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Entropy

Entanglement and Photon Anti-Bunching in Coupled Non-Degenerate Parametric Oscillators

Yoshitaka Inui, Y. Yamamoto

Published May 17, 2021• 8 citations
Publisher

Abstract

We analytically and numerically show that the Hillery-Zubairy's entanglement criterion is satisfied both below and above the threshold of coupled non-degenerate optical parametric oscillators (NOPOs) with strong nonlinear gain saturation and dissipative linear coupling. We investigated two cases: for large pump mode dissipation, below-threshold entanglement is possible only when the parametric interaction has an enough detuning among the signal, idler, and pump photon modes. On the other hand, for a large dissipative coupling, below-threshold entanglement is possible even when there is no detuning in the parametric interaction. In both cases, a non-Gaussian state entanglement criterion is satisfied even at the threshold. Recent progress in nano-photonic devices might make it possible to experimentally demonstrate this phase transition in a coherent XY machine with quantum correlations.

DOI
10.3390/e23050624

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We analytically and numerically show that the Hillery-Zubairy's entanglement criterion is satisfied both below and above the threshold of coupled non-degenerate optical parametric oscillators (NOPOs) with strong nonlinear gain saturation and dissipative linear coupling. We investigated two cases: for large pump mode dissipation, below-threshold entanglement is possible only when the parametric interaction has an enough detuning among the signal, idler, and pump photon modes. On the other hand, for a large dissipative coupling, below-threshold entanglement is possible even when there is no detuning in the parametric interaction. In both cases, a non-Gaussian state entanglement criterion is satisfied even at the threshold. Recent progress in nano-photonic devices might make it possible to experimentally demonstrate this phase transition in a coherent XY machine with quantum correlations.
We investigate the steady-state photon-number squeezing and quantum entanglement in a network of nondegenerate optical parametric oscillators (NOPOs). We treat each NOPO with Shen's Raman laser model, whose lasing mode provides a photon-number-squeezed state. Two dissipatively coupled NOPOs satisfy Hillery-Zubairy's HZ1HZ1HZ1 entanglement criterion if they are pumped far above the threshold and the dissipative coupling is sufficiently larger than the NOPO cavity loss.
Non-Gaussian continuous-variable states play a central role both in the foundations of quantum theory and for emergent quantum technologies. In particular, ``cat states,'' i.e., two-component macroscopic quantum superpositions, embody quantum coherence in an accessible way and can be harnessed for fundamental tests and quantum information tasks alike. Degenerate optical parametric oscillators can naturally produce single-mode cat states and thus represent a promising platform for their realization and harnessing. We show that a dissipative coupling between degenerate optical parametric oscillators extends this to two-mode entangled cat states, i.e., two-mode entangled cat states are naturally produced under such dissipative coupling. While overcoming single-photon loss still represents a major challenge towards the realization of sufficiently pure single-mode cat states in degenerate optical parametric oscillators, we show that the generation of two-mode entangled cat states under such dissipative coupling can then be achieved without additional hurdles. We numerically explore the parameter regime for the successful generation of transient two-mode entangled cat states in two dissipatively coupled degenerate optical parametric oscillators. To certify the cat-state entanglement, we employ a tailored, variance-based entanglement criterion, which can robustly detect cat-state entanglement under realistic conditions.
Abstract Continuous variable multipartite entanglement is an important resource in quantum optics and quantum information. Non-degenerate optical parametric oscillator (NOPO), generally working in a resonant regime, can generate high quality tripartite entanglement. However, the detuning in a real experiment is inevitable and sometimes necessary, for instance, in an optomechanical system. We calculate the tripartite entanglement from a detuned triply quasi-resonant NOPO. Unlike the previous literature using inseparability criterion, we use the positivity of partial transpose, a sufficient and necessary criterion, to characterize the tripartite entanglement with full inseparability generated from a detuned NOPO. We also consider the influence of the pump and signal/idler losses on the tripartite entanglement. The results show that, the tripartite entanglement could exist even with a large detuning of several times cavity linewidth, and may be better for a detuned regime than for the resonant one under some conditions. With a fixed non-zero loss which always exists in a real experiment, an appropriate value of non-zero detuning could lead to the best entanglement. What’s more, unlike the bipartite entanglement, which exists both below and above threshold, the tripartite entanglement only occurs for a nonzero classical amplitude of signal/idler field. The jumping between the tripartite and bipartite entanglement could make the NOPO become a quantum state switch element, which promises a potential application on the multiparty quantum secret sharing.
We explore in detail the possibility of generation of continuous-variable (CV) entangled states of light fields with well-localized phases. We show that such quantum states, called entangled self-phase locked states, can be generated in nondegenerate optical parametric oscillator (NOPO) based on a type-II phase-matched down-conversion combined with polarization mixer in a cavity. A quantum theory of this device, recently realized in the experiment, is developed for both sub-threshold and above-threshold operational regimes. We show that the system providing relative phase coherence between two generated modes also exhibits different types of quantum correlations between photon numbers and phases of these modes. We quantify the entanglement as two-mode squeezing and show that CV entanglement is realized for both unitary, non-dissipative dynamics and for dissipative NOPO in the entire range of pump field intensities.
We developed a quantum analysis of the nondegenerate optical parametric oscillator (NOPO) with unequally injected signal and idler. Both the steady-state output field and the two-mode quantum correlation spectrum are investigated under the condition of different injected idler-to-signal ratios (ISRs) and the relative phase between the pump and the injected seed. It is found that when the seed is injected through the output coupler, the NOPO allows for the robust generation of two-mode quantum entanglement even if the relative phase is free running and the ISR is as high as 0.7. At the specific relative phase of zero, a high degree of entanglement can exist across a whole range of ISRs. An experimental study of the NOPO with unequal seeds is presented, and the observed results verify the theoretical predictions.
Following the analytical work of Ref. [1], a numerical analysis of squeezing and quantum entanglement in a continuous wave singly-resonant optical parametric oscillator approaching threshold is provided. The singly resonant case is mainly relevant to largely non-degenerate signal and idler modes (two-colour output). As the threshold of oscillation is approached the numerical spectra of the intensity difference confirm squeezing of quantum fluctuations and a progressive line-narrowing in the linear case. In the nonlinear case entanglement is confirmed although progressively reduced when approaching threshold with the squeezing spectra still displaying a narrowing of the spectral line. Modification of quantum entanglement approaching threshold is also evaluated via the condition of state inseparability.