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arXiv:1701.04899 · Physical review. B./Physical review. B

Scattering of a composite quasiparticle by an impurity on a lattice

Fumika Suzuki, Marina Litinskaya, William George Unruh

Published Aug 28, 2017• 3 citations
arXivHTMLPDF

Abstract

We study scattering of a composite quasiparticle, which possesses a degree of freedom corresponding to relative separation between two bound excitations, by a $\ensuremath{\delta}$-like impurity potential on a one-dimensional discrete lattice. First, we show that, due to specific properties of their dispersion, lattice excitations bind to impurities with both negative and positive potentials. We demonstrate that the finite size of the composite excitation leads to formation of multiple excitation-impurity bound states. The number and the degree of localization of these bound states depend on the signs and relative magnitudes of the impurity potential and the binding strength of two quasiparticles. We also report the existence of excitation-impurity bound states whose energies are located in the continuum band. Secondly, we study a change in the entanglement between the center of mass and relative coordinate degrees of freedom of a biexciton wave packet during single impurity scattering and decoherence caused by it. For a composite quasiparticle on a lattice, the entanglement between its relative and center of mass coordinate degrees of freedom arises naturally due to inseparability of the two-particle Hamiltonian. One of the main focuses of our study is to investigate how this inseparability affects the creation of the biexciton-impurity bound states and the entanglement dynamics.

DOI
10.1103/physrevb.96.054307

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We study scattering of a composite quasiparticle, which possesses a degree of freedom corresponding to relative separation between two bound excitations, by a \ensuremathδ\ensuremath{\delta}\ensuremathδ-like impurity potential on a one-dimensional discrete lattice. First, we show that, due to specific properties of their dispersion, lattice excitations bind to impurities with both negative and positive potentials. We demonstrate that the finite size of the composite excitation leads to formation of multiple excitation-impurity bound states. The number and the degree of localization of these bound states depend on the signs and relative magnitudes of the impurity potential and the binding strength of two quasiparticles. We also report the existence of excitation-impurity bound states whose energies are located in the continuum band. Secondly, we study a change in the entanglement between the center of mass and relative coordinate degrees of freedom of a biexciton wave packet during single impurity scattering and decoherence caused by it. For a composite quasiparticle on a lattice, the entanglement between its relative and center of mass coordinate degrees of freedom arises naturally due to inseparability of the two-particle Hamiltonian. One of the main focuses of our study is to investigate how this inseparability affects the creation of the biexciton-impurity bound states and the entanglement dynamics.
Although many quantum mechanics problems of a point particle have been well understood, the realistic physical model is often a composite object consisting of particles bound together, and its quantum mechanics is an important problem with applications in many areas of physics. Unlike a point particle, a composite object possesses internal structure described by some degrees of freedom which are often entangled with each other. We call the entanglement among these degrees of freedom ``internal entanglement'', to distinguish it from any other entanglement they may share with an external object. Examples of internal entanglement include the entanglement between a vibrational and a rotational mode of a molecule, and that between its position and its internal clock-state etc. In this thesis, we study quantum mechanics of composite objects by focusing on the effects of internal entanglement. We first look at the tunnelling of a diatomic molecule type composite object through a half-silvered mirror in continuum space and observe that its spatial superposition state made by the mirror can decohere by emission of radiation due to the fact that its internal degrees of freedom are entangled with radiation fields, and that there exists entanglement between its position and its internal (i.e., relative position) degrees of freedom. Secondly, we study its lattice analog in molecular crystals, namely we replace the diatomic molecule by a biexicton, and the mirror by an impurity. We find that discreteness of a lattice makes the wave vector of a biexicton and the relative distance between two excitons of it entangled with each other. We investigate how this inseparability affects the creation of the biexciton-impurity bound states and the entanglement dynamics. Finally we propose a possible application of our study of internal entanglement to the Anderson model of a composite quasiparticle.
We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero Bloch quasimomenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonances appear due to the nonseparability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann-Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.
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Abstract 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 lattice wells and are two-body correlated. This transition is characterized by a crossover from strong to a suppressed interspecies entanglement for increasing impurity-medium repulsion. Turning to the dynamical response of the mixture, upon quenching the interspecies repulsion to smaller values, we reveal that the predominant tunneling process for a single impurity corresponds to that of a particle–hole pair, whose dynamical stability depends strongly on the quench amplitude. During the time-evolution a significant increase of the interspecies entanglement is observed, caused by the build-up of a superposition of states and thus possesses a many-body nature. In the case of two bosonic impurities the particle–hole pair process becomes unstable in the course of the dynamics with the impurities aggregating in adjacent lattice sites while being strongly correlated.
We investigate the effect of coupling between translational and internal degrees of freedom of composite quantum particles on their localization in a random potential. We show that entanglement between the two degrees of freedom weakens localization due to the upper bound imposed on the inverse participation ratio by purity of a quantum state. We perform numerical calculations for a two-particle system bound by a harmonic force in a 1D disordered lattice and a rigid rotor in a 2D disordered lattice. We illustrate that the coupling has a dramatic effect on localization properties, even with a small number of internal states participating in quantum dynamics.
We investigate the tunneling dynamics of an ultracold bosonic impurity species which interacts repulsively with a second, larger Bose gas. Both species are held in a finite-sized quasi-one-dimensional box potential. In addition, the impurity bosons experience a periodic potential generated by an optical lattice. We initially prepare our binary mixture in its ground state, such that the impurities and Bose gas are phase separated and the impurities localize pairwise in adjacent sites of the periodic potential, by tuning the interaction strengths and the lattice depth correspondingly. The dynamics is initiated by suddenly lowering the repulsive interspecies interaction strength, thereby entering a different regime in the crossover diagram. For specific postquench interspecies interaction strengths we find that a single impurity tunnels first to the neighboring empty site and depending on the quench strength can further tunnel to the next-neighboring site. Interestingly, this effect is highly sensitive to the presence of the Bose gas and does not occur when the Bose gas does not interact with the impurity species throughout the dynamics. Moreover, we find that the tunneling process is accompanied by strong entanglement between the Bose gas and the impurity species as well as correlations among the impurities.