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 impurities, whenever the BEC becomes ideal. Finally, we show that our ansatz agrees well with experimental results.
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…
A theoretical investigation of the single particle polariton properties for a microcavity embedding a charged quantum well is presented. The electron gas optical susceptibility is calculated numerically using the method devised by Combescot and Nozières. The role of many-body effects, such as the Fermi edge singularity and Anderson orthogonality catastrophe, in the polariton formation is elucidated. By tuning the light-matter coupling the short time behaviour of the electron gas response function is probed and comparison with earlier results only using the long time response are made. Various …
We address the statistical orthogonality catastrophe induced by a local quench in the Aubry-André model from the perspective of nonequilibrium thermodynamics. We study the average work and the irreversible work production when quenching the impurity potential in proximity of an orthogonality event. We show how this description is able to capture the level crossings generating the orthogonality and the avoided crossings which causes the plateau-like structures, signature of the Aubry-André spectrum, when considering the full statistics of orthogonality events.
We consider a fixed impurity immersed in a Fermi gas at finite temperature. We take the impurity to have two internal spin states, where the $\uparrow$ state is assumed to interact with the medium such that it exhibits the orthogonality catastrophe, while the $\downarrow$ state is a bare noninteracting particle. Introducing a Rabi coupling between the impurity states therefore allows us to investigate the coupling between a discrete spectral peak and the Fermi-edge singularity, i.e., between states with and without a quasiparticle residue. Combining an exact treatment of the uncoupled impurity…
A remarkable feature of quantum many-body systems is the orthogonality catastrophe which describes their extensively growing sensitivity to local perturbations and plays an important role in condensed matter physics. Here we show that the dynamics of the orthogonality catastrophe can be fully characterized by the quantum speed limit and, more specifically, that any quenched quantum many-body system whose variance in ground state energy scales with the system size exhibits the orthogonality catastrophe. Our rigorous findings are demonstrated by two paradigmatic classes of many-body systems -- t…
We study the dynamics of two strongly interacting bosons with an additional impurity atom trapped in a harmonic potential. Using exact numerical diagonalization we are able to fully explore the dynamical evolution when the interaction between the two distinct species is suddenly switched on (quenched). We examine the behavior of the densities, the entanglement, the Loschmidt echo and the spectral function for a large range of inter-species interactions and find that even in such small systems evidence of Anderson's orthogonality catastrophe can be witnessed.
We address the phenomenon of statistical orthogonality catastrophe in insulating disordered systems. More in detail, we analyse the response of a system of non-interacting fermions to a local perturbation induced by an impurity. By inspecting the overlap between the pre and post-quench many-body ground states we fully characterise the emergent statistics of orthogonality events as a function of both the impurity position and the coupling strength. We consider two well-known one-dimensional models, namely the Anderson and the Aubry- André insulators, highlighting the arising differences. Partic…
We derive rigorously the leading asymptotics of the so-called Anderson integral in the thermodynamic limit for one-dimensional, non-relativistic, spin-less Fermi systems. The coefficient, $γ$, of the leading term is computed in terms of the S-matrix. This implies a lower and an upper bound on the exponent in Anderson's orthogonality catastrophe, $\tilde CN^{-\tildeγ}\leq \mathcal{D}_N\leq CN^{-γ}$ pertaining to the overlap, $\mathcal{D}_N$, of ground states of non-interacting fermions.
We investigate the behaviour of a single qubit coupled to a low-dimensional, ultra-cold Fermi gas. The scattering between the system and the fermions leads to the loss of any coherence in the initial state of the qubit and we show that the exact dynamics of this process is strongly influenced by the effect of the orthogonality catastrophe within the gas. We highlight the relationship between the Loschmidt echo and the retarded Green's function - typically used to formulate the dynamical theory of the catastrophe - and demonstrate that the effect can be triggered and characterized via local ope…
We investigate the Loschmidt echo, the overlap of the initial and final wavefunctions of Luttinger liquids after a spatially inhomogeneous interaction quench. In studying the Luttinger model, we obtain an analytic solution of the bosonic Bogoliubov-de Gennes equations after quenching the interactions within a finite spatial region. As opposed to the power law temporal decay following a potential quench, the interaction quench in the Luttinger model leads to a finite, hardly time dependent overlap, therefore no orthogonality catastrophe occurs. The steady state value of the Loschmidt echo after…
We investigate the many-body generalization of the orthogonality catastrophe by studying the generalized Loschmidt echo of Luttinger liquids (LLs) after a global change of interaction. It decays exponentially with system size and exhibits universal behaviour: the steady state exponent after quenching back and forth n-times between 2 LLs (bang-bang protocol) is 2n-times bigger than that of the adiabatic overlap, and depends only on the initial and final LL parameters. These are corroborated numerically by matrix-product state based methods of the XXZ Heisenberg model. An experimental setup cons…
We provide two inequalities for estimating adiabatic fidelity in terms of two other more handily calculated quantities, i.e., generalized orthogonality catastrophe and quantum speed limit. As a result of considering a two-dimensional subspace spanned by the initial ground state and its orthogonal complement, our method leads to stronger bounds on adiabatic fidelity than those previously obtained. One of the two inequalities is nearly sharp when the system size is large, as illustrated using a driven Rice-Mele model, which represents a broad class of quantum many-body systems whose overlap of d…
The probability that a particle will stick to a surface is fundamental to a variety of processes in surface science, including catalysis, epitaxial growth, and corrosion. At ultralow energies, how particles scatter or stick to a surface affects the performance of atomic clocks, matter-wave interferometers, atom chips and other quantum information processing devices. In this energy regime, the sticking probability is influenced by a distinctly quantum mechanical effect: quantum reflection, a result of matter wave coherence, suppresses the probability of finding the particle near the surface and…
We study the ground-state entanglement entropy of a subsystem of size $L$ of non-interacting fermions scattered by a potential of finite range $a$. We derive a general relation between the scattering matrix and the overlap matrix and use it to prove, that for a one-dimensional symmetric potential the von Neumann entropy, the Rényi entropies and the full counting statistics are robust against potential scattering, provided that $L/a\gg 1$. The results of numerical calculations support the validity of this conclusion for a generic potential.
We monitor the correlated quench induced dynamical dressing of a spinor impurity repulsively interacting with a Bose-Einstein condensate. Inspecting the temporal evolution of the structure factor three distinct dynamical regions arise upon increasing the interspecies interaction. These regions are found to be related to the segregated nature of the impurity and to the ohmic character of the bath. It is shown that the impurity dynamics can be described by an effective potential that deforms from a harmonic to a double-well one when crossing the miscibility-immiscibility threshold. In particular…
Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity m…
According to Anderson's orthogonality catastrophe, the overlap of the $N$-particle ground states of a free Fermi gas with and without an (electric) potential decays in the thermodynamic limit. For the finite one-dimensional system various boundary conditions are employed. Unlike the usual setup the perturbation is introduced by a magnetic (vector) potential. Although such a magnetic field can be gauged away in one spatial dimension there is a significant and interesting effect on the overlap caused by the phases. We study the leading asymptotics of the overlap of the two ground states and the …
The adiabatic theorem is a fundamental result established in the early days of quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational recipes in molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space. Here …
We study the response of a highly-excited time dependent quantum many-body state to a sudden local perturbation, a sort of orthogonality catastrophe problem in a transient non-equilibrium environment. To this extent we consider, as key quantity, the overlap between time dependent wave-functions, that we write in terms of a novel two-time correlator generalizing the standard Loschmidt Echo. We discuss its physical meaning, general properties, and its connection with experimentally measurable quantities probed through non-equilibrium Ramsey interferometry schemes. Then we present explicit calcul…
We propose to investigate the full counting statistics of nonequilibrium spin transport with an ultracold atomic quantum gas. The setup makes use of the spin control available in atomic systems to generate spin transport induced by an impurity atom immersed in a spin-imbalanced two-component Fermi gas. In contrast to solid-state realizations, in ultracold atoms spin relaxation and the decoherence from external sources is largely suppressed. As a consequence, once the spin current is turned off by manipulating the internal spin degrees of freedom of the Fermi system, the nonequilibrium spin pop…
Recent experimental realization of strongly imbalanced mixtures of ultracold atoms opens new possibilities for studying impurity dynamics in a controlled setting. We discuss how the techniques of atomic physics can be used to explore new regimes and manifestations of Anderson's orthogonality catastrophe (OC), which could not be accessed in solid state systems. We consider a system of impurity atoms localized by a strong optical lattice potential and immersed in a sea of itinerant Fermi atoms. Ramsey interference experiments with impurity atoms probe OC in the time domain, while radio-frequency…
We consider the quantum transport in a tight-binding chain with a locally applied potential which is oscillating in time. The steady state for such a driven impurity can be calculated exactly for any energy and applied potential using the Floquet formalism. The resulting transmission has a non-trivial, non-monotonic behavior depending on incoming momentum, driving frequency, and the strength of the applied periodic potential. Hence there is an abundance of tuning possibilities, which allows to find resonances of total reflection for any choice of incoming momentum and periodic potential. Remar…
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 crossover of the impurity-induced dynamics, in trapped one-dimensional Bose polarons subject to radio frequency (rf) pulses of varying intensity, from an adiabatic to a diabatic regime. Utilizing adiabatic pulses for either weak repulsive or attractive impurity-medium interactions, a multitude of polaronic excitations or mode-couplings of the impurity-bath interaction with the collective breathing motion of the bosonic medium are spectrally resolved. We find that for strongly repulsive impurity-bath interactions, a temporal orthogonality catastrophe manifests in resonances i…
Universality is a powerful concept in physics, allowing one to construct physical descriptions of systems that are independent of the precise microscopic details or energy scales. A prime example is the Fermi gas with unitarity limited interactions, whose universal properties are relevant to systems ranging from atomic gases at microkelvin temperatures to the inner crust of neutron stars. Here we address the question of whether unitary Bose systems can possess a similar universality. We consider the simplest strongly interacting Bose system, where we have an impurity particle ("polaron") reson…
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 investigate the system of a heavy impurity embedded in a paired two-component Fermi gas at the crossover from a Bose-Einstein condensate (BEC) to a Bardeen--Cooper--Schrieffer (BCS) superfluid via an extension of the functional determinant approach (FDA). FDA is an exact numerical approach applied to study manifestations of Anderson\textquoteright s orthogonality catastrophe (OC) in the system of a static impurity immersed in an ideal Fermi gas. Here, we extend the FDA to a strongly correlated superfluid background described by a BCS mean-field wavefunction. In contrast to the ideal Fermi g…
