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 number of atoms in the dressing cloud around the ion are calculated from thermodynamic arguments, and we finally show that the dynamics ensuing the injection of an ion into the BEC exhibits various regimes governed by coherent quasiparticle propagation and decay.
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 study the properties of the Bose polaron, an impurity strongly interacting with a Bose-Einstein condensate, using a field-theoretic approach and make predictions for the spectral function and various quasiparticle properties that can be tested in experiment. We find that most of the spectral weight is contained in a coherent attractive and a metastable repulsive polaron branch. We show that the qualitative behavior of the Bose polaron is well described by a non-selfconsistent T-matrix approximation by comparing analytical results to numerical data obtained from a fully selfconsistent T-matr…
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…
The mobile impurity in a Bose-Einstein condensate (BEC) is a paradigmatic many-body problem. For weak interaction between the impurity and the BEC, the impurity deforms the BEC only slightly and it is well described within the Fröhlich model and the Bogoliubov approximation. For strong local attraction this standard approach, however, fails to balance the local attraction with the weak repulsion between the BEC particles and predicts an instability where an infinite number of bosons is attracted toward the impurity. Here we present a solution of the Bose polaron problem beyond the Bogoliubov a…
We study the diffusive behavior of a Bose polaron immersed in a coherently coupled two-component Bose-Einstein Condensate (BEC). Polaron superdiffuses if it couples in the same manner to both components, i.e. either attractively or repulsively to both of them. This is the same behavior as that of an impurity immersed in a single BEC. Conversely, the polaron exhibits a transient nontrivial subdiffusive behavior if it couples attractively to one of the components and repulsively to the other. The anomalous diffusion exponent and the duration of the subdiffusive interval can be controlled with th…
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 extend the dynamical variational approach of [Phys.Rev.Lett. 117, 11302 (2016)] 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 non-interacting 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 impu…
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…
Polarons, self-localized composite objects formed by the interaction of a single impurity particle with a host medium, are a paradigm of strong interaction many-body physics. We show that dilute gas Bose-Einstein condensates (BEC's) are the first medium known to self-localize the same impurity particles both in a Landau-Pekar polaron state akin to that of self-localized electrons in a dielectric lattice, and in a bubble state akin to that of electron bubbles in helium. We also show that the BEC-impurity system is fully characterized by just two dimensionless coupling constants, and that it can…
A toolbox for the quantum simulation of polarons in ultracold atoms is presented. Motivated by the impressive experimental advances in the area of ultracold atomic mixtures, we theoretically study the problem of ultracold atomic impurities immersed in a Bose-Einstein condensate mixture (BEC). The coupling between impurity and BEC gives rise to the formation of polarons whose mutual interaction can be effectively tuned using an external laser driving a quasi-resonant Raman transition between the BEC components. Our scheme allows one to change the effective interactions between polarons in diffe…
We investigate the properties of a strongly interacting imbalanced mixture of bosonic $^{41}$K impurities immersed in a Fermi sea of ultracold $^6$Li atoms. This enables us to explore the Fermi polaron scenario for large impurity concentrations including the case where they form a Bose-Einstein condensate. The system is characterized by means of radio-frequency injection spectroscopy and interspecies interactions are widely tunable by means of a well-characterized Feshbach resonance. We find that the energy of the Fermi polarons formed in the thermal fraction of the impurity cloud remains rath…
Bose polarons, quasi-particles composed of mobile impurities surrounded by cold Bose gas, can experience strong interactions mediated by the many-body environment and form bipolaron bound states. Here we present a detailed study of heavy polarons in a one-dimensional Bose gas by formulating a non-perturbative theory and complementing it with exact numerical simulations. We develop an analytic approach for weak boson-boson interactions and arbitrarily strong impurity-boson couplings. Our approach is based on a mean-field theory that accounts for deformations of the superfluid by the impurities …
This study develops a novel experimental method of deducing the profile of interaction induced between impurities in a trapped gas of ultracold Fermi/Bose atoms, which are often referred to as Fermi/Bose polarons. In this method, we consider a two-body Fermi/Bose polaron collision experiment in which impurities and atoms interact only weakly. Numerical simulations of the quantum dynamics reveal the possibility to obtain information regarding the non-local induced interaction between two polarons from a measured profile of the polaron wave packet at several snapshots. This is because the potent…
We study the polaron quasiparticle in a one-dimensional Bose gas. In the integrable case described by the Yang-Gaudin model, we derive an exact result for the polaron mass in the thermodynamic limit. It is expressed in terms of the derivative with respect to the density of the ground-state energy per particle of the Bose gas without the polaron. This enables us to find high-order power series for the polaron mass in the regimes of weak and strong interaction.
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…
We investigate the polarons formed by immersing a spinor impurity in a ferromagnetic state of $F=1$ spinor Bose-Einstein condensate. The ground state energies and effective masses of the polarons are calculated in both weak-coupling regime and strong-coupling regime. In the weakly interacting regime the second order perturbation theory is performed. In the strong coupling regime we use a simple variational treatment. The analytical approximations to the energy and effective mass of the polarons are constructed. Especially, a transition from the mobile state to the self-trapping state of the po…
The application of optical lattices allows a tuning of the geometry of Bose-Einstein condensates to effectively reduced dimensions. In the context of solid state physics the consideration of the low-dimensional Fröhlich polaron results in an extension of the polaronic strong coupling regime. With this motivation we apply the Jensen-Feynman variational principle to calculate the ground state properties of the polaron consisting of an impurity in a Bose-Einstein condensate in reduced dimensions. Also the response of this system to Bragg scattering is calculated. We show that reducing the dimensi…
We report spectroscopic observation of Rydberg polarons in an atomic Bose gas. Polarons are created by excitation of Rydberg atoms as impurities in a strontium Bose-Einstein condensate. They are distinguished from previously studied polarons by macroscopic occupation of bound molecular states that arise from scattering of the weakly bound Rydberg electron from ground-state atoms. The absence of a $p$-wave resonance in the low-energy electron-atom scattering in Sr introduces a universal behavior in the Rydberg spectral lineshape and in scaling of the spectral width (narrowing) with the Rydberg …
We theoretically investigate the role of multiple impurity atoms on the ground state properties of Bose polarons. The Bogoliubov approximation is applied for the description of the condensate resulting in a Hamiltonian containing terms beyond the Fröhlich approximation. The many-body nature of the impurity atoms is taken into account by extending the many-body description for multiple Fröhlich polarons, revealing the static structure factor of the impurities as the key quantity. Within this formalism various experimentally accessible polaronic properties are calculated such as the energy and t…
The properties of a Bose polaron immersed in a dilute two-dimensional medium at finite temperatures are discussed. Assuming that the impurity is weakly-coupled to the bath particles we have perturbatively calculated the polaron energy, effective mass, quasiparticle residue and damping rate. The parameters of impurity spectrum are found to be well-defined in the whole temperature region whereas the pole structure of the impurity Green's function is visible only at absolute zero. At any finite temperatures the quasiparticle residue is logarithmically divergent signalling of the branch-cut behavi…
We study degenerate mixtures of "heavy" bosons and "light" superfluid bosons using a variational polaron transformation. We consider the Mott insulator-superfluid transition of the heavy species and find that at $T=0$ interaction favors the superfluid phase of the heavy species. Our analytic results agree well with numerically exact quantum Monte Carlo simulations in two dimensions. We then show that in three dimensions the variational polaron transformation can be combined with a Gutzwiller approximation to give good results.
We study the quantum motion of an impurity atom immersed in a Bose Einstein condensate in arbitrary dimension. The Bogoliubov excitations of the Bose Einstein condensate act as a bosonic bath for the impurity. We present a detailed derivation of the $d$-dimensional Langevin equations that describe the quantum dynamics of the system, and of the associated generalized tensor that describes the spectral density in the full generality. When the impurity is not trapped, we calculate the mean square displacement, showing that the motion is super diffusive. We obtain also explicit expressions for the…
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.
The weak coupling many-polaron formalism is applied to the case of the polaronic system consisting of impurities in a Bose-Einstein condensate. This allows to investigate the groundstate properties and the response of the system to Bragg spectroscopy. This theory is then applied to the system of spin-polarized fermionic lithium-6 impurities in a sodium condensate. The Bragg spectrum reveals a peak which corresponds to the emission of Bogoliubov excitations. Both ground state properties and the response spectrum show that the polaronic effect vanishes at large densities. We also look at two pos…
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. …
Effects of interaction range on the mean-field dynamics of Bose polarons
Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）；Faculty of Physics, University of Warsaw（华沙大学物理学院）；Institute of Theoretical Physics, Wrocław University of Science and Technology（弗罗茨瓦夫科技大学理论物理研究所）
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…
We present an experimental system to study the Bose polaron by immersion of single, well-controllable neutral Cs impurities into a Rb Bose-Einstein condensate (BEC). We show that, by proper optical traps, independent control over impurity and BEC allows for precision relative positioning of the two sub-systems as well as for independent read-out. We furthermore estimate that measuring the polaron binding energy of Fröhlich-type Bose polarons in the low and intermediate coupling regime is feasible with our experimental constraints and limitations discussed.
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…
We discuss the interaction of a quantum impurity with a one-dimensional degenerate Bose gas forming a Bose-polaron. In three spatial dimensions the quasiparticle is typically well described by the extended Fröhlich model, in full analogy with the solid-state counterpart. This description, which assumes an undepleted condensate, fails however in 1D, where the backaction of the impurity on the condensate leads to a self-bound mean-field polaron for arbitrarily weak impurity-boson interactions. We present a model that takes into account this backaction and describes the impurity-condensate intera…
Bose polarons as relativistic Unruh-DeWitt detectors: Entanglement harvesting from Bose-Einstein condensates
Nordita, KTH Royal Institute of Technology and Stockholm University（诺尔迪塔，皇家理工学院和斯德哥尔摩大学）；Kirchhoff-Institut für Physik, Universität Heidelberg（基希霍夫物理研究所，海德堡大学）
We use variational methods to study a spin impurity in a 1D Bose lattice gas. Both in the strongly interacting superfluid regime and the Mott regime we find that the impurity binds with a hole, forming a polaron. Our calculations for the dispersion of the polaron are consistent with recent experiments by Fukuhara et. al. [Nature Phys. 9, 235 (2013)] and give a better understanding of their numerical simulations. We find that for sufficiently weak interactions there are ranges of momentum for which the polaron is unstable. We propose experimentally studying the stability of the polaron by measu…
The detailed mean-field treatment of the Bose polaron problem in two and three dimensions is presented. Particularly, assuming that impurity is immersed in the dilute Bose gas and interacts with bosons via the hard-sphere two-body potential, we calculate the low-momentum parameters of its spectrum, namely, the binding energy and the effective mass. The limits of applicability of the mean-field approach to a problem of mobile impurity in Bose-Einstein condensates are discussed by comparing our results to the Monte Carlo simulations data.
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 …
The variational Feynman formalism for the polaron, extended to an all-coupling treatment of bipolarons, is applied for two impurity atoms in a Bose-Einstein condensate. This shows that if the polaronic coupling strength is large enough the impurities will form a bound state (the bipolaron). As a function of the mutual repulsion between the impurities two types of bipolaron are distinguished: a tightly bound bipolaron at weak repulsion and a dumbbell bipolaron at strong repulsion. Apart from the binding energy, also the evolution of the bipolaron radius and its effective mass are examined as a …
We study the Bose polaron problem in a nonequilibrium setting, by considering an impurity embedded in a quantum fluid of light realized by exciton-polaritons in a microcavity, subject to a coherent drive and dissipation on account of pump and cavity losses. We obtain the polaron effective mass, the drag force acting on the impurity, and determine polaron trajectories at a semiclassical level. We find different dynamical regimes, originating from the unique features of the excitation spectrum of driven-dissipative polariton fluids, in particular a non-trivial regime of acceleration against the …
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…
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…
We study entanglement and squeezing of two uncoupled impurities immersed in a Bose-Einstein condensate. We treat them as two quantum Brownian particles interacting with a bath composed of the Bogoliubov modes of the condensate. The Langevin-like quantum stochastic equations derived exhibit memory effects. We study two scenarios: (i) In the absence of an external potential, we observe sudden death of entanglement; (ii) In the presence of an external harmonic potential, entanglement survives even at the asymptotic time limit. Our study considers experimentally tunable parameters.
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…
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…
The interaction between a mobile quantum impurity and a bosonic bath leads to the formation of quasiparticles, termed Bose polarons. The elementary properties of Bose polarons, such as their mutual interactions, can differ drastically from those of the bare impurities. Here, we explore Bose polaron physics in a two-dimensional nonequilibrium setting by injecting $σ^-$ polarised exciton-polariton impurities into a bath of coherent $σ^+$ polarised polaritons generated by resonant laser excitation of monolayer MoSe$_2$ embedded in an optical cavity. By exploiting a biexciton Feshbach resonance be…
We present a novel approach to the Bose polaron based on the notion of quantum groups, also known as $q$-deformed Lie algebras. In this approach, a mobile impurity can be depicted as a deformation of the Lie algebra of the bosonic creation and annihilation operators of the bath, in which the impurity is immersed. Accordingly, the Bose polaron can be described as a bath of noninteracting $q$-deformed bosons, which allows us to provide an analytical formulation of the Bose polaron at arbitrary couplings. Particularly, we derive its ground state energy in the phonon branch of the Bogoliubov dispe…
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 …
The emergence of quasiparticles in strongly interacting matter represents one of the cornerstones of modern physics. However, when different phases of matter compete near a quantum critical point, the very existence of quasiparticles comes under question. Here we create Bose polarons near quantum criticality by immersing atomic impurities in a Bose-Einstein condensate (BEC) with near-resonant interactions. Using locally-resolved radiofrequency spectroscopy, we probe the energy, spectral width, and short-range correlations of the impurities as a function of temperature. Far below the superfluid…
We investigate the non-equilibrium dynamics of an impurity coupled to a Bose-Einstein condensate, systematically compared with recent experimental results [M. G. Skou et al., Nat. Phys. (2021)]. The dynamics of the impurity is tracked down by using a time-dependent variational coherent ansatz. For weak coupling between the impurity and the bath, analytical expressions for the time-dependent overlap (or contrast) are derived, matching quite well with previous findings obtained within a master equation approach. For strong coupling instead, the variational ansatz provides a good quantitative des…
We perform an extensive numerical study on the breathing dynamics of a few-body Bose polaron setup in a one-dimensional species-selective harmonic trap. The dynamics is triggered by a quench of the impurity trap. The excitation of the background majority atoms is mediated via the majority-impurity interaction. The breathing spectrum is obtained for different numbers of majority particles, several values of the majority-component interaction strengths and trap ratios. It is further compared to the breathing spectrum of a particle-balanced few-body Bose-Bose mixture. In particular, for equal pos…
Mobile impurity atoms immersed in Bose-Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable microscopic parameters and to explore equilibrium and dynamical properties of polarons using a rich toolbox of atomic physics. In this paper we present a detailed theoretical analysis of Bose polarons in one dimensional systems of ultracold atoms. By combining a non-perturbative renormalization group approach with numerically exact diffusion Monte Carlo calculatio…
