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arXiv:quant-ph/9910094 · Physical Review Letters

Nonlinear Optics and Quantum Entanglement of Ultraslow Single Photons

Mikhail D. Lukin, Ataç İmamoğlu

Published Feb 14, 2000• 619 citations
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Abstract

Two light pulses propagating with slow group velocities in a coherently prepared atomic gas exhibit dissipation-free nonlinear coupling of an unprecedented strength. This enables a single-photon pulse to coherently control or manipulate the quantum state of the other. Processes of this kind result in generation of entangled states of radiation field and open up new prospectives for quantum information processing.

DOI
10.1103/physrevlett.84.1419

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Two light pulses propagating with slow group velocities in a coherently prepared atomic gas exhibit dissipation-free nonlinear coupling of an unprecedented strength. This enables a single-photon pulse to coherently control or manipulate the quantum state of the other. Processes of this kind result in generation of entangled states of radiation field and open up new prospectives for quantum information processing.
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We investigate the nonlinear interaction between two photons in a single-input pulse at an atomic two-level nonlinearity. A one-dimensional model for the propagation of light to and from the atom is used to describe the precise spatiotemporal coherence of the two-photon state. It is shown that the interaction generates spatiotemporal entanglement in the output state similar to the entanglement observed in parametric down-conversion. A method of generating photon pairs from coherent pump light using this quantum-mechanical four-wave mixing process is proposed.
We have studied quantum entanglement generation using nonlinear interaction of slowly propagating quantum field in a solid medium. Due to enhanced nonlinearity based on electromagnetically induced transparency and standing light phenomenon, a reversible nondegenerate four-wave mixing processing results in quantum entanglement generation. Our attention is to determine nonlinear perspectives of the entanglement with single photon fields. To accomplish the quantum entanglement based on the slow light involved standing light scheme, non-Doppler broadening has been required, where multiple atomic coherences have been the basis in a time-reversed manner. This study is potential for nonlinear optics application to quantum information science such as quantum computing and quantum memories using macroscopic optical medium.
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 propose a scheme to realize slow-light soliton beam splitters by using a tripod-type four-level atomic system. We show that optical solitons, which have ultraslow propagation velocity and ultralow generation power, can be generated in the system via electromagnetically induced transparency and can be stored and retrieved with high efficiency and fidelity. In particular, a nonlinear beam splitter that splits one optical soliton into two or more ones can be obtained by switching on and off of two or more control laser fields subsequently. The results reported here open a route not only for active manipulation of nonlinear optical pulses in multistate quantum systems but also for promising applications in optical information processing and transmission.