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 study the Casimir potential between two impurities immersed in a spin-orbit coupled BoseEinstein condensate (BEC) with plane-wave order. We find that, by exchanging the virtual phonons/excitations, a remarkable anisotropic oscillating potential with both positive and negative parts can be induced between the impurities, with the period of the oscillation depending on the spin-orbit coupling strength. As a consequence, this would inevitably lead to a non-central Casimir force, which can be tuned by varying the strength of spin-orbit coupling . These results are elucidated for BECs with one-d…
Virtual phonons of a quantum liquid scatter off impurities and mediate a long-range interaction, analogous to the Casimir effect. In one dimension the effect is universal and the induced interaction decays as $1/r^3$, much slower than the van der Waals interaction $\sim1/r^6$, where $r$ is the impurity separation. The sign of the effect is characterized by the product of impurity-phonon scattering amplitudes, which take a universal form and have been seen to vanish for several integrable impurity models. Thus, if the impurity parameters can be independently tuned to lie on opposite sides of su…
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 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…
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 present a comprehensive discussion of the ground-state properties of dilute $D$-dimensional Bose gas interacting with a few static impurities. Assuming the short-ranged character of the boson-impurity interaction, we calculate the energy of three- and two-dimensional Bose systems with one and two impurities immersed.
The electromagnetic Casimir effect manifests as the interaction between uncharged conducting objects that are placed in a vacuum. More generally, the Casimir-like effect denotes an induced interaction between external bodies in a fluctuating medium. We study the Casimir-like interaction between two impurities embedded in a weakly interacting one-dimensional Bose gas. We develop a theory based on the Gross-Pitaevskii equation that accounts for the effect of quantum fluctuations. At small separations, the induced interaction between the impurities decays exponentially with the distance. This is …
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 exactly calculate the full temperature dependence of Casimir-like forces appearing between two and three static impurities loaded in the ideal Bose gas below the Bose-Einstein condensation transition point. Assuming the short-ranged character of the boson-impurity interaction, the calculation procedure presented here can be easily extended on a Bose system with an arbitrary number of impurities immersed.
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…
The Casimir effect, a two-body interaction via vacuum fluctuations, is a fundamental property of quantum systems. In solid state physics it emerges as a long-range interaction between two impurity atoms via virtual phonons. In the classical limit for the impurity atoms in $D$ dimensions the interaction is known to follow the universal power-law $U(r)\sim r^{-D}$. However, for finite masses of the impurity atoms on a lattice, it was predicted to be $U(r)\sim r^{-2D-1}$ at large distances. We examine how one power-law can change into another with increase of the impurity mass and in presence of …
We formulate a general scheme for calculation of thermodynamic properties of ideal Bose gas with microscopic number of static impurities immersed, when the system is loaded in the harmonic trapping potential with quasi-1D and quasi-2D configurations. The binding energy of a single impurity and a detailed study of the medium-induced Casimir-like forces between two impurities in trapped Bose gas are numerically calculated in wide range of temperatures and interaction strengths.
We develop a theory of the phonon mediated Casimir interaction between two point-like impurities, which is based on the single impurity scattering T-matrix approach. Within this, we show that the Casimir interaction at $T = 0$ falls off as a power law with the distance between the impurities. We find that the power in the weak and in the unitary phonon-impurity scattering limits differs, and we relate the power law to the low-energy properties of the single impurity scattering T-matrix. In addition, we consider the Casimir interaction at finite temperature and show that at finite temperatures …
We unravel the nonequilibrium dynamics of two fermionic impurities immersed in a one-dimensional bosonic gas following an interspecies interaction quench from weak to strong repulsions. Monitoring the temporal evolution of the single-particle density of each species we reveal the existence of four distinct dynamical regimes. For weak interspecies repulsions both species either perform a breathing motion or the impurity density splits into two parts which interact and disperse within the bosonic cloud. Turning to strong interactions we observe the formation of dark-bright states within the mean…
Both mixtures of atomic Bose-Einstein condensates and systems with atoms trapped in optical lattices have been intensely explored theoretically, mainly due to the exceptional developments on the experimental side. We investigate the properties of ultracold atomic impurities (bosons) immersed in a vortex lattice of a second Bose-condensed species. In contrast to the static optical-lattice configuration, the vortex lattice presents intrinsic dynamics given by its Tkachenko modes. These excitations induce additional correlations between the impurities, which consist in a long-range attractive pot…
We unravel the polaronic properties of impurities immersed in a correlated trapped one-dimensional (1D) Bose-Bose mixture. This setup allows for the impurities to couple either attractively or repulsively to a specific host, thus offering a highly flexible platform for steering the emergent polaronic properties. Specifically, the polaronic residue peak and strength of induced interactions can be controlled by varying the coupling of the impurities to the individual bosonic components. In particular, it is possible to maintain the quasiparticle character for larger interaction strengths as comp…
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 study the fluctuation-induced interaction between two impurities in a weakly-interacting one-dimensional Bose gas using the field theoretical approach. At separations between impurities shorter and of the order of the healing length of the system, the induced interaction has a classical origin and behaves exponentially. At separations longer than the healing length, the interaction is of a quantum origin and scales as the third power of the inverse distance. Finite temperature destroys the quasi-long-range order of the Bose gas and, accordingly, the induced interaction becomes exponentially…
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…
The well-known Yukawa and Efimov potentials are two different mediated interaction potentials. The first one arises in quantum field theory from the exchange of virtual particles. The second one is mediated by a real particle resonantly interacting with two other particles. This Letter shows how two impurities immersed in a Bose-Einstein condensate can exhibit both phenomena. For a weak impurity-boson attractive interactionattraction with the condensate, the two impurities form two polarons that interact through a weak Yukawa attraction mediated by virtual excitations. For a resonant attractio…
Impurities immersed into a surrounding ultra-cold Bose gas experience interactions mediated by the surrounding many-body environment. If one focuses on two impurities that are sufficiently close to each other, they can form a bipolaron pair. Here, we discuss how the standard methods based on linearizing the condensate field lead to results only valid in the weak coupling regime and for sufficiently large impurity separations. We show how those shortcomings can be remedied within the Born-Oppenheimer approximation by accounting for boson-boson interactions already on the mean-field level.
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 report a comprehensive study of the ground-state properties of one and two bosonic impurities immersed in small one-dimensional optical lattices loaded with a few interacting bosons. We model the system with a two-component Bose-Hubbard model and solve the problem numerically by means of the exact diagonalization (ED) method. We report binding energies of one and two impurities across the superfluid (SF) to Mott-insulator (MI) transition and confirm the formation of two-body bound states of impurities induced by repulsive interactions. In particular, we found that an insulator bath induces …
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 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.
Recently it was shown that anyons on the two-sphere naturally arise from a system of molecular impurities exchanging angular momentum with a many-particle bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this approach and rigorously demonstrate that in the experimentally realized regime the lowest spectrum of two linear molecules immersed in superfluid helium corresponds to the spectrum of two anyons on the sphere. We develop the formalism within the framework of the recently experimentally observed angulon quasiparticle.
We demonstrate that identical impurities immersed in a two-dimensional many-particle bath can be viewed as flux-tube-charged-particle composites described by fractional statistics. In particular, we find that the bath manifests itself as an external magnetic flux tube with respect to the impurities, and hence the time-reversal symmetry is broken for the effective Hamiltonian describing the impurities. The emerging flux tube acts as a statistical gauge field after a certain critical coupling. This critical coupling corresponds to the intersection point between the quasiparticle state and the ph…
Quantum dynamics of impurities in a bath of bosons is a long-standing problem of solid-state, plasma, and atomic physics. Recent experimental and theoretical investigations with ultracold atoms focused on this problem, studying atomic impurities immersed in a atomic Bose-Einstein condensate (BEC) and for various relative coupling strengths tuned by the Fano-Feshbach resonance technique. Here we report extensive numerical simulations on a closely related problem: the collision between a bosonic impurity made of few $^{41}$K atoms and a BEC made of $^{87}$Rb atoms in a quasi one-dimensional conf…
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 report on the experimental doping of a $^{87}$Rubidium (Rb) Bose-Einstein condensate (BEC) with individual neutral $^{133}$Cesium (Cs) atoms. We discuss the experimental tools and procedures to facilitate Cs-Rb interaction. First, we use degenerate Raman side-band cooling of the impurities to enhance the immersion efficiency for the impurity in the quantum gas. We identify the immersed fraction of Cs impurities from the thermalization of Cs atoms upon impinging on a BEC, where elastic collisions lead to a localization of Cs atoms in the Rb cloud. Second, further enhancement of the immersion…
We study the correlated dynamics of few interacting bosonic impurities immersed in a one-dimensional harmonically trapped bosonic environment. The mixture is exposed to a time-dependent impurity-medium interaction pulse moving it across the relevant phase separation boundary. For modulation frequencies smaller than the trapping one, the system successively transits through the miscible/immiscible phases according to the driving of the impurity-medium interactions. For strong modulations, and driving from the miscible to the immiscible regime, a significant fraction of the impurities is expelle…
We report on spin dynamics of individual, localized neutral impurities immersed in a Bose-Einstein condensate. Single Cesium atoms are transported into a cloud of Rubidium atoms, thermalize with the bath, and the ensuing spin-exchange between localized impurities with quasi-spin $F_i=3$ and bath atoms with $F_b=1$ is resolved. Comparing our data to numerical simulations of spin dynamics we find that, for gas densities in the BEC regime, the dynamics is dominated by the condensed fraction of the cloud. We spatially resolve the density overlap of impurities and gas by the spin-population of impu…
The elementary excitations of a fractional quantum Hall liquid are quasiparticles or quasiholes which are neither bosons nor fermions, but so-called anyons. Here we study impurity particles immersed in a quantum Hall liquid which bind to the quasiholes via repulsive interactions with the liquid. We show that the angular momentum of an impurity is given by the multiple of a fractional "quantum" of angular momentum, and can directly be observed from the impurity density. In a system with several impurities bound to quasiholes, their total angular momentum interpolates between the values for free…
Induced interactions and bound states of charge carriers immersed in a quantum medium are crucial for the investigation of quantum transport. Ultracold atom-ion systems can provide a convenient platform for studying this problem. Here, we investigate the static properties of one and two ionic impurities in a bosonic bath using quantum Monte Carlo methods. We identify three bipolaronic regimes depending on the strength of the atom-ion potential and the number of its two-body bound states: a perturbative regime resembling the situation of a pair of neutral impurities, a non-perturbative regime t…
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 investigate inelastic collision dynamics of a single cold ion in a Bose-Einstein condensate. We observe rapid ion-atom-atom three-body recombination leading to formation of weakly bound molecular ions followed by secondary two-body molecule-atom collisions quenching the rovibrational states towards deeper binding energies. In contrast to previous studies exploiting hybrid ion traps, we work in an effectively field-free environment and generate a free low-energy ionic impurity directly from the atomic ensemble via Rydberg excitation and ionization. This allows us to implement an energy-resol…
We discuss an even-odd effect for an impurity with an $N$-fold degenerate internal states immersed in a two-dimensional superfluid--Mott-insulator quantum critical bath, which is described by an spin-$S$ XY Bose-Kondo impurity model with $N=2S+1$. Using a dimensional- and momentum-cut off regularized renormalization group and unbiased large-scale Monte Carlo numerical simulations, we establish the phase diagram for the $S=1$ impurity with all the relevant terms included. We show that the $S=1$ impurity with 3-fold degeneracy is fully screened by the critical bath, in qualitative contrast to th…
We investigate the system of a heavy impurity immersed in a degenerated Fermi gas, where the impurity's internal degree of freedom (pseudospin) is manipulated by a series of radiofrequency (RF) pulses at several different times. Applying the functional determinant approach, we carry out an essentially exact calculation of the Ramsey-interference-type responses to the RF pulses. These responses are universal functions of the multiple time intervals between the pulses for all time and can be regarded as multidimensional (MD) spectroscopy of the system in the time domain. A Fourier transformation…
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…
We show how impurity atoms can measure moments of ultracold atomic gas densities, using the example of bosons in a one-dimensional lattice. This builds on a body of work regarding the probing of systems by measuring the dephasing of an immersed qubit. We show this dephasing is captured by a function resembling characteristic functions of probability theory, of which the derivatives at short times reveal moments of the system operator to which the qubit couples. For a qubit formed by an impurity atom, in a system of ultracold atoms, this operator can be the density of the system at the location…
We study the ground state of a one-dimensional (1D) trapped Bose gas with two mobile impurity particles. To investigate this set-up, we develop a variational procedure in which the coordinates of the impurity particles are slow-like variables. We validate our method using the exact results obtained for small systems. Then, we discuss energies and pair densities for systems that contain of the order of one hundred atoms. We show that bosonic non-interacting impurities cluster. To explain this clustering, we calculate and discuss induced impurity-impurity potentials in a harmonic trap. Further, …
We investigate numerically the problem of few (one, two) noninteracting spin$-1/2$ fermions in a shallow harmonic trap coupled via contact repulsive interactions to a uniform one-dimensional bath of lattice bosons, described by the Bose-Hubbard model. Through extensive density-matrix renormalization group calculations, we extract the binding energy and the effective mass of quasiparticles, including dressed impurities (polarons) and their two-body bound states (bipolarons), emerging from the effective non-local Casimir interaction between the impurities. We show that the mixture exhibits rathe…
Mixing two kinds of particles that repel each other usually results in either a homogeneous mixture when the repulsion is weak, or a complete phase separation of the two kinds when their repulsion is too strong. It is shown however that there is an intermediate regime where the two kinds can coexist in their ground state as a bubble immersed in a gas of one kind. Such a situation is obtained by adding heavy repulsive impurities into a Bose-Einstein condensate. Above a certain strength of the mutual repulsion, a stable bubble of impurities and bosons can be formed, resulting from the equilibriu…
We study the ground state properties and nonequilibrium dynamics of two spinor bosonic impurities immersed in a one-dimensional bosonic gas upon applying an interspecies interaction quench. For the ground state of two non-interacting impurities we reveal signatures of attractive induced interactions in both cases of attractive or repulsive interspecies interactions, while a weak impurity-impurity repulsion forces the impurities to stay apart. Turning to the quench dynamics we inspect the time-evolution of the contrast unveiling the existence, dynamical deformation and the orthogonality catastr…
This article considers the bound states of two heavy and two light bosons, when a short-range force attracts the bosons of different mass, and a short-range force repel the light bosons. The existence of such four-body bound states results from the competition between these two forces. For a given strength of the attraction, the critical strength of the repulsion necessary to unbind the four particles is calculated. This study is motivated by the experimental realisation of impurity atoms immersed in an atomic Bose-Einstein condensate, and aims at determining in which regime only one boson con…
In this work we study the formation and dynamics of polarons in a system with a few impurities in a lattice immersed in a Bose-Einstein condensate (BEC). This system has been experimentally realized using ultracold atoms and optical lattices. Here we consider a two-band model for the impurity atoms, along with a Bogoliubov approximation for the BEC, with phonons coupled to impurities via both intra- and inter-band transitions. We decouple this Fröhlich-like term by an extended two-band Lang-Firsov polaron transformation using a variational method. The new effective Hamiltonian with two (polaro…
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…
We propose and investigate a pump-probe spectroscopy scheme to unveil the time-resolved dynamics of fermionic or bosonic impurities immersed in a harmonically trapped Bose-Einstein condensate. In this scheme a pump pulse initially transfers the impurities from a noninteracting to a resonantly interacting spin-state and, after a finite time in which the system evolves freely, the probe pulse reverses this transition. This directly allows to monitor the nonequilibrium dynamics of the impurities as the dynamical formation of coherent attractive or repulsive Bose polarons and signatures of their i…