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Journal of Modern Optics

Multipartite entanglement in nondegenerate triple-photon down-conversion

Sourish Sarkar, Dilip Kumar Giri

Published Apr 23, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1080/09500340.2026.2662654

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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.
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Nondegenerate triple-photon parametric down-conversion (NTPD) is a potential source for unconditional tripartite non-Gaussian entangled states of continuous variables. Recent experiment has demonstrated strong third-order correlations among bright photon triplets via microwave NTPD in a superconducting cavity [C. W. Sandbo Cheng et al., Phys. Rev. X 10, 011011 (2020)]. Previous theoretic works have revealed that only short-time genuine tripartite non-Gaussian entanglement can be generated in NTPD even in the absence of dissipation. In this paper, we investigate the properties of tripartite non-Gaussian entanglement and steering in the cavity output field by taking into account the cavity dissipation. We first derive experimentally detectable criteria for fully inseparable and genuine tripartite non-Gaussian entanglement and steering. With the criteria, we then find that steady-state tripartite non-Gaussian entanglement and steering can be generated in the output field, although they merely exist in the short-time regime inside the cavity. We also find that the initial cavity-field coherent states can obviously enhance the steady-state and transient tripartite entanglement and steering, in comparison to the case of initial vacuum states. We finally show that the output tripartite non-Gaussian steerable correlations can be applied to the remote generation of negative Wigner-function quantum states by homodyne detection.
Abstract Optical downconversion is a key resource for generating nonclassical states. Very recently, direct nondegenerate triple-photon spontaneous downconversion (NTPSD) with bright photon triplets and strong third-order correlations has been demonstrated in a superconducting device (2020 Phys. Rev. X 10 011011). Besides, linear and nonlinear tripartite entanglement in this process have also been predicted (2018 Phys. Rev. Lett . 120 043601; 2020 Phys. Rev. Lett. 125 020502). In this paper, we consider the generation of nonclassical optical quantum superpositions and investigate nonlinear quantum steering effects in NTPSD. We find that large-size Schrödinger cat states of one downconverted mode can be achieved when the other two modes are subjected to homodyne detection. Also, a two-photon Bell entangled state can be generated when only one mode is homodyned. We further reveal that such ability of remote state steering originates from nonlinear quantum steerable correlations among the triplets. This is specifically embodied by the seeming violation of the Heisenberg uncertainty relation for the inferred variances of two noncommutating higher-order quadratures of downconverted modes, based on the outcomes of homodyne detection on the other mode, i.e., nonlinear quantum steering, compared to original Einstein–Podolsky–Rosen steering. Our results demonstrate non-Gaussian nonclassical features in NTPSD and would be useful for the fundamental tests of quantum physics and implementations of optical quantum technologies.
Quantum entanglement is a crucial resource for a wide variety of quantum technologies. However, the current state-of-art methods to generate quantum entanglement in optomechanical systems are not as efficient as all-optical methods utilizing nonlinear crystals. This article proposes a new scheme in which two single-mode squeezed light fields are injected into an optomechanical cavity. We demonstrate through our numerical simulations that the quantum entanglement can be substantially enhanced with the careful selection of squeezing strength and squeezing angle of the two quadrature squeezed light fields. Our results represent a significant improvement in output bipartite photon-photon entanglement over the previously demonstrated schemes using two coherent light fields as inputs. These simulations predict a maximum increase in bipartite optical entanglement by a factor of about 6, as well as increases in the quantum noise of the output light. A perceived loss of quantum information at certain squeezing angles is attributed to tripartite entanglement between the two optical fields and the optomechanical oscillator (OMO). At particular squeezing angles, the bipartite (or tripartite) entanglement can be increased, thus introducing a method of optically controlling the intracavity entanglement. These mechanics can benefit various optical quantum technologies utilizing optomechanical entanglement and continuous variable quantum optics.
Quantum entanglement is a crucial resource for a wide variety of quantum technologies. However, the current state-of-art methods to generate quantum entanglement in optomechanical systems are not as efficient as all-optical methods utilizing nonlinear crystals. This article proposes a new scheme in which two single-mode squeezed light fields are injected into an optomechanical cavity. We demonstrate through our numerical simulations that the quantum entanglement can be substantially enhanced with the careful selection of squeezing strength and squeezing angle of the two quadrature squeezed light fields. Our results represent a significant improvement in output bipartite photon-photon entanglement over the previously demonstrated schemes using two coherent light fields as inputs. These simulations predict a maximum increase in Gaussian entanglement by a factor of about 6 for lossless input coupling, as well as increases in the quantum noise and non-Gaussianity of the output light. This non-Gaussianity is attributed to tripartite entanglement between the two optical fields and the optomechanical oscillator (OMO). At particular squeezing angles, the Gaussianity can be increased, thus introducing a method of optically controlling the intracavity entanglement. These mechanics can benefit various optical quantum technologies utilizing optomechanical entanglement and continuous variable quantum optics.