Interaction-induced decoherence in non-Hermitian quantum walks of ultracold bosons

Abstract

We study the decoherence caused by particle interaction for a conceptually simple model, a quantum walk on a bipartite one-dimensional lattice with decay from every second site. The corresponding noninteracting (linear) system has been shown to have a topological transition described by the average displacement before decay. Here, we use this topological quantity to distinguish coherent quantum dynamics from incoherent classical dynamics caused by a breaking of the translational symmetry. Furthermore, we analyze the behavior by means of a rate equation providing a quantitative description of the incoherent nonlinear dynamics.

Quantum transport in nonlinear Rudner-Levitov models

“…In this paper, we consider specific extensions of the RL model with different types of nonlinear couplings and numerically study the quantum transport therein. As it happens for the case of on-site nonlinearities [23,24], our results show that the nonlinear coupling generates departures from the typical quantized behavior of the particle transport. Our hopping nonlinearities turn out to be responsible for new effects, such as (i.)…”

“…Specifically, if one initializes a single particle at a neutral site, the mean displacement ∆m takes the value of 0 for ν < µ and takes the value of 1 for ν > µ, which precisely predicts the topological phase transition of this model. Such an archetype model has been well investigated both theoretically [1,3] and experimentally [4], and has also been extended in many directions [23,24,[30][31][32][33][34][35][36][37][38]. In the following, we generalize the RL model to a few instances with nonlinear hopping terms and study the quantum transport therein.…”

“…Most recently, Xia et al have considered a nonlinear PT-symmetric optical waveguide lattice to investigate the mutual interplay between topology, PT symmetry, and nonlinearity [22], demonstrating that global effects, i.e., topological and PT transitions, can be actively controlled by the local nonlinearity. The RL model has already been generalized by including on-site Kerr-type nonlinearities, which shows that the quantized quantum transport is severely affected by the nonlinearity induced decoherence effects [23] and that the nonlinear effect becomes pronounced in the PTbroken region [24]. However, the study of the influence of nonlinearity on the quantum transport in the RL model is still at the initial stage.…”

Computations in quantum mechanics made easy

“…It is of interest to realize that the Bose-Hubbard dimer also appears naturally for a collection of N bosonic atoms in a double-well potential, which is deep enough so that only the lowest state in each well is populated. In this two-mode approximation the system can be described by the Hamiltonian (15).…”

“…The following Matlab program calculates the eigenvalues of the Hamiltonian (15). First the creation and annihilation operators at the two sites are constructed by means of the kron product as well as the Hamiltonian, whose eigenvalues and eigenstates are then calculated for N = 24, i.e.…”