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arXiv:2011.11931 · Physical Review Letters

Quantum Chaos Driven by Long-Range Waveguide-Mediated Interactions

A. V. Poshakinskiy, Janet Zhong, Alexander N. Poddubny

Published May 21, 2021• 22 citations
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Abstract

We study theoretically quantum states of a pair of photons interacting with a finite periodic array of two-level atoms in a waveguide. Our calculation reveals two-polariton eigenstates that have a highly irregular wave function in real space. This indicates the Bethe ansatz breakdown and the onset of quantum chaos, in stark contrast to the conventional integrable problem of two interacting bosons in a box. We identify the long-range waveguide-mediated coupling between the atoms as the key ingredient of chaos and nonintegrability. Our results provide new insights in the interplay between order, chaos, and localization in many-body quantum systems and can be tested in state-of-the-art setups of waveguide quantum electrodynamics.

DOI
10.1103/physrevlett.126.203602

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We study theoretically quantum states of a pair of photons interacting with a finite periodic array of two-level atoms in a waveguide. Our calculation reveals two-polariton eigenstates that have a highly irregular wave function in real space. This indicates the Bethe ansatz breakdown and the onset of quantum chaos, in stark contrast to the conventional integrable problem of two interacting bosons in a box. We identify the long-range waveguide-mediated coupling between the atoms as the key ingredient of chaos and nonintegrability. Our results provide new insights in the interplay between order, chaos, and localization in many-body quantum systems and can be tested in state-of-the-art setups of waveguide quantum electrodynamics.
We provide the first classification of three-photon eigenstates in a finite periodic array of two-level atoms coupled to a waveguide. We focus on the strongly subwavelength limit and show the hierarchical structure of the eigenstates in the complex plane. The main characteristic eigenstates are explored using entanglement entropy as a distinguishing feature. We show that the rich interplay of order, chaos and localization found in two-photon systems extends naturally to three-photon systems. There also exist interaction-induced localized states unique to three-photon systems such as bound trimers, corner states, and trimer edge states.
We study theoretically quantum eigenstates in an array of two-level atoms coupled to the waveguide. We show that this system features double-excited states where the two excitations are localized at the opposite edges of the array. Such bound states of distant excitations result from the long-ranged photon-mediated coupling in the waveguide setup, which mediates repulsion at larger distances. These results could be useful for the rapidly developing field of waveguide quantum electrodynamics, studying waveguide-coupled arrays of cold atoms or superconducting qubits.
We theoretically predict the formation of two-photon bound states in a two-dimensional waveguide network hosting a lattice of two-level atoms. The properties of these bound pairs and the exclusive domains of the parameter space where they emerge due to the interplay between the on-site photon blockade and peculiar shape of polariton dispersion resulting from the long-range radiative couplings between the qubits are investigated in detail. In addition, we analyze the effect of the finite-size system on localization characteristics of these excitations.
Atom arrays are a new type of quantum light-matter interface.Here we propose to employ one-dimensional ordered arrays as atomic waveguides.These arrays support optical guided modes that do not decay into free space.We show that these modes can be harnessed to mediate tunable, long-range interactions between additional "impurity qubits" coupled to the chain, without need for photonic structures.The efficient coupling between qubits and atomic waveguides enables the realization of tunable qubit-qubit interactions, which can be short or long range, dissipative or coherent, as well as chiral.Moreover, owing to the two-level nature of atoms, these waveguides are intrinsically quantum.In contrast to classical waveguides, where photons do not interact with each other, atomic waveguides display strong nonlinearities, which create a tunable dissipative channel for qubit-qubit interactions, and opens the door to the exploration of many-body physics between guided photons.This physics is universal as it only relies on photon interference and can also be observed with other types of quantum emitters, such as those in molecular or solid-state systems.
Quantum emitters coupled to a waveguide are a paradigm of quantum optics, whose essential properties are described by waveguide quantum electrodynamics (QED). We study the possibility of observing the typical features of the conventional waveguide QED scenario in a system where the role of the waveguide is played by a one-dimensional subwavelength atomic array. For the role of emitters, we propose to use antisymmetric states of atomic dimers---a pair of closely spaced atoms---as effective two-level systems, which significantly reduces the effect of free-space spontaneous emission. We solve the dynamics of the system both when the dimer frequency lies inside and when it lies outside the band of modes of the array. Along with well-known phenomena of collective emission into the guided modes and waveguide-mediated long-range dimer-dimer interactions, we uncover significant non-Markovian corrections which arise from both the finiteness of the array and through retardation effects.