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arXiv:1105.2662 · Physical Review A

Three-dimensional theory of quantum memories based on Λ -type atomic ensembles

Emil Zeuthen, Anna Grodecka-Grad, Anders Søndberg Sørensen

Published Oct 24, 2011• 22 citations
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Abstract

We develop a three-dimensional theory for quantum memories based on light storage in ensembles of $\ensuremath{\Lambda}$-type atoms, where two long-lived atomic ground states are employed. We consider light storage in an ensemble of finite spatial extent and we show that within the paraxial approximation the Fresnel number of the atomic ensemble and the optical depth are the only important physical parameters determining the quality of the quantum memory. We analyze the influence of these parameters on the storage of light followed by either forward or backward read-out from the quantum memory. We show that for small Fresnel numbers the forward memory provides higher efficiencies, whereas for large Fresnel numbers the backward memory is advantageous. The optimal light modes to store in the memory are presented together with the corresponding spin waves and outcoming light modes. We show that for high optical depths such $\ensuremath{\Lambda}$-type atomic ensembles allow for highly efficient backward and forward memories even for small Fresnel numbers $F\ensuremath{\gtrsim}0.1$.

DOI
10.1103/physreva.84.043838

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We develop a three-dimensional theory for quantum memories based on light storage in ensembles of \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type atoms, where two long-lived atomic ground states are employed. We consider light storage in an ensemble of finite spatial extent and we show that within the paraxial approximation the Fresnel number of the atomic ensemble and the optical depth are the only important physical parameters determining the quality of the quantum memory. We analyze the influence of these parameters on the storage of light followed by either forward or backward read-out from the quantum memory. We show that for small Fresnel numbers the forward memory provides higher efficiencies, whereas for large Fresnel numbers the backward memory is advantageous. The optimal light modes to store in the memory are presented together with the corresponding spin waves and outcoming light modes. We show that for high optical depths such \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type atomic ensembles allow for highly efficient backward and forward memories even for small Fresnel numbers F\ensuremath≳0.1F\ensuremath{\gtrsim}0.1F\ensuremath≳0.1.
We study spatial multimode quantum memories based on light storage in extended ensembles of Λ-type atoms. We show that such quantum light-matter interfaces allow for highly efficient storage of many spatial modes. In particular, forward operating memories possess excellent scaling with the important physical parameters: quadratic scaling with the Fresnel number and even cubic with the optical depth of the atomic ensemble. Thus, the simultaneous use of both the longitudinal and transverse shape of the stored spin wave modes constitutes a valuable and so far overlooked resource for multimode quantum memories.
We study the coherent storage and retrieval of a very short multimode light pulse in an atomic ensemble. We consider a quantum memory process based on the conversion of a signal pulse into a long-lived spin coherence via light matter interaction in an on-resonant $\ensuremath{\Lambda}$ -type system. In order to study the writing and reading processes we analytically solve the partial differential equations describing the evolution of the field and of the atomic coherence in time as well as in space. We show how to optimize the process for writing as well as for reading. If the medium length is fixed, for each length, there is an optimal value of the pulse duration. We discuss the information capacity of this memory scheme and we estimate the number of transverse modes that can be stored as a quantum hologram.
We present a new scheme of quantum memory for optical images (spatially multimode light fields) that allows mapping the quantum state of the signal onto the long-lived coherence of the ground state of an ensemble of stationary atoms or impurity centers. The memory medium is embedded in an optical cavity with degenerate transverse modes, which increases the effective optical thickness of the medium and allows one, in principle, to store information in optically thin atomic layers. Since, in reality, storage and retrieval of limited-duration signals, including signals shorter than the lifetime of the field in the cavity, is of interest, we do not use the low- Q cavity approximation. The influence of losses due to partial reflection of the nonstationary signal field incident on a coupling mirror on the storage efficiency is considered. We used the method of approximate impedance matching, wherein losses due to reflection can be minimized by controlling the coupling parameter of the light field with memory medium in time, thus creating conditions for destructive interference of the signal and local fields on the coupling mirror. The influence of diffraction on the transverse resolution of memory at the writing and readout stages is investigated, and the number of effectively stored transverse spatial modes of the signal is estimated.
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.