Generation of a coherent squeezed-like state defined with the Lie–Trotter product formula using a nonlinear photonic crystal

In this paper, we investigate how to generate coherent squeezed-like light using a nonlinear photonic crystal. Because the photonic crystal reduces the group velocity of the incident light, if it is composed of a material with a second-order nonlinear optical susceptibility χ ( 2 ) , the interaction between the nonlinear material and the light passing through it strengthens and the quantum state of the emitted light is largely squeezed. Thus, we can generate a coherent squeezed-like light with a resonating cavity in which the nonlinear photonic crystal is placed. This coherent squeezed-like state is defined with the Lie–Trotter product formula and its mathematical expression is different from those of conventional coherent squeezed states. We show that we can obtain this coherent squeezed-like state with a squeezing level 15.9 dB practically by adjusting the physical parameters for our proposed method. Feeding the squeezed light whose average number of photons is given by one or two into a beam splitter and splitting the flow of the squeezed light into a pair of entangled light beams, we estimate their entanglement quantitatively. This paper is a sequel to Azuma (2022 J. Phys. D: Appl. Phys. 55 315106).