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arXiv:0704.3663 · Physical Review A

Quantum storage on subradiant states in an extended atomic ensemble

А. А. Калачев

Published Oct 11, 2007• 29 citations
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Abstract

A scheme for coherent manipulation of collective atomic states is developed such that total subradiant states, in which spontaneous emission is suppressed into all directions due to destructive interference between neighbor atoms, can be created in an extended atomic ensemble. The optimal conditions for creation of such states and suitability of them for quantum storage are discussed. It is shown that in order to achieve the maximum signal-to-noise ratio the shape of a light pulse to be stored and reconstructed using a homogeneously broadened absorption line of an atomic system should be a time-reversed regular part of the response function of the system. In the limit of high optical density, such pulses allow one to prepare collective subradiant atomic states with near flat spatial distribution of the atomic excitation in the medium.

DOI
10.1103/physreva.76.043812

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A scheme for coherent manipulation of collective atomic states is developed such that total subradiant states, in which spontaneous emission is suppressed into all directions due to destructive interference between neighbor atoms, can be created in an extended atomic ensemble. The optimal conditions for creation of such states and suitability of them for quantum storage are discussed. It is shown that in order to achieve the maximum signal-to-noise ratio the shape of a light pulse to be stored and reconstructed using a homogeneously broadened absorption line of an atomic system should be a time-reversed regular part of the response function of the system. In the limit of high optical density, such pulses allow one to prepare collective subradiant atomic states with near flat spatial distribution of the atomic excitation in the medium.
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.
A scheme for creating subradiant states in an extended system of atoms, based on the use of an external inhomogeneous electric field, is proposed. It is shown that the maximum signal-to-noise ratio at the output of a quantum memory device using such subradiant states for data storage is obtained when the temporal shape of recorded single-photon wave packets (quantum information carriers) is a time-reversed pulse characteristic of a resonant atomic system. In this case, the quantum memory efficiency tends to unity in the limit of large optical thickness of the resonant medium.
A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell–Bloch equations. However, these equations are semi-phenomenological, as they treat emission of the atoms into other directions other than the mode of interest as being independent. On the other hand, in systems such as dense, ordered atomic arrays, atoms interact with each other strongly and spatial interference of the emitted light might be exploited to suppress emission into unwanted directions, thereby enabling improved error bounds. Here, we develop a general formalism that fully accounts for spatial interference, and which finds the maximum storage efficiency for a single photon with known spatial input mode into a collection of atoms with discrete, known positions. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number N a like , and that, remarkably, an array of just 4 × 4 atoms in principle allows for an error of less than 1%, which is comparable to a disordered ensemble with an optical depth of around 600.
Collective excitations in ordered subwavelength atomic arrays can exhibit strongly suppressed radiative decay due to interference between light scattered by neighboring emitters. These so-called subradiant states make these systems a promising platform for storing and manipulating photonic excitations. The external geometry of the array, combined with dynamical control of the atomic dipole orientation, enables localized trapping and coherent transport of these subradiant excitations. Here, we theoretically demonstrate these capabilities in ring-shaped atomic arrays. Specifically, we show adiabatic transport of a localized excitation around a single ring, coherent transfer of a single excitation between two neighboring rings with geometry-controlled selectivity, and interaction-induced conditional phase shifts between two simultaneously trapped excitations in neighboring rings. The latter can be interpreted as effective controlled-phase operations between stored excitations. Together, these results demonstrate the potential of ordered atomic arrays as a platform for coherent photonic quantum information processing with dissipation-protected collective excitations.
Abstract The optically trapped ensembles of atoms provide a versatile platform for storing and coherent manipulation of quantum information. However, efficient realization of quantum information processing requires long‐lived quantum states protected from the decoherence e.g. via spontaneous emission. Here, we theoretically study collective dipolar oscillations in finite planar arrays of quantum emitters in free space and analyze mechanisms that govern the emergence of strongly subradiant collective states. We demonstrate that the external coupling between the collective states associated with the symmetry of the array and with the quasi‐flat dispersion of the corresponding infinite lattice plays a crucial role in the boost of their radiative lifetime. We show that among different regular arrangements of the atoms the square atomic arrays support eigenstates with minimal radiative losses scaled with the total number of atoms N tot .