Engineering Anderson Localization in Arbitrary Dimensions with Interacting Quasiperiodic Kicked Bosons

TL;DR

This paper demonstrates how interactions and quasiperiodic driving in a 1D bosonic system can simulate Anderson localization in higher dimensions, revealing critical behavior across various effective dimensions.

Contribution

It introduces a method to engineer Anderson localization in arbitrary dimensions using interacting quasiperiodic kicked bosons, extending the known mappings to higher-dimensional models.

Findings

Interactions promote an effective two-dimensional Anderson model.

Quasiperiodic modulations extend the system to three and four dimensions.

Numerical simulations show Anderson localization and critical behavior in the orthogonal class.

Abstract

We study the interplay of interactions and quasiperiodic driving in the Lieb-Liniger model of one-dimensional bosons subjected to a sequence of delta kicks. Building on the known mapping between the kicked rotor and the Anderson model, we show that both interparticle interactions and quasiperiodic modulations of the kicking strength can independently and simultaneously generate synthetic dimensions. In the absence of modulation, interactions between two bosons already promote an effective two-dimensional Anderson model. Introducing one or two additional incommensurate frequencies further extends the system to three and four effective dimensions, respectively. Through extensive numerical simulations of the two-body dynamics and finite-time scaling analysis, we observe Anderson localization and the associated critical behavior characteristic of the orthogonal universality class. This combined use of interactions and quasiperiodic driving thus provides a versatile framework for emulating Anderson localization and its transition in arbitrary dimensions.