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Journal of Experimental and Theoretical Physics

Bipartite Entanglement in Nondegenerate Sum Frequency Generation under Second-Order Hamiltonian Interaction

Dilip Kumar Giri, Ghizal Firdous Ansari

Published Aug 1, 2026• 0 citations
Publisher

Abstract

Abstract We present a theoretical investigation of two-mode squeezing and bipartite entanglement in the nondegenerate sum-frequency generation (NSFG) process, based on a second-order Hamiltonian under the short-time approximation. Both first- and second-order amplitude squeezing are shown to depend strongly on the coherent input amplitudes, nonlinear coupling strength, and relative phase. Asymmetric input configurations, especially those with enhanced signal-mode intensity, substantially enhance squeezing and deepen nonclassicality. In particular, second-order quadrature squeezing proves highly sensitive to phase and amplitude imbalances, making it a robust probe of higher-order quantum correlations. Entanglement is assessed using the Duan inseparability criterion and both variants of the Hillery–Zubairy (HZ) criteria. Under coherent excitation, the Duan condition approaches the separability threshold, indicating notable entanglement. Both HZ-1 and HZ-2 reveal bipartite entanglement under suitable field configurations, with HZ-2 displaying greater sensitivity at higher field intensities. The entanglement primarily resides in the pump modes, which symmetrically engage in the nonlinear interaction. These findings highlight the critical role of field asymmetry and higher-order effects in quantum-state engineering, establishing NSFG as a promising, tunable platform for generating nonclassical light in integrated photonics and continuous-variable quantum technologies.

DOI
10.1134/s106377612660203x

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We demonstrate production of short wavelength beams with nonclassical intensity correlations and quadrature entanglement using second harmonic generation in a nonlinear resonator with two output ports. The two output beams at the harmonic frequency have no direct interaction but are both nonlinearly coupled to a common pump beam. The nonlinear coupling produces amplitude and phase correlations between the beams which results in quadrature entanglement. The output beams at λ = 428.5 nm are shown to exhibit 0.6 dB of amplitude quadrature squeezing, 0.9 dB of nonclassical intensity correlations, and 0.3 dB of entanglement using about 30 mW of pump power.