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arXiv:quant-ph/0603268

Modematching an optical quantum memory

Joshua Nunn, Ian A. Walmsley, M. G. Raymer, Karl Surmacz, F. C. Waldermann, Z Wang, Dieter Jaksch

Published Mar 29, 2006• 110 citations
arXivHTMLPDF

Abstract

We analyse the off-resonant Raman interaction of a single broadband photon, copropagating with a classical `control' pulse, with an atomic ensemble. It is shown that the classical electrodynamical structure of the interaction guarantees canonical evolution of the quantum mechanical field operators. This allows the interaction to be decomposed as a beamsplitter transformation between optical and material excitations on a mode-by-mode basis. A single, dominant modefunction describes the dynamics for arbitrary control pulse shapes. Complete transfer of the quantum state of the incident photon to a collective dark state within the ensemble can be achieved by shaping the control pulse so as to match the dominant mode to the temporal mode of the photon. Readout of the material excitation, back to the optical field, is considered in the context of the symmetry connecting the input and output modes. Finally, we show that the transverse spatial structure of the interaction is characterised by the same mode decomposition.

DOI
10.48550/arxiv.quant-ph/0603268

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We analyse the off-resonant Raman interaction of a single broadband photon, copropagating with a classical `control' pulse, with an atomic ensemble. It is shown that the classical electrodynamical structure of the interaction guarantees canonical evolution of the quantum mechanical field operators. This allows the interaction to be decomposed as a beamsplitter transformation between optical and material excitations on a mode-by-mode basis. A single, dominant modefunction describes the dynamics for arbitrary control pulse shapes. Complete transfer of the quantum state of the incident photon to a collective dark state within the ensemble can be achieved by shaping the control pulse so as to match the dominant mode to the temporal mode of the photon. Readout of the material excitation, back to the optical field, is considered in the context of the symmetry connecting the input and output modes. Finally, we show that the transverse spatial structure of the interaction is characterised by the same mode decomposition.
We analyze a quantum optical memory based on the off-resonant Raman interaction of a single broadband photon, copropagating with a classical control pulse, with an atomic ensemble. The conditions under which the memory can perform optimally are found, by means of a universal mode decomposition. This enables the memory efficiency to be specified in terms of a single parameter, and the control field pulse shape to be determined via a simple nonlinear scaling. We apply the same decomposition to determine the optimal configurations for read-out.
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We show how to capture a single photon of arbitrary temporal shape with one atom coupled to an optical cavity. Our model applies to Raman transitions in three-level atoms with one branch of the transition controlled by a (classical) laser pulse, and the other coupled to the cavity. Photons impinging on the cavity normally exhibit partial reflection, transmission, and/or absorption by the atom. Only a control pulse of suitable temporal shape ensures impedance matching throughout the pulse, which is necessary for complete state mapping from photon to atom. For most possible photon shapes, we derive an unambiguous analytic expression for the shape of this control pulse, and we discuss how this relates to a quantum memory.
Summary form only given. The authors present a theoretical analysis of a quantum memory which shows how to efficiently transfer an ultrashort single photon wavepacket to a long-lived collective excitation of an ensemble of absorbers with the well-known three level Lambda-structure, by application of an ancillary control field. We describe a general prescription for optimizing the efficiency of the storage process for arbitrary detunings, and then we show how the dynamics simplify in the off-resonant limit. In this case spontaneous emission losses are eliminated and the interaction becomes unitary; being characterized by a universal mode decomposition.
Summary form only given. The authors present a theoretical analysis of a quantum memory which shows how to efficiently transfer an ultrashort single photon wavepacket to a long-lived collective excitation of an ensemble of absorbers with the well-known three level Lambda-structure, by application of an ancillary control field. We describe a general prescription for optimizing the efficiency of the storage process for arbitrary detunings, and then we show how the dynamics simplify in the off-resonant limit. In this case spontaneous emission losses are eliminated and the interaction becomes unitary; being characterized by a universal mode decomposition.
We analyse the properties of a Raman quantum light-atom interface in long atomic ensemble and its applications as a quantum memory or two-mode squeezed state generator. We consider the weak-coupling regime and include both Stokes and anti-Stokes scattering and the effects of Doppler broadening in buffer gas assuming frequent velocity-averaging collisions. We find the Green functions describing multimode transformation from input to output fields of photons and atomic excitations. Proper mode basis is found via singular value decomposition for short interaction times. It reveals that triples of modes are coupled by a transformation equivalent to a combination of two beamsplitters and a two-mode squeezing operation. We analyse the possible transformations on an example of warm rubidium-87 vapour. The model we present bridges the gap between the Stokes only and anti-Stokes only interactions providing simple, universal description in a temporally and longitudinally multimode situation. Our results also provide an easy way to find an evolution of the states in a Schrödinger picture thus facilitating understanding and design.