Impurity coupled to a lattice with disorder
arXiv:1807.07744 · doi:10.1103/PhysRevA.98.053607
Abstract
We study the time-dependent occupation of an impurity state hybridized with a continuum of extended or localized states. Of particular interest is the return probability, which gives the long-time limit of the average impurity occupation. In the extended case, the return probability is zero unless there are bound states of the impurity and continuum. We present exact expressions for the return probability of an impurity state coupled to a lattice, and show that the existence of bound states depends on the dimension of the lattice. In a disordered lattice with localized eigenstates, the finite extent of the eigenstates results in a non-zero return probability. We investigate different parameter regimes numerically by exact diagonalization, and show that the return probability can serve as a measure of the localization length in the regime of weak hybridization and disorder. Possible experimental realizations with ultracold atoms are discussed.
19 pages, 17 figures
References in corpus (36)
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Observation of many-body localization of interacting fermions in a quasi-random optical lattice
- Direct observation of Anderson localization of matter-waves in a controlled disorder
- The Kernel Polynomial Method
- Exploring the many-body localization transition in two dimensions
- Single-Spin Addressing in an Atomic Mott Insulator
- Statistical Signatures of Photon Localization
- Quantum dynamics of a single, mobile spin impurity
- Observation of the critical regime near Anderson localization of light
- Direct observation of a localization transition in quasi-periodic photonic lattices
- Three-dimensional localization of ultracold atoms in an optical disordered potential
- Strongly Correlated Quantum Walks in Optical Lattices
- Coupling Identical 1D Many-Body Localized Systems
- Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
- Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
- Disorder-induced Localization in a Strongly Correlated Atomic Hubbard Gas
- Fano Resonance in a Quantum Wire with a Side-coupled Quantum Dot
- Measurement of the mobility edge for 3D Anderson localization
- Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
- Observation of the Fano-Kondo Anti-Resonance in a Quantum Wire with a Side-Coupled Quantum Dot
- One-dimensional Anderson localization in certain correlated random potentials
- Single atom detection in ultracold quantum gases: a review of current progress
- Breakdown of Diffusion in Dynamics of Extended Waves in Mesoscopic Media
- Quantum-gas microscopes - A new tool for cold-atom quantum simulators
- Photon Localization in Resonant Media
- Anderson localization in two-dimensional graphene with short-range disorder: One-parameter scaling and finite-size effects
- Anderson localization of ultracold atoms: Where is the mobility edge?
- Recurrent scattering and memory effect at the Anderson localization transition
- Three-Dimensional Anderson Localization in Variable Scale Disorder
- Measurement of spectral functions of ultracold atoms in disordered potentials
- Anderson mobility gap probed by dynamic coherent backscattering
- Singular Behavior of Eigenstates in Anderson's Model of Localization
- Microwave conductance in random waveguides in the crossover to Anderson localization and single parameter scaling
- Lattice assisted spectroscopy: a generalized scanning tunnelling microscope for ultra-cold atoms
- An investigation of equilibration in small quantum systems: the example of a particle in a 1D random potential
- Impurity-directed Transport within a Finite Disordered Lattice