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arXiv:2406.12390 · Physical Review A

Multimer states in multilevel waveguide QED

Jiaming Shi, Alexander N. Poddubny

Published Nov 12, 2024• 8 citations
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Abstract

We study theoretically the interplay of spontaneous emission and interactions for the multiple-excited quasistationary eigenstates in a finite periodic array of multilevel atoms coupled to the waveguide. We develop an analytical approach to calculate such eigenstates based on the subradiant dimer basis. Our calculations reveal the peculiar multimerization effect driven by the anharmonicity of the atomic potential: while a general eigenstate is an entangled one, there exist eigenstates that are products of dimers, trimers, or tetramers, depending on the size of the system and the fill factor. At half-filling, these product states acquire a periodic structure with all-to-all connections inside each multimer and become the most subradiant ones.

DOI
10.1103/physreva.110.053707

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We study theoretically the interplay of spontaneous emission and interactions for the multiple-excited quasistationary eigenstates in a finite periodic array of multilevel atoms coupled to the waveguide. We develop an analytical approach to calculate such eigenstates based on the subradiant dimer basis. Our calculations reveal the peculiar multimerization effect driven by the anharmonicity of the atomic potential: while a general eigenstate is an entangled one, there exist eigenstates that are products of dimers, trimers, or tetramers, depending on the size of the system and the fill factor. At half-filling, these product states acquire a periodic structure with all-to-all connections inside each multimer and become the most subradiant ones.
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.
We theoretically study subradiant states in an array of atoms coupled to photons propagating in a one-dimensional waveguide focusing on the strongly interacting many-body regime with large excitation fill factor f. We introduce a generalized many-body entropy of entanglement based on exact numerical diagonalization followed by a high-order singular value decomposition. This approach has allowed us to visualize and understand the structure of a many-body quantum state. We reveal the breakdown of fermionized subradiant states with increase of f with the emergence of short-ranged dimerized antiferromagnetic correlations at the critical point f=1/2 and the complete disappearance of subradiant states at f>1/2.
Recent experiments on spontaneous emission of atomic matter waves [Krinner et al., Nature (London) 559, 589 (2018); Stewart et al., Phys. Rev. Research 2, 043307 (2020)] open a window into the behavior of quantum emitters coupled to a waveguide. Here we develop an approach based on infinite products to study this system theoretically, without the need to approximate the band dispersion relation of the waveguide. We solve the system for a one-dimensional array of one, multiple, and an infinite number of quantum emitters and compare with the experiments. This leads to a detailed characterization of the decay spectrum, with a family of in-gap bound states, mechanisms for enhanced Markovian emission different from superradiance, and the emergence of matter-wave polaritons.
We study theoretically driven quantum dynamics in periodic arrays of two-level qubits coupled to the waveguide. We demonstrate, that strongly subradiant eigenstates of the master equation for the density matrix emerge under strong coherent driving for arrays with the anti-Bragg periods d=λ/4,3λ/4d=λ/4,3λ/4d=λ/4,3λ/4... This happens even though are no such states at low driving powers. Thus, our findings show that in the quantum nonlinear regime the domain of existence of subradiant states expands beyond conventional subwavelength structures. These driven states are directly manifested in long-living quantum correlations between the qubit excitations.
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.
Multiple emitters coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separation of the emitters. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging collective effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most superradiant state increases linearly as a function of the filling factor and exceeds that of two-level systems in magnitude. Furthermore, with bosonic systems, dark states are formed at each filling factor. These are in strong contrast with two-level systems, where the maximal superradiance is observed at half-filling and with larger filling factors superradiance diminishes and no dark states are formed. As an experimentally relevant setup of bosonic waveguide QED, we focus on arrays of transmon devices embedded inside a rectangular waveguide. Specifically, we study the setup of two transmon pairs realized experimentally in Zanner et al. [Nat. Phys. 18, 538 (2022)] and show that it is necessary to consider transmons as bosonic multilevel emitters to accurately recover correct collective effects for the higher excitation manifolds.