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arXiv:2110.15878

Polariton interaction in one-dimensional arrays of atoms coupled to waveguides

Björn Schrinski, Anders Søndberg Sørensen

Published Oct 29, 2021• 0 citations
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Abstract

Photons strongly coupled to material systems constitute a novel system for studying the dynamics of non-equilibrium quantum many-body systems. We give a fully analytical description of the dynamics of photons coupled to a one-dimensional array of two-level atoms. The description incorporates input, scattering inside the medium, and the ejection of photons from the array. We show that inelastic collisions, previously identified in small systems, also occur in infinite systems and elucidate the physics behind this effect. The developed theory constitutes an effective field theory for the dynamics, which can be used as a starting point for studies of many-body dynamics. We discuss different parameter regimes and touch upon possible applications and the limit of many excitations.

DOI
10.48550/arxiv.2110.15878

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Photons strongly coupled to material systems constitute a novel system for studying the dynamics of non-equilibrium quantum many-body systems. We give a fully analytical description of the dynamics of photons coupled to a one-dimensional array of two-level atoms. The description incorporates input, scattering inside the medium, and the ejection of photons from the array. We show that inelastic collisions, previously identified in small systems, also occur in infinite systems and elucidate the physics behind this effect. The developed theory constitutes an effective field theory for the dynamics, which can be used as a starting point for studies of many-body dynamics. We discuss different parameter regimes and touch upon possible applications and the limit of many excitations.
Abstract Photons strongly coupled to material systems constitute a novel system for realizing non-linear optics at the level of individual photons and studying the dynamics of non-equilibrium quantum many-body system. We give a simple physical polariton-picture of the dynamics of photons coupled to a one-dimensional array of two-level atoms. This picture allows a fully analytical description of the dynamics in terms of polariton scattering inside the medium and reflections of the polaritons from the edge of the array. We show that inelastic collisions, previously identified in small systems, also occur in infinite systems and are related to the existence of multiple bands in the dispersion relation. The developed theory constitutes an effective field theory for the dynamics, which can be used for studies of non-linear optics and many-body dynamics. As a specific example we map the system to the Lieb–Liniger model and show that a so-called Tonks–Girardeau gas of photons is a stable eigenstate of the system in the limit of many emitters.
A lattice of trapped atoms strongly coupled to a one-dimensional nanophotonic waveguide is investigated in exploiting polaritons as natural collective eigenstates. We derive polariton-polariton kinematic interactions by applying a bosonization procedure to transform excitation spin-12\frac{1}{2}21​ operators into interacting bosons. In solving the scattering problem we extract the effective potential, which is shown to be modulated by using the excitation-photon detuning as a control parameter. We examine the regime in which polaritons behave as a dilute degenerate boson gas and in the limit where polaritons can be treated as weakly interacting photons we propose the system for realizing superfluidity of photons. We implement the kinematic interaction as a mechanism for nonlinear optical processes that provide an observation tool for the system properties, e.g., the interaction strength produces a blue shift in pump-probe experiments.
We study the dynamics of a single-photon pulse traveling through a linear atomic chain coupled to a one-dimensional (1D) single mode photonic waveguide. We derive a time-dependent dynamical theory for this collective many-body system which allows us to study the real time evolution of the photon transport and the atomic excitations. Our analytical result is consistent with previous numerical calculations when there is only one atom. For an atomic chain, the collective interaction between the atoms mediated by the waveguide mode can significantly change the dynamics of the system. The reflectivity of a photon can be tuned by changing the ratio of coupling strength and the photon linewidth or by changing the number of atoms in the chain. The reflectivity of a single-photon pulse with finite bandwidth can even approach 100100%100. The spectrum of the reflected and transmitted photon can also be significantly different from the single-atom case. Many interesting physical phenomena can occur in this system such as the photonic band-gap effects, quantum entanglement generation, Fano-like interference, and superradiant effects. For engineering, this system may serve as a single-photon frequency filter, single-photon modulation, and may find important applications in quantum information.
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Subwavelength arrays of quantum emitters offer an efficient free-space approach to coherent light-matter interfacing, using ultracold atoms or two-dimensional solid-state quantum materials. The combination of collectively suppressed photon losses and emerging optical nonlinearities due to strong photon coupling to mesoscopic numbers of emitters holds promise for generating nonclassical light and engineering effective interactions between freely propagating photons. While most studies have thus far relied on numerical simulations, we describe here a diagrammatic Green's function approach that permits analytical investigations of nonlinear processes. We illustrate the method by deriving a simple expression for the scattering matrix that describes photon-photon interactions in an extended two-dimensional array of quantum emitters and reproduces the results of numerical simulations of coherently driven arrays. The approach yields intuitive insights into the nonlinear response of the system and offers a promising framework for the systematic development of a theory for interacting photons and many-body effects on collective radiance in two-dimensional arrays of quantum emitters. Published by the American Physical Society 2024
Waveguide quantum electrodynamics studies photon-mediated interactions of quantum emitters in a one-dimensional radiation channel. Although signatures of such interactions have been observed previously in a variety of physical systems, observation of coherent cooperative dynamics has been obscured by radiative decay of atoms into the waveguide. Employing transmon qubits as artificial atoms coupled to a microwave coplanar waveguide, here we observe dynamical oscillations in an open system where a designated probe qubit interacts with an entangled dark state of an array of qubits which effectively traps radiation as an atomic cavity. The qubit-cavity system is shown to achieve a large cooperativity of C=172 due to collective enhancement of photon-mediated interactions, entering the strong coupling regime. The quantum coherence of the dark state cavity is also explored through its nonlinear response at the single-excitation level. With realistic refinements, this system is suitable for studying the many-body dynamics of large (N>10) quantum spin chains, synthesizing highly non-classical radiation fields on demand, and implementing universal quantum logic operations with high fidelity on information encoded within decoherence-free subspaces.