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Physical Review A

Generation of frequency-correlated narrowband biphotons from four-wave mixing in cold atoms

Sujun Yun, Jianming Wen, Ping Xu, Min Xiao, S. N. Zhu

Published Dec 27, 2010• 16 citations
Publisher

Abstract

Generation of frequency-correlated narrowband biphotons from the four-wave mixing process is theoretically analyzed through manipulating optical properties of light propagation inside a cold atomic ensemble. In contrast with the spontaneous parametric down-conversion case, we find a much looser condition, which allows producing such frequency-correlated paired photons. We propose a two-photon temporal conditional correlation measurement to detect these photons. In addition, our results provide other evidence for observing backward pulse propagation from the viewpoint of two-photon correlation measurement.

DOI
10.1103/physreva.82.063830

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Generation of frequency-correlated narrowband biphotons from the four-wave mixing process is theoretically analyzed through manipulating optical properties of light propagation inside a cold atomic ensemble. In contrast with the spontaneous parametric down-conversion case, we find a much looser condition, which allows producing such frequency-correlated paired photons. We propose a two-photon temporal conditional correlation measurement to detect these photons. In addition, our results provide other evidence for observing backward pulse propagation from the viewpoint of two-photon correlation measurement.
Generating nonclassical light offers a benchmark tool for fundamental research and potential applications in quantum optics. Conventionally, it has become a standard technique to produce nonclassical light through the nonlinear optical processes occurring in nonlinear crystals. We describe this process using cold atomic-gas media to generate such nonclassical light, especially focusing on narrowband biphoton generation. Compared with the standard procedure the new biphoton source has such properties as long coherence time, long coherence length, high spectral brightness, and high conversion efficiency. Although there exist two methodologies describing the physical process, we concentrate on the theoretical aspect of the entangled two-photon state produced from the four-wave mixing in a multilevel atomic ensemble using perturbation theory. We show that both linear and nonlinear optical responses to the generated fields play an important role in determining the biphoton waveform and, consequently, on the two-photon temporal correlation. There are two characteristic regimes determined by whether the linear or nonlinear coherence time is dominant. In addition, our model provides a clear physical picture that brings insight into understanding biphoton optics with this new source. We apply our model to recent work on generating narrowband (and even subnatural linewidth) paired photons using the technique of electromagnetically induced transparency and slow-light effect in cold atoms and find good agreement with experimental results.
In this short review some essentials concerning creation and testing of nonclassically correlated photons (biphotons) are given. In the introduction we remind the role which the experimentally produced entangled states have been playing for the foundations of the quantum physics, by witnessing against the model of local hidden variables. The well established sources of biphotons are based on spontaneous parametric down conversion in nonlinear crystals. A popular source with two BBO crystals is described, which generates pairs of photons nearly maximally entangled in polarization. Crystalbased sources rely on intrinsically broadband transitions, therefore thus produced biphotons are also broadband. Additional efforts (like applying optical cavities) are needed to reach narrowband biphotons which would comply with the requirements of some implementations in the quantum communication science. The topical issue of our article is a review of another, more recent approaches based on narrowband transitions between levels in cold atoms. Such method provides naturally narrowband biphotons. First, the principles are given of an atomic source of nonclassically paired photons, which is operated in a pulsed write-read mode. Such source is based on two separated in time Raman transitions triggered successively in two Λ-schemes. Next, cw-mode sources based (mainly) on spontaneous four wave mixing process (SFWM) are presented in a generic four-level scheme. Some underlying physics is sketched and profiles of biphoton correlation functions in the time domain are explained. Among other presented SFWM sources, one proves in testing high degree entanglement of generated biphotons, both in time-frequency and polarization (hyperentanglement).
The nonclassical photon pair, generated via a parametric process, is naturally endowed with a specific form of frequency-time quantum correlations. Here, we report complete control of frequency-time quantum correlations of narrow-band biphotons generated via spontaneous four-wave mixing in a cold atomic ensemble. We have experimentally confirmed the generation of frequency-anticorrelated, frequency-correlated, and frequency-uncorrelated narrow-band biphoton states, as well as verifying the strong nonclassicality of the correlations. Our work opens up new possibilities for engineering narrow-band entangled photons for various quantum optical and quantum information applications.
We observe time-correlated four photons within a correlation window of 20ns from spontaneous four-wave mixing via a double-Lambda scheme in a cold cloud of Rb-87 atoms. In contrast to high-power pulsed pumping of chi^(2) nonlinear processes in crystals, our scheme generates correlated four-photon states by direct continuous-wave pumping at nominal powers. We verify the presence of genuinely correlated four-photon states over accidentals by higher-order intensity cross-correlation measurements and accidental subtraction. We infer a time-correlated four-photon generation rate of 2.5(4)x10^6 counts per second close to saturation. The photons produced are near-resonant with atomic transitions, and have a bandwidth in the order of MHz, making them readily compatible with quantum networking applications involving atoms.
Non-classical paired photons are generated by a four-wave mixing process in a far-detuning three-level system with cold atoms. A violation of the Cauchy-Schwartz inequality of a factor of 310 is observed. This phenomenon shows that paired photons have a non-classical correlation. The experimental results are compared with theoretical results obtained using perturbation theory. The oscillation frequencies of the two-photon intensity correlation functions are in reasonable agreement with the effective Rabi frequencies of the coupling laser. However, we find that the dephasing rates (or decay rates) observed are far larger than the theoretical values.