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arXiv:quant-ph/0611228 · Physical Review A

Spectral theory of quantum memory and entanglement via Raman scattering of light by an atomic ensemble

O. S. Mishina, Dmitriy V. Kupriyanov, Jörg Helge Müller, Eugene Simon Polzik

Published Apr 25, 2007• 23 citations
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Abstract

We discuss theoretically quantum interface between light and a spin polarized ensemble of atoms with the spin $\ensuremath{\geqslant}1$ based on an off-resonant Raman scattering. We present the spectral theory of the light--atom interaction and show how particular spectral modes of quantum light couple to spatial modes of the extended atomic ensemble. We show how this interaction can be used for quantum memory storage and retrieval and for deterministic entanglement protocols. The proposed protocols are attractive due to their simplicity since they involve just a single pass of light through atoms without the need for elaborate pulse shaping or quantum feedback. As a practically relevant example we consider the interaction of a light pulse with hyperfine components of ${D}_{1}$ line of $^{87}\mathrm{Rb}$. The quality of the proposed protocols is verified via analytical and numerical analysis.

DOI
10.1103/physreva.75.042326

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We discuss theoretically quantum interface between light and a spin polarized ensemble of atoms with the spin \ensuremath⩾1\ensuremath{\geqslant}1\ensuremath⩾1 based on an off-resonant Raman scattering. We present the spectral theory of the light--atom interaction and show how particular spectral modes of quantum light couple to spatial modes of the extended atomic ensemble. We show how this interaction can be used for quantum memory storage and retrieval and for deterministic entanglement protocols. The proposed protocols are attractive due to their simplicity since they involve just a single pass of light through atoms without the need for elaborate pulse shaping or quantum feedback. As a practically relevant example we consider the interaction of a light pulse with hyperfine components of D1{D}_{1}D1​ line of 87Rb^{87}\mathrm{Rb}87Rb. The quality of the proposed protocols is verified via analytical and numerical analysis.
We present two protocols, one for the storage of light in an atomic ensemble and the subsequent retrieval, and another one for the generation of entanglement between light and atoms. They rely on two passes of a single pulse through the ensemble, Larmor precessing in an external field. Both protocols work deterministically and the relevant figures of merit---such as the fidelity or the EPR variance---scale exponentially in the coupling strength. We solve the corresponding Maxwell-Bloch equations describing the scattering process and determine the resulting input-output relations which only involve one relevant light mode that, in turn, can be easily accessed experimentally.
This thesis contributes to the theory of a light-matter quantum interface based on the Kerr-effect arising in the dispersive interaction of pulsed laser light with a spin-polarized atomic ensemble. The scattering process can be described on the basis of a simple, yet fully quantum mechanical model involving only a small number of bosonic modes referring to transverse spin components and quadratures of forward scattered light. Based on this model we derive protocols for the creation of entangled states of light and atoms and the teleportation of quantum states of light onto atoms employing this entanglement. Furthermore we present a protocol, which allows one to exchange the state of light and atoms and thus provides a quantum memory for states of the light field. For both, the storage and the teleportation of coherent states we prove a benchmark on the average fidelity, which is achievable by purely classical protocols. Both protocols allow one to significantly surpass this threshold and to demonstrate thereby a gain in employing quantum strategies. Under common experimental conditions the initial state of light and atoms is Gaussian and the given interaction preserves this property. Motivated by this observation, we examine in this context, how a given interaction can be used to simulate others and how it can be employed to create entanglement at optimal rates. The results are applied to construct protocols based on several passes of light through an atomic ensemble.
In this thesis, we explore the quantum dynamics of light interactions with optically thick collections of atoms. We provide a theoretical description of several recent experiments in which some key operations necessary for the implementation of quantum communication networks are demonstrated. Collective Raman scattering from an atomic ensemble is shown to produce probabilistic entanglement between the polarization of a scattered photon and an associated collective atomic excitation. The predicted correlations agree with experimental observations. We also propose a method to use cascade transitions to produce entanglement between a photon with a frequency in the telecom range (ideal for transmission over optical fibers) and a near infrared photon (ideal for storage in an atomic ensemble), and a description of the experimental demonstration is provided. We also propose and describe the implementation of a deterministic source of single photons.\n\nIn addition, we generalize the theory of dark-state polaritons in ensembles of three level Lambda atoms to account for the nuclear spin degeneracy of alkali atoms. This generalized theory provides a description of the first demonstration of single photon storage and retrieval from atomic ensembles. Additionally, in the presence of a uniform magnetic field, we predict the occurrence of collapses and revivals of the photon retrieval efficiency as a function of storage time within the ensemble. These predictions are in very good agreement with subsequent experimental observations. We also exploit the ability of photon storage to entangle remote atomic qubits.
We present an experimentally feasible protocol for the complete storage and retrieval of arbitrary light states in an atomic quantum memory using the Faraday interaction between light and matter. Our protocol relies on multiple passages of a single light pulse through the atomic ensemble without the impractical requirement of kilometer-long delay lines between the passages. A time-dependent interaction strength enables the storage and retrieval of states with arbitrary pulse shapes. The fidelity approaches unity exponentially without squeezed or entangled initial states, as illustrated by calculations for a photonic qubit.
Summary form only given. A new approach to the problem of the quantum interface between light and atoms has been recently developed. The method utilizes free space dispersive interaction between pulses of light and spin polarized atomic ensembles. Entanglement between the polarization state of light and the collective spin state of atoms is established by measurement, more precisely by detection of light in a certain polarization basis. In the first demonstration of this approach we have generated a long-lived entangled state of two separate macroscopic atomic samples by a polarization measurement on light transmitted through the samples. We then have shown that this approach also works for mapping of a quantum state of light onto long-lived atomic spin state paving the road towards realization of the quantum memory for light. Recently we have also extended the free space light-atoms interface beyond the continuous variables in the proposal, where a coherent superposition "cat" state of an atomic ensemble is generated by a measurement sequence. Progress with other communication protocols such as atomic state teleportation and multiparty networks will be presented.