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Journal of Experimental and Theoretical Physics

Two-Mode Squeezing and Entangled States of Light in Third Harmonic Generation Process

Sourish Sarkar, Dilip Kumar Giri

Published Jun 1, 2026• 0 citations
Publisher

Abstract

Abstract We theoretically investigate the emergence of nonclassical features, two-mode squeezing, sub-Poissonian photon statistics, and bipartite entanglement, in the third harmonic generation (THG) process, employing a first-order interaction Hamiltonian within the short-time approximation. The study reveals that both first- and second-order squeezing exhibit strong dependence on the input field amplitudes, relative phase, and interaction strength. Asymmetric coherent inputs, where the harmonic mode carries greater intensity than the fundamental, enhance the degree of squeezing and lead to deeper nonclassical minima. The squeezing parameters display periodic phase-dependent oscillations, indicating phase-sensitive control of quantum correlations. Sub-Poissonian photon statistics in the fundamental mode further confirm the quantum nature of the generated light. Entanglement is analyzed through the Duan et al. inseparability criterion and the Hillery–Zubairy (HZ) criteria. While the Duan criterion fails to detect entanglement under purely coherent excitation in the short-time regime, both the HZ-1 and HZ-2 criteria confirm entanglement under specific phase conditions, with HZ-2 exhibiting greater sensitivity at elevated field strengths. These results underscore the potential of THG as a viable platform for the controllable generation of nonclassical light, with implications for continuous-variable quantum optics and integrated quantum photonics.

DOI
10.1134/s1063776126601382

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We present a theoretical study of nonclassical light generation in Nondegenerate Triple-Photon Down-Conversion (NTPDC), using a first-order interaction Hamiltonian within the short-time approximation. The analysis reveals quadrature squeezing and both bipartite and tripartite entanglement, indicating strong multimode quantum correlations. We show that increasing the coherent input amplitude and the nonlinear coupling enhances the degree of two-mode squeezing, while the squeezing depth is strongly controlled by the relative phase, enabling suppression of quantum noise. Bipartite entanglement is stronger and persists over a wider parameter range than tripartite entanglement, which occurs only under symmetric excitation and precise phase matching. The presence of bipartite entanglement is quantitatively verified using the Hillery-Zubairy (HZ) criteria (HZ-1 and HZ-2), with HZ-1 exhibiting higher sensitivity in high-coherence regimes. The results demonstrate that NTPDC is a promising scheme for generating scalable quantum resources for applications in quantum information and integrated photonics.
The nonclassical effects of light in the fifth harmonic generation are investigated by quantum mechanically up to the first-order Hamiltonian interaction. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics in the fundamental mode have also been investigated and found to be sub-Poissonian in nature. It is observed that there is no possibility to produce squeezed light in the harmonic mode up to first-order Hamiltonian interaction. Further, we have found that the normal squeezing in the harmonic mode directly depends upon the fifth power of the field amplitude of the initial pump field up to second-order Hamiltonian interaction. This gives a method of converting higher-order squeezing in the fundamental mode into normal squeezing in the harmonic mode and vice versa. The analytic expression of fifth-order squeezing of the fundamental mode in the fifth harmonic generation is established.
Nonclassical properties exhibited by a chain of cavity modes second harmonic generation in coupled oscillators system, designed by using multichannel optical waveguides, is explored. The solution for the Hamiltonian of the coupled-modes driven by coherent excitation is obtained via an exact formulation of the normal-ordered Fokker-Planck equation. Nonclassical effects, namely the sub-Poissonian photons, squeezing and entanglement are noticed. Multichannel coupling of the coupled oscillators induces new possibilities for correlation between the modes in different channels, henceforth, provides an effective way towards manipulation of quantum light.
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