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arXiv:quant-ph/0406050 · Physical Review Letters

Temporal Dynamics of Photon Pairs Generated by an Atomic Ensemble

Sergey Vladimirovich Polyakov, C. W. Chou, D. Felinto, Harry J. Kimble

Published Dec 20, 2004• 44 citations

Abstract

The time dependence of nonclassical correlations is investigated for two fields $(1,2)$ generated by an ensemble of cold cesium atoms via the protocol of Duan et al. [Nature (London) 414, 413 (2001)]. The correlation function $R({t}_{1},{t}_{2})$ for the ratio of cross to autocorrelations for the $(1,2)$ fields at times $({t}_{1},{t}_{2})$ is found to have a maximum value ${R}^{\mathrm{max}}=292\ifmmode\pm\else\textpm\fi{}57$, which significantly violates the Cauchy-Schwarz inequality $R\ensuremath{\le}1$ for classical fields. Decoherence of quantum correlations is observed over ${\ensuremath{\tau}}_{d}\ensuremath{\simeq}175\text{ }\text{ }\mathrm{n}\mathrm{s}$, and is described by our model, as is a new scheme to mitigate this effect.

DOI: 10.1103/physrevlett.93.263601

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The time dependence of nonclassical correlations is investigated for two fields

(1,2)

generated by an ensemble of cold cesium atoms via the protocol of Duan et al. [Nature (London) 414, 413 (2001)]. The correlation function

R({t}_{1},{t}_{2})

for the ratio of cross to autocorrelations for the

(1,2)

fields at times

({t}_{1},{t}_{2})

is found to have a maximum value

{R}^{\mathrm{max}﻿}=292\ifmmode\pm\else\textpm\fi{}57

, which significantly violates the Cauchy-Schwarz inequality

R\ensuremath{\le}1

for classical fields. Decoherence of quantum correlations is observed over

{\ensuremath{\tau}}_{d}\ensuremath{\simeq}175\text{ }\text{ }\mathrm{n}\mathrm{s}

, and is described by our model, as is a new scheme to mitigate this effect.

We present the quantum theory for creation of collective atomic memory and generation of nonclassically correlated photon pairs from an ensemble via the protocol of Duan et al. [Nature (London) 414, 413 (2001)]. The temporal evolution of photon numbers, photon statistics, and cross-correlation between the Stokes and anti-Stokes fields is found by solving the equation of motion for atomic spin-wave excitations. We consider a low-finesse cavity model with collectively enhanced signal-to-noise ratio, which remains still considerably large in the free-space limit. Our results describe analytically the dependence of quantum correlations on spin decoherence time and time delay between the write and read lasers and reproduce the observed data very well including the generated pulse shapes, strong violation of Cauchy-Schwarz inequality and conditional generation of anti-Stokes single-photon pulse. The approach we developed may be used also for quantum description of storage and retrieval of quantum information, especially when the statistical properties of nonclassical pulses are studied.

Single photons are generated from an ensemble of cold Cs atoms via the protocol of Duan et al. [Nature (London), ()]]. Conditioned upon an initial detection from field 1 at 852 nm, a photon in field 2 at 894 nm is produced in a controlled fashion from excitation stored within the atomic ensemble. The single-quantum character of field 2 is demonstrated by the violation of a Cauchy-Schwarz inequality, namely w(1(2),1(2)|1(1))=0.24+/-0.05 not > or = 1, where w(1(2),1(2)|1(1)) describes the detection of two events (1(2),1(2)) conditioned upon an initial detection 1(1), with w-->0 for single photons.

We report experimental generation of nonclassically correlated photon pairs from collective emission in a room-temperature atomic vapor cell. The nonclassical feature of the emission is demonstrated by observing a violation of the Cauchy-Schwarz inequality. Each pair of correlated photons is separated by a controllable time delay up to $2\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. This experiment demonstrates an important step towards the realization of the Duan-Lukin-Cirac-Zoller scheme for scalable long-distance quantum communication.

A scheme for the generation of nonclassical pairs of photons in atomic vapors is proposed. The scheme exploits the fact that the cross correlation of the emission of photons from the extreme transitions of a four-level cascade system shows antibunching, unlike the case of the three-level cascade emission, which shows bunching. The Cauchy-Schwarz inequality, which is the ratio of the cross-correlation to the autocorrelation function, in this case is estimated to be

{10}^{3}--{10}^{6}

for controllable time delay, and is one to four orders of magnitude larger compared to previous experiments. The choice of Doppler-free geometry, in addition to the fact that at three-photon resonance the excitation and deexcitation processes occur in a very narrow frequency band, ensures cleaner signals.