We investigate the ground-state energy of a one-dimensional Fermi gas with two bosonic impurities. We consider spinless fermions with no fermion-fermion interactions. The fermion-impurity and impurity-impurity interactions are modelled with Dirac delta functions. First, we study the case where impurity and fermions have equal masses, and the impurity-impurity two-body interaction is identical to the fermion-impurity interaction, such that the system is solvable with the Bethe ansatz. For attractive interactions, we find that the energy of the impurity-impurity subsystem is below the energy of the bound state that exists without the Fermi gas. We interpret this as a manifestation of attractive boson-boson interactions induced by the fermionic medium, and refer to the impurity-impurity subsystem as an in-medium bound state. For repulsive interactions, we find no in-medium bound states. Second, we construct an effective model to describe these interactions, and compare its predictions to the exact solution. We use this effective model to study non-integrable systems with unequal masses and/or potentials. We discuss parameter regimes for which impurity-impurity attraction induced by the Fermi gas can lead to the formation of in-medium bound states made of bosons that repel each other in the absence of the Fermi gas.
We unravel the periodically driven dynamics of two repulsively interacting bosonic impurities within a bosonic bath upon considering either the impact of a finite pulse or a continuous shaking of the impurities harmonic trap. Following a pulse driving of initially miscible components we reveal a variety of dynamical response regimes depending on the driving frequency. At resonant drivings the impurities decouple from their host while if exposed to a high frequency driving they remain trapped in the bosonic gas. For continuous shaking we showcase that in the resonantly driven regime the impurit…
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 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…
We consider the problem of two heavy impurity particles embedded in a gas of weakly-interacting light mass bosonic particles in the condensed state. Using the Bogoliubov approach to describe the bosonic gas and the Born-Oppenheimer approximation for the three-body dynamics, we calculate the modification to the heavy-heavy two-body potential due to the presence of the condensate. For the case of resonant interaction between the light bosons and the impurities, we present (semi)-analytical results for the potential in the limit of a large condensate coherence length. In particular, we find a for…
We investigate the ground state properties and the nonequilibrium dynamics of a lattice trapped bosonic mixture consisting of an impurity species and a finite-sized medium. For the case of one as well as two impurities we observe that, depending on the lattice depth and the interspecies interaction strength, a transition from a strongly delocalized to a localized impurity distribution occurs. In the latter regime the two species phase separate, thereby forming a particle-hole pair. For two impurities we find that below a critical lattice depth they are delocalized among two neighboring outer l…
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…
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 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…
We unravel the many-body dynamics of a harmonically trapped impurity colliding with a bosonic medium confined in a double-well upon quenching the initially displaced harmonic trap to the center of the double-well. We reveal that the emerging correlation dynamics crucially depends on the impurity-medium interaction strength allowing for a classification into different dynamical response regimes. For strong attractive impurity-medium couplings the impurity is bound to the bosonic bath, while for intermediate attractions it undergoes an effective tunneling. In the case of weak attractive or repul…
The effects of induced interactions are calculated in both clean and dirty situations, for balanced and imbalanced Fermi gases. We investigate the effects of nonmagnetic impurities on the induced interactions corrections to the transition temperature in the case of a balanced gas, and to the tricritical point in the case of an imbalanced Fermi gas at unitarity. We find that impurities act in detriment of the induced interactions, or particle-hole fluctuations, for the transition temperature and the tricritical point. For large impurity parameter, the particle-hole fluctuations are strongly sup…
We investigate cold bosonic impurity atoms trapped in a vortex lattice formed by condensed bosons of another species. We describe the dynamics of the impurities by a bosonic Hubbard model containing occupation-dependent parameters to capture the effects of strong impurity-impurity interactions. These include both a repulsive direct interaction and an attractive effective interaction mediated by the BEC. The occupation dependence of these two competing interactions drastically affects the Hubbard model phase diagram, including causing the disappearance of some Mott lobes
The existence of a self-localization transition in the polaron problem has been under an active debate ever since Landau suggested it 83 years ago. Here we reveal the self-localization transition for the rotational analogue of the polaron -- the angulon quasiparticle. We show that, unlike for the polarons, self-localization of angulons occurs at finite impurity-bath coupling already at the mean-field level. The transition is accompanied by the spherical-symmetry breaking of the angulon ground state and a discontinuity in the first derivative of the ground-state energy. Moreover, the type of th…
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…
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 investigate the dynamics of heavy impurities embedded in an ultra-cold Fermi gas by using a Generalized Langevin equation. The latter -- derived by means of influence functional theory -- describes the stochastic classical dynamics of the impurities and the quantum nature of the fermionic bath manifests in the emergent interaction between the impurities and in the viscosity tensor. By focusing on the two-impurity case, we predict the existence of bound states, in different conditions of coupling and temperature, and whose life-time can be analytically estimated. Our predictions should be te…
We consider magnetic impurities in a two dimensional superfluid Fermi gas in the presence of spin-orbit coupling. By using the methods of t-matrix and Green's function, we find spin-orbit coupling has some dramatic impacts on the effects of magnetic impurities. For the single impurity problem, the number of bound states localized around the magnetic impurity is doubled. For the finite concentration $n$ of impurities, the energy gap is reduced and the density of states in the gapless region is greatly modified.
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…
Using a species-selective dipole potential, we create initially localized impurities and investigate their interactions with a majority species of bosonic atoms in a one-dimensional configuration during expansion. We find an interaction-dependent amplitude reduction of the oscillation of the impurities' size with no measurable frequency shift, and study it as a function of the interaction strength. We discuss possible theoretical interpretations of the data. We compare, in particular, with a polaronic mass shift model derived following Feynman variational approach.
We investigate the decoherence of $^{40}$K impurities interacting with a three-dimensional Fermi sea of $^{6}$Li across an interspecies Feshbach resonance. The decoherence is measured as a function of the interaction strength and temperature using a spin-echo atom interferometry method. For weak to moderate interaction strengths, we interpret our measurements in terms of scattering of K quasiparticles by the Fermi sea and find very good agreement with a Fermi liquid calculation. For strong interactions, we observe significant enhancement of the decoherence rate, which is largely independent of…
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 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 use a mobile impurity or depleton model to study elementary excitations in one-dimensional integrable systems. For Lieb-Liniger and bosonic Yang-Gaudin models we express two phenomenological parameters characterising renormalised inter- actions of mobile impurities with superfluid background: the number of depleted particles, $N$ and the superfluid phase drop $πJ$ in terms of the corresponding Bethe Ansatz solution and demonstrate, in the leading order, the absence of two-phonon scattering resulting in vanishing rates of inelastic processes such as viscosity experienced by the mobile impuri…
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…
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 fastest possible collective response of a quantum many-body system is related to its excitations at the highest possible energy. In condensed-matter systems, the corresponding timescale is typically set by the Fermi energy. Taking advantage of fast and precise control of interactions between ultracold atoms, we report on the observation of ultrafast dynamics of impurities coupled to an atomic Fermi sea. Our interferometric measurements track the non-perturbative quantum evolution of a fermionic many-body system, revealing in real time the formation dynamics of quasiparticles and the quantu…
We investigate the nonequilibrium quantum dynamics of a single and two heavy fermionic impurities being harmonically trapped and repulsively interacting with a finite ensemble of majority fermions. A quench of the potential of the majority species from a double-well to a harmonic trap is applied, enforcing its counterflow which in turn perturbs the impurities. For weak repulsions it is shown that the mixture undergoes a periodic mixing and demixing dynamics, while stronger interactions lead to a more pronounced dynamical spatial separation. In the presence of correlations the impurity exhibits…
We study the Hall response of topologically-trivial mobile impurities (Fermi polarons) interacting weakly with majority fermions forming a Chern-insulator background. This setting involves a rich interplay between the genuine many-body character of the polaron problem and the topological nature of the surrounding cloud. When the majority fermions are accelerated by an external field, a transverse impurity current can be induced. To quantify this polaronic Hall effect, we compute the drag transconductivity, employing controlled diagrammatic perturbation theory in the impurity-fermion interactio…
Mass-gap functional determinant approach for mobile Fermi polarons
Université Paris Cité（巴黎西岱大学）；Institut für Theoretische Physik, Universität Heidelberg（海德堡大学理论物理研究所）；Center for the Physical Foundations of Computation, Heidelberg University（海德堡大学计算物理基础中心）
A new excitation mode has been predicted to exist in the unitary Fermi gas. It has a form of a spin-polarized impurity, which was dubbed as ferron. It is characterized by a closed nodal surface of the pairing field surrounding a partially spin-polarized superfluid region, where the phase differs by $π$. In this paper, we discuss the effect of temperature on the generation of the ferron and the adiabaticity of the spin-polarizing potential together with ferron's ground state properties.
We theoretically investigate the interplay between the fermionic mobile impurity atoms and a Larkin-Ovchinnikov (LO) superfluid in a two dimensional optical lattice. We find that the impurity atoms get localized and can form pairs when the interaction between the impurity atoms and the LO superfluid is strong enough. These features are due to the phenomena of self-localization whose underlying mechanism is revealed by an effective model. The impurity atoms with finite concentrations can drive the transition from a two-dimensional-checkerboard-like LO state to a quasi-one-dimensional-stripe-lik…
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, …
Problems involving quantum impurities, in which one or a few particles are interacting with a macroscopic environment, represent a pervasive paradigm, spanning across atomic, molecular, and condensed-matter physics. In this paper we introduce new variational approaches to quantum impurities and apply them to the Fröhlich polaron -- a quasiparticle formed out of an electron (or other point-like impurity) in a polar medium, and to the angulon -- a quasiparticle formed out of a rotating molecule in a bosonic bath. We benchmark these approaches against established theories, evaluating their accura…
We report the observation of many-body interaction effects for a homonuclear bosonic mixture in a three-dimensional optical lattice with variable state dependence along one axis. Near the superfluid-to-Mott insulator transition for one component, we find that the presence of a second component can reduce the apparent superfluid coherence, most significantly when it either experiences a strongly localizing lattice potential or none at all. We examine this effect by varying the relative populations and lattice depths, and discuss the observed behavior in view of recent proposals for scattering f…
We study the properties of spin-less non-interacting fermions trapped in a confining potential in one dimension but in the presence of one or more impurities which are modelled by delta function potentials. We use a method based on the single particle Green's function. For a single impurity placed in the bulk, we compute the density of the Fermi gas near the impurity. Our results, in addition to recovering the Friedel oscillations at large distance from the impurity, allow the exact computation of the density at short distances. We also show how the density of the Fermi gas is modified when th…
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…
A magnetic impurity in a fermionic superfluid hosts bound quasiparticle states known as Yu-Shiba-Rusinov (YSR) states. We argue here that, if the impurity is mobile (i.e., has a finite mass), the impurity and its bound YSR quasiparticle move together as a midgap molecule, which has an unusual "Mexican-hat" dispersion that is tunable via the fermion density. We map out the impurity dispersion, which consists of an "atomic" branch (in which the impurity is dressed by quasiparticle pairs) and a "molecular" branch (in which the impurity binds a quasiparticle). We discuss the experimental realizati…
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…
Finite-temperature mass gap and quench dynamics of mobile impurities in a Fermi gas
MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi’an Jiaotong University（西安交通大学物理学院凝聚态物质非平衡合成与调制教育部重点实验室）
We explore the effect of using two-dimensional matter-wave vortices to confine an ensemble of bosonic quantum impurities. This is modelled theoretically using a mass-imbalanced homogeneous two component Gross-Pitaevskii equation where each component has independent atom numbers and equal atomic masses. By changing the mass imbalance of our system we find the shape of the vortices are deformed even at modest imbalances, leading to barrel shaped vortices; which we quantify using a multi-component variational approach. The energy of impurity carrying vortex pairs are computed, revealing a mass-de…
We have experimentally studied few-body impurity systems consisting of a single fermionic atom and a small bosonic field on the sites of an optical lattice. Quantum phase revival spectroscopy has allowed us to accurately measure the absolute strength of Bose-Fermi interactions as a function of the interspecies scattering length. Furthermore, we observe the modification of Bose-Bose interactions that is induced by the interacting fermion. Because of an interference between Bose-Bose and Bose-Fermi phase dynamics, we can infer the mean fermionic filling of the mixture and quantify its increase (…
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 discuss the master equation approach to diffusive current of bosonic or fermionic carriers in one- and two-dimensional lattices. This approach is shown to reproduce all known results of the linear response theory, including the integer quantum Hall effect for fermionic carriers. The main advantage of the approach is that it allows to calculate the current beyond the linear response regime where new effects are found. In particular, we show that the Hall current can be inverted by changing orientation of the static force (electric field) relative to the primary axes of the lattice.
