The recent experimental realization of strongly imbalanced mixtures of ultracold atoms opens new possibilities for studying impurity dynamics in a controlled setting. In this paper, 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. Specifically, we consider a system of impurity atoms, localized by a strong optical-lattice potential, immersed in a sea of itinerant Fermi atoms. We point out that the Ramsey-interference-type experiments with the impurity atoms allow one to study the OC in the time domain, while radio-frequency (RF) spectroscopy probes the OC in the frequency domain. The OC in such systems is universal, not only in the long-time limit, but also for all times and is determined fully by the impurity-scattering length and the Fermi wave vector of the itinerant fermions. We calculate the universal Ramsey response and RF-absorption spectra. In addition to the standard power-law contributions, which correspond to the excitation of multiple particle-hole pairs near the Fermi surface, we identify a novel, important contribution to the OC that comes from exciting one extra particle from the bottom of the itinerant band. This contribution gives rise to a nonanalytic feature in the RF-absorption spectra, which shows a nontrivial dependence on the scattering length, and evolves into a true power-law singularity with the universal exponent 1=4 at the unitarity. We extend our discussion to spin-echo-type experiments, and show that they probe more complicated nonequilibirum dynamics of the Fermi gas in processes in which an impurity switches between states with different interaction strength several times; such processes play an important role in the Kondo problem, but remained out of reach in the solid-state systems. We show that, alternatively, the OC can be seen in the energy-counting statistics of the Fermi gas following a sudden quench of the impurity state. The energy distribution function, which can be measured in time-of-flight experiments, exhibits characteristic power-law singularities at low energies. Finally, systems in which the itinerant fermions have two or more hyperfine states provide an even richer playground for studying nonequilibrium impurity physics, allowing one to explore the nonequilibrium OC and even to simulate quantum transport through nanostructures. This provides a previously missing connection between cold atomic systems and mesoscopic quantum transport.

General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. The nonequilibrium dynamics of integrable systems are highly constrained by the conservation of certain charges. There is substantial evidence that after a quantum quench they do not thermalize but their asymptotic steady state can be described by a generalized Gibbs ensemble (GGE) built from the conserved charges. Most of the studies on the GGE so far have focused on models that can be mapped to quadratic systems, while analytic treatment in nonquadratic systems remained elusive. We obtain results on interaction quenches in a nonquadratic continuum system, the one-dimensional (1D) Bose gas described by the integrable Lieb-Liniger model. The direct implementation of the GGE prescription is prohibited by the divergence of the conserved charges, which we conjecture to be endemic to any continuum integrable systems with contact interactions undergoing a sudden quench. We compute local correlators for a noninteracting initial state and arbitrary final interactions as well as two-point functions for quenches to the Tonks-Girardeau regime. We show that in the long time limit integrability leads to significant deviations from the predictions of the grand canonical ensemble, allowing for an experimental verification in cold-atom systems.

Recent experimental advances enabled the realization of mobile impurities immersed in a Bose-Einstein condensate (BEC) of ultracold atoms. Here, we consider impurities with two or more internal hyperfine states, and study their radio-frequency (rf) absorption spectra, which correspond to transitions between two different hyperfine states. We calculate rf spectra for the case when one of the hyperfine states involved interacts with the BEC, while the other state is noninteracting, by performing a nonperturbative resummation of the probabilities of exciting different numbers of phonon modes. In the presence of interactions, the impurity gets dressed by Bogoliubov excitations of the BEC, and forms a polaron. The rf signal contains a δ-function peak centered at the energy of the polaron measured relative to the bare impurity transition frequency with a weight equal to the amount of bare impurity character in the polaron state. The rf spectrum also has a broad incoherent part arising from the background excitations of the BEC, with a characteristic power-law tail that appears as a consequence of the universal physics of contact interactions. We discuss both the direct rf measurement, in which the impurity is initially in an interacting state, and the inverse rf measurement, in which the impurity is initially in a noninteracting state. In the latter case, in order to calculate the rf spectrum, we solve the problem of polaron formation: a mobile impurity is suddenly introduced in a BEC, and dynamically gets dressed by Bogoliubov phonons. Our solution is based on a time-dependent variational ansatz of coherent states of Bogoliubov phonons, which becomes exact when the impurity is localized. Moreover, we show that such an ansatz compares well with a semiclassical estimate of the propagation amplitude of a mobile impurity in the BEC. Our technique can be extended to cases when both initial and final impurity states are interacting with the BEC.

Abstract. In this article we demonstrate a recently developed technique which addresses the problem of obtaining non-universal prefactors of the correlation functions of 1D systems at zero temperature. Our approach combines the effective field theory description of generic 1D quantum liquids with the finite size scaling of form factors (matrix elements) which are obtained using microscopic techniques developed in the context of integrable models. We thus establish exact analytic forms for the prefactors of the long-distance behavior of equal time correlation functions as well as prefactors of singularities of dynamic response functions. In this article our focus is on three specific integrable models: the CalogeroSutherland, Lieb-Liniger, and XXZ models.Exact prefactors of correlation functions of 1D quantum integrable models 2

We develop a general approach to calculating "nonuniversal" prefactors in static and dynamic correlation functions of 1D quantum liquids at zero temperature, by relating them to the finite size scaling of certain matrix elements (form factors). This represents a new, powerful tool for extracting data valid in the thermodynamic limit from finite-size effects. As the main application, we consider weakly interacting spinless fermions with an arbitrary pair interaction potential, for which we perturbatively calculate certain prefactors in static and dynamic correlation functions. We also non-perturbatively evaluate prefactors of the long-distance behavior of correlation functions for the exactly solvable Lieb-Liniger model of 1D bosons.

We consider a single-impurity atom confined to an optical lattice and immersed in a homogeneous Bose-Einstein condensate (BEC). Interaction of the impurity with the phonon modes of the BEC leads to the formation of a stable quasiparticle, the polaron. We use a variational mean-field approach to study dispersion renormalization and derive equations describing nonequilibrium dynamics of polarons by projecting equations of motion into mean-field-type wave functions. As a concrete example, we apply our method to study dynamics of impurity atoms in response to a suddenly applied force and explore the interplay of coherent Bloch oscillations and incoherent drift. We obtain a nonlinear dependence of the drift velocity on the applied force, including a sub-Ohmic dependence for small forces for dimensionality d > 1 of the BEC. For the case of heavy impurity atoms, we derive a closed analytical expression for the drift velocity. Our results show considerable differences with the commonly used phenomenological Esaki-Tsu model.

The antiferromagnetic spin-1 chain has a venerable history and has been thought to be well understood. Here we show that inclusion of both next nearest neighbor (α) and biquadratic (β) interactions results in a rich phase diagram with a multicritical point that has not been observed before. We study the problem using a combination of the density matrix renormalization group (DMRG), an analytic variational matrix product state wavefunction, and conformal field theory. For negative β < β * , we establish the existence of a spontaneously dimerized phase, separated from the Haldane phase by the critical line αc(β) of second-order phase transitions. In the opposite regime, β > β * , the transition from the Haldane phase becomes first-order into the next nearest neighbor (NNN) AKLT phase. Based on the field-theoretical arguments and DMRG calculations, we find that these two regimes are separated by a multicritical point (β * , α * ) of a different universality class, described by the level-4 SU (2) Wess-Zumino-Witten conformal theory. From the DMRG calculations we estimate this multicritical point to lie in the range −0.2 < β * < −0.15 and 0.47 < α * < 0.53. We further find that the dimerized and NNN-AKLT phases are separated from each other by a line of first-order phase transitions that terminates at the multicritical point. We establish that transitions out of Haldane phase into dimer or NNN-AKLT phase are topological in nature and occur either with or without closing of the bulk gap, respectively.We also study short-range incommensurate-to-commensurate transitions in the resulting phase diagram. Inside the Haldane phase, we show the existence of two incommensurate crossovers: the Lifshitz transition and the disorder transition of the first kind, marking incommensurate correlations in momentum and real space, respectively. Notably, these crossover lines stretch across the entire (β, α) phase diagram, merging into a single incommensurate-to-commensurate transition line for negative β < ∼ β * inside the dimer phase. This behavior is qualitatively similar to that seen in classical frustrated two dimensional spin models, by way of the quantum (1 + 1)D to classical 2D correspondence.