Generation of energy-time entangled triphotons in a six-level cold atomic system

TL;DR

This paper investigates the generation of energy-time-entangled triphotons in a six-level cold atomic ensemble, revealing complex nonlinear susceptibilities and unique entanglement properties crucial for quantum information applications.

Contribution

It provides a detailed analysis of triphoton generation mechanisms in six-level systems, highlighting the role of fifth-order nonlinear susceptibility and temporal correlations.

Findings

Triphoton generation involves two sets of spontaneous six-wave mixing.

Triphoton counts show asymmetrically damped Rabi oscillations.

Conditional two-photon states preserve temporal correlation properties.

Abstract

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 $W$-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.