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Acta Physica Sinica

Generation of narrowband triphoton frequency-entangled states via cold-atom ensembles

Rui Liu, Yu Ya-Fei, Zhi‐Ming Zhang

Published Jan 1, 2014• 1 citation
Publisher

Abstract

We propose a scheme for the generation of narrowband triphoton frequency-entangled states. This scheme uses the four-wave mixing and the electromagnetically induced transparency in two cold-atom ensembles. By using the second-order perturbation theory, some relevant calculations are performed. By analyzing the coincidence-counting rate, we study the correlation and nonclassical properties of these states, and find that they have a similar feature to that of the discrete-variable W state, and can show the antibunching effect.

DOI
10.7498/aps.63.144203

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We propose a scheme for the generation of narrowband triphoton frequency-entangled states. This scheme uses the four-wave mixing and the electromagnetically induced transparency in two cold-atom ensembles. By using the second-order perturbation theory, some relevant calculations are performed. By analyzing the coincidence-counting rate, we study the correlation and nonclassical properties of these states, and find that they have a similar feature to that of the discrete-variable W state, and can show the antibunching effect.
We propose a method to generate a narrowband triphoton W state entangled in time (or energy) via two four-wave mixing processes in cold atomic gas media. The calculation of such a triphoton W state is performed with second-order perturbation theory. To characterize the optical properties of the state, we analyze the two-photon and three-photon temporal correlations in the photon coincidence counting measurement. Considering the role of determining the time coherence of triphotons between the nonlinear susceptibilities and phase matchings, we concentrate on two regimes, damped Rabi oscillation and group delay, to look at the temporal correlations. To further enhance the nonlinear interactions, it may be promising to consider cold atoms confined within hollow fibers or loaded into a high-Q cavity.
We explore a mechanism for producing time-frequency entangled photon pairs (termed a biphoton) from an ensemble of atom-like solid-state quantum emitters. Four distinct energy levels of the solid-state system render four spin-conserving optical transitions as observed in color centers. This feature opens up the possibility to generate a four-wave mixing biphoton based on an electromagnetic induced transparency (EIT) for long-coherence quantum communication as demonstrated in cold atomic systems. We propose a narrow EIT window below a lifetime-limited linewidth of a SiV− in diamond, assuming a few hundred MHz. Consequently, the EIT-induced narrowband guarantees biphoton coherence time to be at least a few tens of a nanosecond without a cavity. Assessing the criteria of solid-state parameters applicable to the existing biphoton model from cold atoms will accelerate solid-state biphoton source research. This study shows that a realization of negligible ground state dephasing of a solid-state sample will be a crucial step toward a solid-state biphoton generation for more than a 100 ns time scale with a subnatural atomic linewidth of a few MHz.
Multiphoton entangled states are pivotal resources for implementing optical quantum information protocols. Recently, energy-time-entangled triphotons have been observed in hot atomic ensembles. However, in these protocols, the complex fifth-order nonlinear susceptibility entailed by four- or five-level systems limits our understanding of triphoton generation. Here, to directly capture the generation mechanism of triphotons and their associated optical properties, we investigate the generation of energy-time-entangled triphotons in a six-level cold atomic ensemble. The fifth-order nonlinear susceptibility indicates the existence of two sets of spontaneous six-wave mixing in the system. Notably, triphoton generation in this system is subject to stringent timing constraints. Collectively, these characteristics give rise to threefold coincidence counts, which -- dominated by the fifth-order nonlinear susceptibility -- exhibit asymmetrically damped Rabi oscillations in the two-dimensional time domain. Furthermore, we analytically derive that the temporal correlation properties of conditional two-photon states are preserved -- a unique feature of WWW-class tripartite entanglement. These results not only lay the groundwork for the experimental preparation of triphotons using six-level systems but also provide key support for understanding the generation mechanism of triphotons involving more complex fifth-order nonlinear susceptibilities.
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.
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.