Generation of single-mode and two-mode quantum squeezed states of light by degenerate four-wave mixing in a plasmonic...

Squeezed states of light represent one of the most fundamental concepts in quantum optics. They play a crucial role in various fields of science, quantum technology, and photonics, with applications in quantum information processing, quantum computation, quantum sensing, and gravitational wave detection. In this paper, we propose a plasmonic waveguide for the generation of squeezed states via four-wave mixing. The designed waveguide consists of two gold layers deposited on a SiO₂ substrate. DDMEBT, an organic material with a high third-order nonlinear refractive index, is placed on the gold layers and fills the gap between them. To determine the effective refractive indices and corresponding mode wavelengths, the waveguide was simulated using the Mode Analysis module of COMSOL Multiphysics. The coupled equations describing degenerate four-wave mixing for the pump, signal, and idler fields were derived. Furthermore, we present the quantum mechanical formulation of four-wave mixing in terms of expectation values and fluctuations, introducing both single-mode and two-mode squeezing factors. The influence of pump power on the squeezing factor is analyzed, revealing that higher pump powers enhance the squeezing level and reduce the required propagation length to reach maximum squeezing. Compared with previous studies based on second-harmonic generation, the required waveguide length to achieve maximum squeezing in our proposed structure is reduced by three order of magnitude. The detrimental effects of optical losses on the squeezing process are also investigated. Finally, the impact of the interlayer gap width on the squeezing factor is examined, demonstrating that increasing the gap between the gold layers leads to a degradation in the squeezing quality.