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Physica Scripta

Generation of a tripartite photonic state via a double-Λ configuration in a four-level system

Jie Yang, Xiang Yan

Published Aug 9, 2024• 0 citations
Publisher

Abstract

Abstract Triphotons have a more abundant energy structure compared to biphotons. Furthermore, as the number of photons increases, excellent properties such as entangled multi-qubit states, high security, flexibility, and information capacity are observed. This leads to a growing demand for multi-body quantum information processing. Here, a method is proposed to generate a three-photon entangled state using a single six-wave mixing process in an atomic ensemble. The research examines the temporal correlation characteristics of the triphoton produced in photon coincidence counting measurements, with a focus on the linear and nonlinear susceptibilities of the six-wave mixing process. These properties primarily depend on the fifth-order nonlinear coupling coefficients responsible for the damping Rabi oscillations and the group delay determined by the longitudinal detuning function. To enhance the nonlinear interaction between the optical field and the atomic ensemble, placing the atomic ensemble in a high-quality cavity and utilizing laser cooling techniques to eliminate the internal Doppler broadening effect in the atomic gas hold promise.

DOI
10.1088/1402-4896/ad6da7

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Abstract Triphotons have a more abundant energy structure compared to biphotons. Furthermore, as the number of photons increases, excellent properties such as entangled multi-qubit states, high security, flexibility, and information capacity are observed. This leads to a growing demand for multi-body quantum information processing. Here, a method is proposed to generate a three-photon entangled state using a single six-wave mixing process in an atomic ensemble. The research examines the temporal correlation characteristics of the triphoton produced in photon coincidence counting measurements, with a focus on the linear and nonlinear susceptibilities of the six-wave mixing process. These properties primarily depend on the fifth-order nonlinear coupling coefficients responsible for the damping Rabi oscillations and the group delay determined by the longitudinal detuning function. To enhance the nonlinear interaction between the optical field and the atomic ensemble, placing the atomic ensemble in a high-quality cavity and utilizing laser cooling techniques to eliminate the internal Doppler broadening effect in the atomic gas hold promise.
Abstract Compared with biphotons, the three‐body photons have a more plentiful energy construction. Further, excellent properties such as entangled multiqubit states, high security, flexibility, and information capacity are observed as the increased number of photons is manipulated, in turn increasing the need for a multiple‐body quantum information process. Here, a novel method is proposed to generate natural narrowband three‐body photons of W state, entangled in time (or energy) via a single step of six‐wave mixing process (SWMP). Emphasizing on the linear and nonlinear susceptibilities of the SWMP, the properties of temporal correlation of the generated triphoton in the photon coincidence counting measurements are studied. Based on the photon–atom interfaces, these susceptibilities compete or coexist with each other. Meanwhile, in a dressed‐state picture, the nonlinear susceptibility decides the temporal correlation of the triphoton wave packet as damped multiperiodic Rabi oscillation, suggesting the property of the high‐dimensional time−energy entangled triphoton state. Moreover, combining the topology energy level constructions with the optical responses is a significant method for investigating the peculiarity in the temporal correlation of the generated three‐body photons.
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.
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.
Narrow-band multiphoton entanglement sources serve as a core enabling resource for advanced quantum information technologies. Recently, researchers have directly generated energy-time entangled triphoton W states in a hot atomic medium via spontaneous six-wave mixing for the first time. However, a rigorous theoretical framework for this process remains lacking to date, confining our understanding to a mere extension of the biphoton model. Here, we analytically investigate the generation mechanism of energy-time entangled triphotons and their classically controllable optical properties in an electromagnetically induced transparency-assisted five-level cold atomic system. Notably, triphoton generation follows strict temporal ordering, resulting in asymmetric quantum interference in triple coincidence counts--unreplicable and unexplainable by the inherently symmetric biphoton model. These results establish a rigorous physical framework for spontaneous six-wave mixing-generated triphotons, clarify their distinctions from states produced via cascaded nonlinear models, and substantially advance their utility in quantum information protocols.
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)].
In quantum communication and quantum computation, adding each entangled photon leads to an exponential increase in communication and computational capabilities. Utilizing a fifth-order nonlinear process, narrow-band non-Gaussian W-triphotons are experimentally generated through the spontaneous six -wave mixing (SSWM), but the manipulation of such entangled state in the group delay regime is still lacked. For the first time, the observation of optical precursors at the triphoton level is reported through the SSWM process. By appropriately adjusting the optical depth, optical precursors are effectively separated from the main wave through utilizing the slow-light effect to manipulate the triphoton temporal correlations in the group delay regime. In biphoton and conditional two-photon, the intensity ratio between the precursor and the main wave is tunable by adjusting the detuning and power of the laser. These pivotal breakthroughs mark a significant advancement in the study of optical precursors and open new possibilities for their application in quantum technologies.