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 interaction. We show that the impurity Hall drag is not simply proportional to the Chern number characterizing the topological transport of the insulator on its own - it also depends continuously on particle-hole breaking terms, to which the Chern number is insensitive. However, when the insulator is tuned across a topological phase transition, a sharp jump of the impurity Hall drag results, for which we derive an analytical expression. We describe how the Hall drag and jump can be extracted from a circular dichroic measurement of impurity excitation rates, particularly suited for ultracold gas experiments.
The impurities, introduced intentionally or accidentally into certain materials, can significantly modify their characteristics or reveal their intrinsic physical properties, and thus play an important role in solid-state physics. Different from those static impurities in a solid, the impurities realized in cold atomic systems are naturally mobile. Here we propose an effective theory for treating some unique behaviors exhibited by ultracold mobile impurities. Our theory reveals the interaction-induced transition between the extended and localized impurity states, and also explains the essentia…
Mobile impurities in cold atomic gases constitute a new platform for investigating polaron physics. Here we show that when impurity atoms interact with a two-dimensional Fermi gas with quadratic band touching the polaron picture may either hold or break down depending on the particle-hole asymmetry of the band structure. If the hole band has a smaller effective mass than the particle band, the quasiparticle is stable and its diffusion coefficient varies with temperature as $D(T) \propto \ln^2 T$. If the hole band has larger mass, the quasiparticle weight vanishes at low energies due to an emer…
We scrutinize the hydrodynamic approach for calculating dynamical correlations in one-dimensional superfluids near integrability and calculate the characteristic time scale τ beyond which this approach is valid. For time scales shorter than τ hydrodynamics fails and we develop an approach based on kinetics of fermionic quasiparticles described as mobile impurities. New universal results for the dynamical structure factor relevant to experiments in ultracold atomic gases are obtained.
We study a one-dimensional interacting quantum liquid hosting a pair of mobile impurities causing backscattering. We determine the effective retarded interaction between the two impurities mediated by the liquid. We show that for strong backscattering this interaction gives rise to resonances and antiresonances in the finite-frequency mobility of the impurity pair. At the antiresonances, the two impurities remain at rest even when driven by a (small) external force. At the resonances, their synchronous motion follows the external drive in phase and reaches maximum amplitude. Using a perturbati…
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 overview the main features of mobile impurities moving in one-dimensional superfluid backgrounds by modeling it as a mobile Josephson junction, which leads naturally to the periodic dispersion of the impurity. The dissipation processes, such as radiative friction and quantum viscosity, are shown to result from the interaction of the collective phase difference with the background phonons. We develop a more realistic depleton model of an impurity-hole bound state that provides a number of exact results interpolating between the semiclassical weakly-interacting picture and the strongly intera…
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 …
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 show that a distinguishable mobile impurity inside a one-dimensional many-body state at zero temperature generally does not behave like a quasiparticle (QP). Instead, both the impurities dynamics as well as the ground state of the bath are fundamentally transformed by a diverging number of zero-energy excitations being generated, leading to what we call infrared-dominated (ID) dynamics. Combining analytics and DMRG numerics we provide a general formula for the power law governing ID dynamics at zero momentum, discuss a threshold beyond which quasiparticle dynamics may occur again, and study…
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…
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）
We investigate the properties of a neutral impurity atom coupled with the Tkachenko modes of a two-dimensional vortex lattice Bose-Einstein condensate. In contrast with polarons in homogeneous condensates, the marginal impurity-boson interaction in the vortex lattice leads to infrared singularities in perturbation theory and to the breakdown of the quasiparticle picture in the low energy limit. These infrared singularities are interpreted in terms of a renormalization of the coupling constant, quasiparticle weight and effective impurity mass. The divergence of the effective mass in the low ene…
We study dynamics of a mobile impurity moving in a one-dimensional quantum liquid. Such an impurity induces a strong non-linear depletion of the liquid around it. The dispersion relation of the combined object, called depleton, is a periodic function of its momentum with the period 2πn, where n is the mean density of the liquid. In the adiabatic approximation a constant external force acting on the impurity leads to the Bloch oscillations of the impurity around a fixed position. Dynamically such oscillations are accompanied by the radiation of energy in the form of phonons. The ensuing energy …
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…
Topological quantum phases cannot be characterized by Ginzburg-Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include "synthetic" many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states. Here we propose a general scheme for detecting topological order using interferometric measurements of elementary excitations. The key ingredient is the use of mobile impurities which bind to …
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）
Anderson localization in a two-dimensional ultracold Bose-gas has been demonstrated experimentally. Atoms were released within a dumbbell-shaped optical trap, where the channel of variable aspect ratio provided the only path for particles to travel between source and drain reservoirs. This channel can be populated with columnar (repulsive) optical potential spikes of square cross section with arbitrary pattern. These spikes constitute impurities, the scattering centres for the otherwise free propagation of the particles. This geometry does not allow for classical potential trapping which can b…
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 the radio-frequency spectroscopy of impurities interacting with a quantum gas at finite temperature. In the limit of a single impurity, we show using Fermi's golden rule that introducing (or injecting) an impurity into the medium is equivalent to ejecting an impurity that is initially interacting with the medium, since the "injection" and "ejection" spectral responses are simply related to each other by an exponential function of frequency. Thus, the full spectral information for the quantum impurity is contained in the injection spectral response, which can be determined using …
We analyze the properties of an impurity in a dilute Bose-Einstein condensate (BEC). First the quasiparticle residue of a static impurity in an ideal BEC is shown to vanish with increasing particle number as a stretched exponential, leading to a bosonic orthogonality catastrophe. Then we introduce a variational ansatz, which recovers this exact result and describes the macroscopic dressing of the impurity including its back-action onto the BEC as well as boson-boson repulsion beyond the Bogoliubov approximation. This ansatz predicts that the orthogonality catastrophe also occurs for mobile imp…
Mobile quantum impurities interacting with a fermionic bath form quasiparticles known as Fermi polarons. We demonstrate that a force applied to the bath particles can generate a drag force of similar magnitude acting on the impurities, realizing a novel, nonperturbative Coulomb drag effect. To prove this, we calculate the fully self-consistent, frequency-dependent transconductivity at zero temperature in the Baym-Kadanoff conserving approximation. We apply our theory to excitons and exciton polaritons interacting with a bath of charge carriers in a doped semiconductor embedded in a microcavity…
A few years ago, flow equations were introduced as a technique for calculating the ground-state energies of cold Bose gases with and without impurities. In this paper, we extend this approach to compute observables other than the energy. As an example, we calculate the densities, and phase fluctuations of one-dimensional Bose gases with one and two impurities. For a single mobile impurity, we use flow equations to validate the mean-field results obtained upon the Lee-Low-Pines transformation. We show that the mean-field approximation is accurate for all values of the boson-impurity interaction…
We investigate the propagation of spin impurity atoms through a strongly interacting one-dimensional Bose gas. The initially well localized impurities are accelerated by a constant force, very much analogous to electrons subject to a bias voltage, and propagate as a one-dimensional impurity spin wave packet. We follow the motion of the impurities in situ and characterize the interaction induced dynamics. We observe a very complex non-equilibrium dynamics, including the emergence of large density fluctuations in the remaining Bose gas, and multiple scattering events leading to dissipation of th…
It is a common knowledge that an effective interaction of a quantum impurity with an electromagnetic field can be screened by surrounding charge carriers, whether mobile or static. Here we demonstrate that very strong, `anomalous' screening can take place in the presence of a neutral, weakly-polarizable environment, due to an exchange of orbital angular momentum between the impurity and the bath. Furthermore, we show that it is possible to generalize all phenomena related to isolated impurities in an external field to the case when a many-body environment is present, by casting the problem in …
We investigate the dipole mediated transport of Rydberg impurities through an ultracold gas of atoms excited to an auxiliary Rydberg state. In one experiment we continuously probe the system by coupling the auxiliary Rydberg state to a rapidly decaying state which realizes a dissipative medium. In-situ imaging of the impurities reveals diffusive spreading controlled by the intensity of the probe laser. By preparing the same density of hopping partners but then switching off the dressing fields the spreading is effectively frozen. This is consistent with numerical simulations which indicate the…
