Supercorrelated decay in a quasiperiodic nonlinear waveguide: From Markovian to non-Markovian transitions

TL;DR

This paper explores how quasiperiodic potentials affect photon interactions in a Bose-Hubbard chain, revealing mobility edges for doublon states and a transition from Markovian to non-Markovian dynamics in photon emission.

Contribution

It extends single-photon mobility edge theories to two-photon states and demonstrates the transition in emission dynamics linked to these edges.

Findings

Existence of mobility edges for doublon states in a quasiperiodic Bose-Hubbard chain

Transition from Markovian to non-Markovian emission dynamics around the mobility edges

Feasible experimental setup using superconducting circuits to observe these phenomena

Abstract

Mobility edges (MEs) are critical boundaries in disordered quantum systems that separate localized from extended states, significantly affecting transport properties and phase transitions. Although MEs are well-understood in single-photon systems, their manifestation in many-body contexts remains an active area of research. In this work, we investigate a one-dimensional Bose-Hubbard chain with a quasiperiodic potential modulating photon-photon interactions, effectively creating a mosaic lattice. We identify MEs for doublon states (i.e, bound photon pairs resulting from strong interactions) within the two-photon subspace. Our analytical solutions and numerical simulations confirm the existence of these MEs, extending single-photon MEs theories to the two-photon regime. Additionally, we analyze the dynamics of two emitters coupled to the waveguide, enabling the emission of supercorrelated photon pairs into the waveguide. Our findings reveal that coupling to extended states results in Markovian dynamics, characterized by exponentially supercorrelated decay, while coupling to localized states gives rise to non-Markovian dynamics, marked by suppressed decay and persistent oscillations. Here, a transition from Markovian to non-Markovian behavior occurs around the MEs of the doublons. Finally, we propose a feasible experimental implementation using superconducting circuits, providing a platform to observe the interplay between interactions and disorder in quantum systems.