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Physical Review A

Optical control of collective states in one-dimensional ordered atomic chains beyond the linear regime

Nikos Fayard, Igor Ferrier-Barbut, Antoine Browaeys, Jean‐Jacques Greffet

Published Aug 14, 2023• 10 citations
Publisher

Abstract

Driven by the need to develop efficient atom-photon interfaces, recent efforts have proposed replacing cavities by large arrays of cold atoms that can support subradiant or superradiant collective states. In practice, subradiant states are decoupled from radiation, which constitutes a hurdle to most applications. In this work, we study theoretically a protocol that bypasses this limit using a one dimensional chain composed of $N$ three-level atoms in a V-shaped configuration. Throughout the protocol, the chain behaves as a time-varying metamaterial: enabling absorption, storage, and on-demand emission in a spectrally and spatially controlled mode. Taking into account the quantum nature of atoms, we establish the boundary between the linear regime and the nonlinear regime. In the nonlinear regime, we demonstrate that doubly excited states can be coherently transferred from superradiant to subradiant states, opening the way to the optical characterization of their entanglement.

DOI
10.1103/physreva.108.023116

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Driven by the need to develop efficient atom-photon interfaces, recent efforts have proposed replacing cavities by large arrays of cold atoms that can support subradiant or superradiant collective states. In practice, subradiant states are decoupled from radiation, which constitutes a hurdle to most applications. In this work, we study theoretically a protocol that bypasses this limit using a one dimensional chain composed of NNN three-level atoms in a V-shaped configuration. Throughout the protocol, the chain behaves as a time-varying metamaterial: enabling absorption, storage, and on-demand emission in a spectrally and spatially controlled mode. Taking into account the quantum nature of atoms, we establish the boundary between the linear regime and the nonlinear regime. In the nonlinear regime, we demonstrate that doubly excited states can be coherently transferred from superradiant to subradiant states, opening the way to the optical characterization of their entanglement.
Driven by the need to develop efficient atom-photon interfaces, recent efforts have proposed replacing cavities by large arrays of cold atoms that can support subradiant or superradiant collective states. In practice, subradiant states are decoupled from radiation, which constitutes a hurdle to most applications. In this work, we study theoretically a protocol that bypasses this limit using a one dimensional (1D) chain composed of N three-level atoms in a V-shaped configuration. Throughout the protocol, the chain behaves as a time-varying metamaterial: enabling absorption, storage and on-demand emission in a spectrally and spatially controlled mode. Taking into account the quantum nature of atoms, we establish the boundary between the linear regime and the nonlinear regime. In the nonlinear regime, we demonstrate that doubly-excited states can be coherently transferred from superradiant to subradiant states, opening the way to the optical characterization of their entanglement.
Ordered ensembles of atoms, such as atomic arrays, exhibit distinctive features from their disordered counterpart. In particular, while collective modes in disordered ensembles show a linear optical response, collective subradiant excitations of subwavelength arrays are endowed with an intrinsic nonlinearity. Such nonlinearity has both a coherent and a dissipative component: two excitations propagating in the array scatter off each other leading to formation of correlations and to emission into free-space modes. We show how to take advantage of such nonlinearity to coherently prepare a single excitation in a subradiant (dark) collective state of a one-dimensional array as well as to perform an entangling operation on dark states of parallel arrays. We discuss the main source of errors represented by disorder introduced by atomic center-of-mass fluctuations, and we propose a practical way to mitigate its effects.
When quantum emitters couple indistinguishably to light, they can synchronize into a collective light matter system with radiative properties profoundly different from those of independent particles. To date, the resulting collective effects have largely been confined to point like or homogeneous ensembles. Here, we open access to a qualitatively new collective regime by realizing geometrically ordered, spatially extended atom arrays with subwavelength spacing. This establishes a fundamentally new platform in which collective emission is no longer confined to a single Dicke mode but instead emerges from an ordered network of photon mediated interactions. We find that 2D atom arrays undergo strong super and subradiant emission. Despite subwavelength spacing, we achieve site resolved imaging and directly observe the buildup of spatial correlations, demonstrating the transformation of cooperative decay into a strongly correlated many-body process. We observe extensive scaling of superradiance, uncover superradiant revivals, and reveal the ferromagnetic nature of superradiance and the antiferromagnetic nature of subradiance. Our results realize a novel programmable platform for exploring and utilizing dissipative many-body quantum physics, opening new possibilities for photon capture, storage, and atom photon entanglement.
While artificially fabricated patterned metasurfaces are providing paradigm-shifting optical components for classical light manipulation, strongly interacting, controllable, and deterministic quantum interfaces between light and matter in free space remain an outstanding challenge.Here, we theoretically demonstrate how to achieve quantum control of both the electric and magnetic components of an incident single-photon pulse by engineering the collective response of a two-dimensional atomic array.High-fidelity absorption and storage in a long-lived subradiant state, and its subsequent retrieval, are achieved by controlling classically or quantum-mechanically the ac Stark shifts of the atomic levels and suppressing the scattering during the absorption.Quantum wave-front control of the transmitted photon with nearly zero reflection is prepared by coupling the collective state of the array to another photon in a cavity and by engineering a Huygens' surface of atoms using only a single coherent standing wave.The proposed schemes allow for the generation of entanglement between the cavity, the lattice, and hence the state of the stored, reflected, or transmitted light, and for quantum-state transfer between the cavity and propagating photons.Bipartite entanglement generation is explicitly calculated between a stored single-photon excitation of the array and the cavity photon.We illustrate the control by manipulating the phase, phase superposition, polarization, and direction of a transmitted or reflected photon, providing quantum-optical switches and functional quantum interfaces between light and atoms that could form links in a larger quantum information platform.
Coherent control of collective spontaneous emission in an extended atomic ensemble resonantly interacting with single-photon wave packets is analyzed. A scheme for coherent manipulation of collective atomic states is developed such that superradiant states of the atomic system can be converted into subradiant ones and vice versa. Possible applications of such a scheme for optical quantum-state storage and single-photon wave packet shaping are discussed. It is shown that also in the absence of inhomogeneous broadening of the resonant line, single-photon wave packets with arbitrary pulse shape may be recorded as a subradiant state and reconstructed even although the duration of the wave packets is larger than the superradiant lifetime. Specifically the applicability for storing time-bin qubits, which are used in quantum cryptography, is analyzed.
When an ensemble of quantum emitters interacts with a common radiation field, their emission becomes collective, giving rise to superradiant and subradiant states, characterized by broadened and narrowed linewidths. In this work, we propose to harness subradiant states for quantum metrology; such states naturally arise in subwavelength-spaced atomic arrays in free space and in small ensembles of emitters coupled to one-dimensional waveguides. We demonstrate that their collective optical response yields sharp, narrow features in the transmittance spectrum, which can be used to enhance sensitivity to external perturbations. This improved sensitivity can be applied to atomic clock operation, spatially resolved imaging of emitter positions, and enables precise detection of both global and spatially varying detunings (such as those induced by electromagnetic fields or gravitational gradients).