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Dressed emitters as impurities

Luca Leonforte, Davide Valenti, Bernardo Spagnolo, Angelo C. M. Carollo, Francesco Ciccarello

Published Nov 1, 2021• 14 citations
Publisher

Abstract

Dressed states forming when quantum emitters or atoms couple to a photonic bath underpin a number of phenomena and applications, in particular nonradiating effective interactions occurring within photonic bandgaps. Here, we present a compact formulation of the resolvent-based theory for calculating atom-photon dressed states built on the idea that the atom behaves as an effective impurity. This establishes an explicit connection with the standard impurity problem in condensed matter. Moreover, it allows us to formulate and settle - independently of the bath Hamiltonian - a number of properties previously known only for specific models or not entirely formalized. The framework is next extended to the case of more than one emitter, which is used to derive a general expression of dissipationless effective Hamiltonians explicitly featuring the overlap of single-emitter dressed bound states.

DOI
10.1515/nanoph-2021-0490

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Dressed states forming when quantum emitters or atoms couple to a photonic bath underpin a number of phenomena and applications, in particular nonradiating effective interactions occurring within photonic bandgaps. Here, we present a compact formulation of the resolvent-based theory for calculating atom-photon dressed states built on the idea that the atom behaves as an effective impurity. This establishes an explicit connection with the standard impurity problem in condensed matter. Moreover, it allows us to formulate and settle - independently of the bath Hamiltonian - a number of properties previously known only for specific models or not entirely formalized. The framework is next extended to the case of more than one emitter, which is used to derive a general expression of dissipationless effective Hamiltonians explicitly featuring the overlap of single-emitter dressed bound states.
We identify a class of dressed atom-photon states forming at the same energy of the atom at any coupling strength. As a hallmark, their photonic component is an eigenstate of the bare photonic bath with a vacancy in place of the atom. The picture accommodates waveguide-QED phenomena where atoms behave as perfect mirrors, connecting in particular dressed bound states (BSs) in the continuum with geometrically confined photonic modes. When applied to photonic lattices, the framework establishes a one-to-one correspondence between topologically robust dressed states and topologically robust photonic BSs seeded by a vacancy. This is used to predict new classes of dressed BSs in the photonic Creutz-ladder and Haldane models. In the latter case, states with nonzero local photon flux occur in which an atom is dressed by a photon orbiting around it.
Abstract We present a general framework to tackle quantum optics problems with giant atoms, i.e. quantum emitters each coupled non-locally to a structured photonic bath (typically a lattice) of any dimension. The theory encompasses the calculation and general properties of Green’s functions, atom-photon bound states, collective master equations and decoherence-free Hamiltonians (DFHs), and is underpinned by a formalism where a giant atom is formally viewed as a normal atom lying at a fictitious location. As a major application, we provide for the first time a general criterion to predict/engineer DFHs of giant atoms, which can be applied both in and out of the photonic continuum and regardless of the structure or dimensionality of the photonic bath. This is used to show novel DFHs in 2D baths such as a square lattice, photonic graphene and an extended photonic Lieb lattice.
Photon-mediated interaction between quantum emitters in engineered photonic baths is an emerging area of quantum optics. At the same time, non-Hermitian (NH) physics is currently thriving, spurred by the exciting possibility to access new physics in systems ruled by non-trivial NH Hamiltonians—in particular, photonic lattices—which can challenge longstanding tenets such as the Bloch theory of bands. Here, we combine these two fields and study the exotic interaction between emitters mediated by the photonic modes of a lossy photonic lattice described by a NH Hamiltonian. We show in a paradigmatic case study that structured losses in the field can seed exotic emission properties. Photons can mediate dissipative, fully non-reciprocal interactions between emitters with range critically dependent on the loss rate. When this loss rate corresponds to a bare-lattice exceptional point, the effective couplings are exactly nearest neighbor, implementing a dissipative, fully non-reciprocal Hatano–Nelson model. Counterintuitively, this can occur irrespective of the lattice boundary conditions. Thus photons can mediate an effective emitter’s Hamiltonian which is translationally invariant despite the fact that the field is not. We interpret these effects in terms of metastable atom–photon dressed states, which can be exactly localized on only two lattice cells or extended across the entire lattice. These findings introduce a paradigm of light-mediated interactions with unprecedented features such as non-reciprocity, non-trivial dependence on field boundary conditions, and range tunability via a loss rate.
The dressed atom approach provides a tool to investigate the dynamics of an atom-laser system by fully retaining the quantum nature of the coherent mode. In its standard derivation, the internal atom-laser evolution is described within the rotating-wave approximation, which determines a doublet structure of the spectrum and the peculiar fluorescence triplet in the steady state. However, the rotating wave approximation may fail to apply to atomic systems subject to femtosecond light pulses, light-matter systems in the strong-coupling regime or sustaining permanent dipole moments. This work aims to demonstrate how the general features of the steady-state radiative cascade are affected by the interaction of the dressed atom with propagating radiation modes. Rather than focusing on a specific model, we analyze how these features depend on the parameters characterizing the dressed eigenstates in arbitrary atom-laser dynamics, given that a set of general hypotheses is satisfied. Our findings clarify the general conditions in which a description of the radiative cascade in terms of transition between dressed states is self-consistent. We provide a guideline to determine the properties of photon emission for any atom-laser interaction model, which can be particularly relevant when the model should be tailored to enhance a specific line. We apply the general results to the case in which a permanent dipole moment is a source of low-energy emission, whose frequency is of the order of the Rabi coupling.
Quantum emitters (QEs) coupled to structured baths can localize multiple photons around them and form qubit-photon bound states.In the Markovian or weak coupling regime, the interaction of QEs through these single-photon bound states is known to lead to effective many-body QE Hamiltonians with tuneable but yet perturbative interactions.In this work we study the emergence of such models in the non-Markovian or strong coupling regime in different excitation subspaces.The effective models for the non-Markovian regime with up to three excitations are characterized using analytical methods, uncovering the existence of doublons or triplon states.Furthermore, we provide numerical results for systems with multiple excitations and demonstrate the emergence of polariton models with optically tuneable interactions, whose many-body ground state exhibits a superfluid-Mott insulator transition.
Quantum emitters (QEs) coupled to structured baths can localize multiple photons around them and form qubit-photon bound states. In the Markovian or weak coupling regime, the interaction of QEs through these single-photon bound states is known to lead to effective many-body QE Hamiltonians with tuneable but yet perturbative interactions. In this work we study the emergence of such models in the non-Markovian or strong coupling regime in different excitation subspaces. The effective models for the non-Markovian regime with up to three excitations are characterized using analytical methods, uncovering the existence of doublons or triplon states. Furthermore, we provide numerical results for systems with multiple excitations and demonstrate the emergence of polariton models with optically tuneable interactions, whose many-body ground state exhibits a superfluid-Mott insulator transition.