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arXiv:quant-ph/0401147 · Physical Review Letters

Single-Photon Generation from Stored Excitation in an Atomic Ensemble

C. W. Chou, Sergey Vladimirovich Polyakov, A. Kuzmich, Harry J. Kimble

Published May 25, 2004• 253 citations
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Abstract

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.

DOI
10.1103/physrevlett.92.213601

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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.
In the famous quantum communication scheme developed by Duan et al. [L.M. Duan, M.D. Lukin, J.I. Cirac, and P. Zoller, Nature (London) 414 (2001) 413 ], the probability of successful generating a symmetric collective atomic state with a single-photon emitted have to be far smaller than 1 to obtain an acceptable entangled state. Based on strong dipole-dipole interaction between two Rydberg atoms, two simultaneous excitations in an atomic ensemble are greatly suppressed, which makes it possible to excite a mesoscopic cold atomic ensemble into a near-ideal singly-excited symmetric collective state accompanied by a signal-photon with near unity success probability.
The time dependence of nonclassical correlations is investigated for two fields (1,2)(1,2)(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(t1,t2)R({t}_{1},{t}_{2})R(t1​,t2​) for the ratio of cross to autocorrelations for the (1,2)(1,2)(1,2) fields at times (t1,t2)({t}_{1},{t}_{2})(t1​,t2​) 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 report an investigation to establish the physical mechanisms responsible for decoherence in the generation of photon pairs from atomic ensembles, via the protocol of Duan et al. for long-distance quantum communication [Nature (London) 414, 413 (2001)] and present the experimental techniques necessary to properly control the process. We develop a theory to model in detail the decoherence process in experiments with magneto-optical traps. The inhomogeneous broadening of the ground state by the trap magnetic field is identified as the principal mechanism for decoherence. The theory includes the Zeeman structure of the atomic hyperfine levels used in the experiment, and the polarization of both excitation fields and detected photons. In conjunction with our theoretical analysis, we report a series of measurements to characterize and control the coherence time in our experimental setup. We use copropagating stimulated Raman spectroscopy to access directly the ground-state energy distribution of the ensemble. These spectroscopic measurements allow us to switch off the trap magnetic field in a controlled way, optimizing the repetition rate for single-photon measurements. With the magnetic field off, we then measure nonclassical correlations for pairs of photons generated by the ensemble as a function of the storage time of the single collective atomic excitation. We report coherence times longer than $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, corresponding to an increase of two orders of magnitude compared to previous results in cold ensembles. The coherence time is now two orders of magnitude longer than the duration of the excitation pulses. The comparison between these experimental results and the theory shows good agreement. Finally, we employ our theory to devise ways to improve the experiment by optical pumping to specific initial states.
Photons are good candidates for carrying quantum information because they are very stable particles: they interact weakly with the medium and barely with each other. However, this has drawbacks when you want to process the information because, in this case, it is preferable to have photon-photon interactions. For example, for applications in quantum repeaters, such interactions would allow deterministic Bell state measurements, increasing the entanglement distribution rate between two remote nodes. Getting two photons to interact with each other efficiently requires mapping them into a nonlinear medium at the single-photon level, that is, a medium that reacts differently when it interacts with a single photon than when it does with two. Such strong nonlinearity has been demonstrated with Rydberg atoms, which are atoms excited to a state with a high principal quantum number. In this thesis we have performed nonlinear quantum optics experiments using an ensemble of cold Rydberg atoms, where we have studied the properties of the quantum light emitted by these atoms. First, we demonstrated nonlinearities at the single-photon level. To reach this stage, we made several improvements to the previous experimental setup available in the group, of which the implementation of a dipole trap was especially relevant. We evidence quantum nonlinearity by measuring photon antibunching for the transmitted light after interacting with the Rydberg state under electromagnetically induced transparency (EIT). We also showed the generation of single photons on-demand after storing weak coherent states of light pulses as collective Rydberg excitations. Then, we studied the variation of the light statistic throughout the output pulse after propagating through the medium as Rydberg polaritons, which are superposition states of light and Rydberg excitations. We showed that the properties at the beginning and the end of the pulse were different from those of the steady state. In particular, the light detected after the input pulse was abruptly turned off gave much stronger suppression of two-photon events. Then, we investigated how to exploit this effect to generate single photons on demand. To do this, we analyzed the quality of the single photons detected at the end of the pulse as a function of the detection probability and compared the results with those obtained by storing the input pulse as collective Rydberg excitations. We showed that the photons were generated more efficiently when increasing the detection window at the cost of deteriorating the single photons statistics. Finally, we investigated the indistinguishability of the photons emitted by our Rydberg atomic ensemble, a crucial property for using Rydberg atoms as nodes in quantum networks. We also compared the single photons generated after storage under EIT conditions with those obtained using a two-photon Raman excitation to the Rydberg state. We measured the indistinguishability by making them interfere with weak coherent states of light in a Hong-Ou-Mandel experiment. And we showed that, although we obtained better photon statistics under EIT conditions, the indistinguishability from those obtained with Raman excitation was significantly higher.
We report significant improvements in the retrieval efficiency of a single excitation stored in an atomic ensemble and in the subsequent generation of strongly correlated pairs of photons. A 50% probability of transforming the stored excitation into one photon in a well-defined spatio-temporal mode at the output of the ensemble is demonstrated. These improvements are illustrated by the generation of high-quality heralded single photons with a suppression of the two-photon component below 1% of the value for a coherent state. A broad characterization of our system is performed for different parameters in order to provide input for the future design of realistic quantum networks.