the system over a wide range of repulsion strength. We further get analytical solutions in the regimes of phase separation and weak interaction. We obtain static density profiles and the frequency of the radial breathing mo…
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 consider two identical impurities immersed in a Fermi sea for a broad range of masses and for both interacting and non-interacting impurities. The interaction between the particles is described through attractive zero-range potentials and the problem is solved in momentum space. The two impurities can attach to a fermion from the sea and form three-body bound states. The energy of these states increase as function of the Fermi momentum $k_F$, leading to three-body bound states below the Fermi energy. The fate of the states depends highly on two- and three-body thresholds and we find evidenc…
In this brief review, we report some new development in the functional determinant approach (FDA), an exact numerical method, in the studies of a heavy quantum impurity immersed in Fermi gases and manipulated with radio-frequency pulses. FDA has been successfully applied to investigate the universal dynamical responses of a heavy impurity in an ultracold ideal Fermi gas in both the time and frequency domain, which allows the exploration of the renowned Anderson's orthogonality catastrophe (OC). In such a system, OC is induced by the multiple particle-hole excitations of the Fermi sea, which is…
The precise measurement of low temperatures is a challenging, important and fundamental task for quantum science. In particular, in-situ thermometry is highly desirable for cold atomic systems due to their potential for quantum simulation. Here we demonstrate that the temperature of a non-interacting Fermi gas can be accurately inferred from the non-equilibrium dynamics of impurities immersed within it, using an interferometric protocol and established experimental methods. Adopting tools from the theory of quantum parameter estimation, we show that our proposed scheme achieves optimal precisi…
We establish an experimental method for a detailed investigation of inelastic collisional properties between ytterbium (Yb) in the metastable ${}^3\mathrm{P}_2$ state and ground state lithium (Li). By combining an optical lattice and a direct excitation to the ${}^3\mathrm{P}_2$ state we achieve high selectivity on the collisional partners. Using this method we determine inelastic loss coefficients in collisions between $^{174}$Yb(${}^3\mathrm{P}_2$) with magnetic sublevels of $m_J=0$ and $-2$ and ground state $^6$Li to be $(4.4\pm0.3)\times10^{-11}~\mathrm{cm}^3/\mathrm{s}$ and $(4.7\pm0.8)\t…
We investigate the polaronic properties of a single impurity immersed in a weakly interacting bosonic environment confined within a one-dimensional double-well potential using an exact diagonalization approach. We find that an increase of the impurity-bath coupling results in a vanishing residue, signifying the occurrence of the polaron orthogonality catastrophe. Asymptotic configurations of the systems' ground state wave function in the strongly interacting regime are obtained by means of a Schmidt decomposition, which in turn accounts for the observed orthogonality catastrophe of the polaron…
