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arXiv:2503.07257 · Physical Review A

Steady-state tripartite non-Gaussian entanglement and steering in the output field from intracavity triple-photon parametric down-conversion

Miaomiao Wei, Huatang Tan

Published Aug 27, 2024• 3 citations
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Abstract

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.

DOI
10.1103/physreva.110.023729

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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.
Nonlocal quantum correlations are important for potential applications in quantum optics and quantum information. Multipartite quantum correlations are relevant to access to high-dimensional systems such as qudits. There are also different proposals for the generation of quantum steering based on nonlinear systems and cavities. Here, we consider the Hamiltonian of a triple photon parametric down-conversion process to investigate the regions where bipartite and tripartite steering are generated. In this model, three beams interact with a nonlinear medium inside a cavity through the process of parametric down-conversion, creating three output fields. The positive P representation is used to analyze this system and steady-state solutions are obtained. We calculated the intracavity fluctuation spectra to analyze steering in the frequency domain and used different criteria to certify this quantum correlation. We certified bipartite steering for the three output fields from the cavity. In the case of full tripartite two-way steering inseparability, it is also present for all the bipartitions under consideration. Our results show regimes where bipartite and tripartite steering is certified for this model.
The generation of entangled photons through spontaneous parametric down-conversion (SPDC) is a critical resource for many key experiments and technologies in the domain of quantum optics. Historically, SPDC was limited to the generation of photon pairs. However, the use of the strong nonlinearities in circuit quantum electrodynamics has recently enabled the observation of three-photon SPDC (3P-SPDC). Despite great interest in the entanglement structure of the resultant states, entanglement between photon triplets produced by a 3P-SPDC source has still not been confirmed. Here, we report on the observation of genuine tripartite non-Gaussian entanglement in the steady-state output field of a 3P-SPDC source consisting of a superconducting parametric cavity coupled to a transmission line. We study this non-Gaussian tripartite entanglement using an entanglement witness built from three-mode correlation functions, observing a maximum violation of the bound by 15 standard deviations of the statistical noise. Furthermore, we find strong agreement between the observed and the analytically predicted scaling of the entanglement witness. We then explore the impact of the temporal function used to define the photon mode on the observed value of the entanglement witness.
Triple-photon states generated by three-mode spontaneous parametric down-conversion are the paradigm of unconditional non-Gaussian states, essential assets for quantum advantage. How to fully characterize their non-Gaussian entanglement remains however elusive. We propose here a set of sufficient and necessary conditions for separability of the broad family of spontaneously generated three-mode non-Gaussian states. We further derive state-of-the-art conditions for genuine tripartite non-Gaussian entanglement, the strongest class of entanglement. We apply our criteria to triple-photon states revealing that they are fully inseparable and genuinely entangled in moments of order 3n. Our results establish a systematic framework for characterizing the entanglement of triple-photon states and thus fostering their application in quantum information protocols.
Triple-photon states generated by three-mode spontaneous parametric down-conversion are the paradigm of unconditional non-Gaussian states, essential assets for quantum advantage. How to fully characterize their non-Gaussian entanglement remains however elusive. We propose here a hierarchy of sufficient and necessary conditions for separability of the broad family of spontaneously-generated three-mode non-Gaussian states. We further derive state-of-the-art conditions for genuine tripartite non-Gaussian entanglement, the strongest class of entanglement. We apply our criteria to triple-photon states revealing that they are fully inseparable and genuinely entangled in moments of order 3n. Our results establish a systematic framework for characterizing the entanglement of triple-photon states and thus fostering their application in quantum information protocols.
We show that the states generated by a three-mode spontaneous parametric down-conversion (SPDC) interaction Hamiltonian possess tripartite entanglement of a different nature to other paradigmatic three-mode entangled states generated by the combination of two-mode SPDC interactions. While two-mode SPDC generates Gaussian states whose entanglement can be characterized by standard criteria based on two-mode quantum correlations, these criteria fail to capture the entanglement generated by three-mode SPDC. We use criteria built from three-mode correlation functions to show that the class of states recently generated in a superconducting-circuit implementation of three-mode SPDC ideally have tripartite entanglement, contrary to recent claims in the literature. These criteria are suitable for triple SPDC but we show that they fail to detect tripartite entanglement in other states which are known to possess it, which illustrates the existence of two fundamentally different notions of tripartite entanglement in three-mode continuous-variable systems.