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Physical Review Letters

Four-Wave Mixing and Biphoton Generation in a Two-Level System

Shengwang Du, Jianming Wen, Morton H. Rubin, G. Y. Yin

Published Jan 29, 2007• 130 citations
Publisher

Abstract

We find that in a two-level system there are two kinds of four-wave mixing processes which destructively contribute to the third-order nonlinear susceptibility. In a paired-photon generation scheme by using a single retroreflected pump beam, these two processes occur with definite time orders. The biphoton temporal correlation, which is measured with a back-to-back geometry in a laser-cooled two-level atomic ensemble, shows a damped Rabi oscillation and photon antibunching. Without suppressing the background of Rayleigh scattering, the upper limit of Cauchy criteria is estimated.

DOI
10.1103/physrevlett.98.053601

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We find that in a two-level system there are two kinds of four-wave mixing processes which destructively contribute to the third-order nonlinear susceptibility. In a paired-photon generation scheme by using a single retroreflected pump beam, these two processes occur with definite time orders. The biphoton temporal correlation, which is measured with a back-to-back geometry in a laser-cooled two-level atomic ensemble, shows a damped Rabi oscillation and photon antibunching. Without suppressing the background of Rayleigh scattering, the upper limit of Cauchy criteria is estimated.
We have theoretically studied the space-time entangled biphoton state generated from a two-level atomic system. In the photon counting measurement, the two-photon coincidence counting rate is a damped oscillation. The oscillation period is determined by the effective Rabi frequency and the damping rate is determined by the linewidth of the inhomogeneous-broadened ground state and the dipole dephasing rate. In an optical-pathway-balanced configuration, the two-photon temporal correlation shows an antibunching effect which corresponds to the interference between two types of nonlinear four-wave mixing processes occurring in such a two-level system. The visibility of the normalized second-order quantum coherence function ${g}^{(2)}(\ensuremath{\tau})$ increases along with the increase of the effective Rabi frequency, but has an upper limit at 45%. We find agreement between the theory and the experiments [P. Kolchin et al., Phys. Rev. Lett. 97, 113602 (2006); S. Du, J.-M. Wen, M. H. Rubin, and G. Y. Yin, ibid 98, 053601 (2007)].
The interference of degenerate four-wave mixing (FWM) in three-level systems is examined in both the classical and quantum regimes with a backward configuration. In classical FWM, we find that the phase difference between two indistinguishable FWM transition paths can be varied by different driving laser parameters, and leads to interference in the amplitude and polarization of the generated conjugate field. In the paired-photon generation case, the interference in the nonlinearity disappears because of the time ordering in biphoton generation. However, because of the slow group velocity at the degenerate frequency and polarization, the biphoton-amplitude interference between two Feynman paths can erase the time-ordering information at the detectors. For small group delay, the biphoton correlation, determined by the third-order nonlinearity, shows antibunching and damped Rabi oscillations. For large group delay, where the biphoton bandwidth is determined by phase matching, we show that the biphoton interference leads to a bunching effect. The feasibility of generating polarization entanglement is also discussed.
We have theoretically analyzed nonclassical paired photons generated spontaneously from a four-level inverted-Y atomic system. We discuss the feasibility of biphoton generation due to different pumping arrangements. Two types of correlated photon pair emissions have been carefully examined: dressed cascade and dressed double-$\ensuremath{\Lambda}$ emissions. In the dressed cascade two-photon emission, the coincidence counting rate may exhibit a damped Rabi oscillation, in contrast with a simple exponential decay feature in the literatures. In the dressed double-$\ensuremath{\Lambda}$ configuration, we show that not only is the temporal correlation of entangled Stokes--anti-Stokes photons in agreement with discussions presented by Wen et al. [Phys. Rev. A 76, 013825 (2007)], but also the oscillation period may be manipulated by altering either the control Rabi frequency or the dressing Rabi frequency or both. All the observed damped Rabi oscillations in the two-photon coincidences result from the destructive interference among the possible four-wave mixing processes occurring in the atom-field interaction system. This feature of the two-photon amplitude is governed by the convolution between the phase matching and third-order nonlinear susceptibility. The methodology adopted here can be applied to other atomic-level configurations and provides a useful tool to study the spectroscopy of the system. The generated narrow-band photon pairs may have potential applications in long-distance quantum communication and quantum information processing.
Abstract We investigate the parametrically amplified four-wave mixing, spontaneous parametric four-wave-mixing, second- and fourth-order fluorescence signals coming from the four-level double-Λ electromagnetically induced transparency system of a hot 85Rb atomic vapor. The biphoton temporal correlation is obtained from spontaneous parametric four-wave-mixing and fourth-order fluorescence processes. Meanwhile, we first observed the biphoton Rabi oscillation with a background of linear Rayleigh scattering and uncorrelated second-order fluorescence. The outcomes of the investigation may contribute potentially to the applications in dense coding quantum communication systems.
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.