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Journal of Modern Optics

Entanglement analyses of a nondegenerate optical parametric oscillator with a higher-transmissivity cavity mirror

Dong Wang, Shuhong Hao, Lixu Xie, Xianshan Huang

Published Oct 6, 2017• 0 citations
Publisher

Abstract

Nondegenerate optical parametric oscillator (NOPO) above threshold is a simple set-up to generate entangled beams. To more accurately calculate the entanglement between the generated twin beams from the NOPO, we use the Langevin equations for the NOPO with a higher-transmissivity cavity mirror. The obtained new expressions for the amplitude-difference and phase-sum noise spectra suggest that increasing the transmissivity of the output mirror can enhance the entanglement beyond the previous expectation.

DOI
10.1080/09500340.2017.1382593

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Nondegenerate optical parametric oscillator (NOPO) above threshold is a simple set-up to generate entangled beams. To more accurately calculate the entanglement between the generated twin beams from the NOPO, we use the Langevin equations for the NOPO with a higher-transmissivity cavity mirror. The obtained new expressions for the amplitude-difference and phase-sum noise spectra suggest that increasing the transmissivity of the output mirror can enhance the entanglement beyond the previous expectation.
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.
Quantum noise and squeezing of the field produced by a degenerate optical parametric oscillator operating below threshold are considered. This analysis extends previously reported calculations for single cavities to double cavities whose mirror transmission coefficients are arbitrary. The double-cavity configuration improves the overall squeezing of the system for both the intracavity field as well as the output field. The double-cavity configuration may be conducive to experimental verification of this and previous work.
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.
It has been recently shown theoretically1 and experimentally2 that nondegenerate optical parametric oscillators generate above threshold intense and highly correlated twin beams. More precisely, the noise on the difference between the intensities of the two beams is well below the shot noise for noise frequencies inside the cavity bandwidth. An application of this quantum correlation is to measure the intensity of one beam and use this information to correct the fluctuations of the other beam by optoelectronic means (photodiode, amplifier, and electrooptic modulator). The correction may be applied either on the pumping beam (feedback correction) or directly on the twin beam itself (feed-forward correction).