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arXiv:2103.10926 · Physical Review A

Photon-emitter dressed states in a closed waveguide

Davide Lonigro, Paolo Facchi A, Andrew D. Greentree, Saverio Pascazio, Francesco Vincenzo Pepe, Domenico Pomarico

Published Nov 8, 2021• 7 citations
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Abstract

We study a system made up of one or two two-level quantum emitters, coupled to a single transverse mode of a closed waveguide, in which photon wavenumbers and frequencies are discretized, and characterize the states in which one excitation is steadily shared between the field and the emitters. We unearth finite-size effects in the field-emitter interactions and identify a family of dressed bound states that represent the forerunners of bound states in the continuum in the limit of an infinite waveguide. We finally consider the potential interest of such states for applications in the field of quantum information.

DOI
10.1103/physreva.104.053702

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We study a system made up of one or two two-level quantum emitters, coupled to a single transverse mode of a closed waveguide, in which photon wavenumbers and frequencies are discretized, and characterize the states in which one excitation is steadily shared between the field and the emitters. We unearth finite-size effects in the field-emitter interactions and identify a family of dressed bound states that represent the forerunners of bound states in the continuum in the limit of an infinite waveguide. We finally consider the potential interest of such states for applications in the field of quantum information.
We study the bound states in the continuum for a system of nnn two-level quantum emitters, coupled with a one-dimensional photon field, when a single excitation is shared among the different components of the system. The emitters are equally spaced at fixed positions. We first consider the approximation of distant emitters and exhibit degenerate eigenspaces of bound states corresponding to resonant discrete values of the energy. We then consider the full form of the eigenvalue equation, in which the effects of the finite spacing and the field dispersion relation become relevant, yielding significant nonperturbative effects that can lift some degeneracies. We explicitly solve the cases n=3n=3n=3 and n=4n=4n=4 emitters.
We discuss the properties of atom-photon bound states in waveguide QED systems consisting of single or multiple atoms coupled strongly to a finite-bandwidth photonic channel. Such bound states are formed by an atom and a localized photonic excitation and represent the continuum analog of the familiar dressed states in single-mode cavity QED. Here we present a detailed analysis of the linear and nonlinear spectral features associated with single- and multiphoton dressed states and show how the formation of bound states affects the waveguide-mediated dipole-dipole interactions between separated atoms. Our results provide both a qualitative and quantitative description of the essential strong-coupling processes in waveguide QED systems, which are currently being developed in the optical and microwave regimes.
The physics of systems of quantum emitters in waveguide quantum electrodynamics is significantly influenced by the relation between their spatial separation and the wavelength of the emitted photons. If the distance that separates a pair of emitters meets specific resonance conditions, the photon amplitudes produced from decay may destructively interfere. In an infinite-waveguide setting, this effect gives rise to bound states in the continuum, where a photon remains confined between the emitters. In the case of a finite-length waveguide with periodic boundary conditions, there exist two such relevant distances for a given arrangement of the quantum emitters, leading to states in which a photon is confined to either the shorter or the longer path that connects the emitters. If the ratio of the shorter and the longer path is a rational number, these two kinds of resonant eigenstates are allowed to co-exist for the same Hamiltonian. In this paper, we investigate the existence of quasi-degenerate resonant doublets of a pair of identical emitters coupled to a linear waveguide mode. The states that form the doublet are searched among the ones in which a single excitation tends to remain bound to the emitters. We investigate the spectrum in a finite range around degeneracy points to check whether the doublet remains well separated from the closest eigenvalues in the spectrum. The identification of quasi-degenerate doublets opens the possibility to manipulate the emitters-waveguide system as an effectively two-level system in specific energy ranges, providing an innovative tool for quantum technology tasks.
Photon bound states have been identified as particular solutions to the scattering of two photons from a single emitter, but from these results the full nature of these states remains elusive. We study a novel, clear and unambiguous signature that these bound states are truly bound. To this end we consider a new configuration of close-by waveguides, each chirally coupled to two-level emitters. We show that in this system the photon bound states behave like rigid molecules, where photons do not tunnel individually but rather collectively, such that there is rarely a single photon in each waveguide. We further identify new classes of bound states in this system.
Emergent Oscillating bound states in a semi-infinite linear waveguide with a point-like ΛΛΛ-type quantum emitter driven by a classical field
An oscillating bound state is a phenomenon where excitations mediated by the continuum modes oscillate persistently. Although it is generated by the superposition of two bound states in the continuum (BICs), such phenomenon is said to be unique to giant atoms. We present the phenomenon of an oscillating bound state with an alternative waveguide QED system, which is a one-dimensional semi-infinite waveguide coupled to a \textit{point-like} quantum emitter. This \textit{point-like} quantum emitter is ΛΛΛ-type quantum system with one transition driven by a classical field.
Light-matter interaction at the single-quantum level is the heart of many regimes of high fundamental importance to modern quantum technologies. Strong interaction of a qubit with a single photon of an electromagnetic field mode is described by the cavity/circuit electrodynamics (QED) regime which is one of the most advanced platforms for quantum computing. The opposite regime of the waveguide QED, where qubits interact with a continuum of modes in an infinite one-dimensional space, is also at the focus of recent research revealing novel quantum phenomena. Despite the demonstration of several key features of waveguide QED, the transition from an experimentally realizable finite-size system to the theoretically assumed infinite device size is neither rigorously justified nor fully understood. In this paper, we formulate a unifying theory which under a minimal set of standard approximations accounts for physical boundaries of a system in all parameter domains. Considering two qubits in a rectangular waveguide which naturally exhibits a low frequency cutoff we are able to account for infinite number of modes and obtain an accurate description of the waveguide transmission, a life-time of a qubit-photon bound state and the exchange interaction between two qubit-photon bounds states. For verification, we compare our theory to experimental data obtained for two superconducting qubits in a rectangular waveguide demonstrating how the infinite size limit of waveguide QED emerges in a finite-size system. Our theory can be straightforwardly extended to other waveguides such as the photonic crystal and coupled cavity arrays.