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Quantum correlations over a large bandwidth in cascaded optical parametric system

Jingyan Li, Qing Ye

Published Dec 18, 2019• 0 citations
Publisher

Abstract

The availability of quantum entanglement and EPR steering over a large frequency will bring further flexibility to the linking of quantum processes at different wavelengths, especially related to quantum memory. In this paper, a cascaded optical parametric system, with three interacting modes spanning two octaves of frequency difference, is investigated. This process combine degenerate optical parametric oscillation (OPO) and second harmonic generation (SHG), which is shown to be a useful way to obtain the quantum entanglement and EPR steering at three differing frequencies. The results are shown that compared to the normal only SHG, the existence of the OPO interaction eliminates the selfpulsing effect, and the threshold conditions of single OPO interaction is also changed due to the presence of the SHG. Above or below threshold, the system exhibits different quantum correlations features. The tripartite entanglement are only violated above threshold. The entanglement and EPR steering are both present in two conditions, but the system behaves totally different at the threshold. The effect of the ratio of loss rates of the three modes on the quantum correlations is also investigated. It is shown that the symmetric property of the quantum EPR steering is controlled by these ratios. This system is flexible to be adjusted and controlled, which potentially provides a significant resource for quantum correlations over a large bandwidth.

DOI
10.1117/12.2542544

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The availability of quantum entanglement and EPR steering over a large frequency will bring further flexibility to the linking of quantum processes at different wavelengths, especially related to quantum memory. In this paper, a cascaded optical parametric system, with three interacting modes spanning two octaves of frequency difference, is investigated. This process combine degenerate optical parametric oscillation (OPO) and second harmonic generation (SHG), which is shown to be a useful way to obtain the quantum entanglement and EPR steering at three differing frequencies. The results are shown that compared to the normal only SHG, the existence of the OPO interaction eliminates the selfpulsing effect, and the threshold conditions of single OPO interaction is also changed due to the presence of the SHG. Above or below threshold, the system exhibits different quantum correlations features. The tripartite entanglement are only violated above threshold. The entanglement and EPR steering are both present in two conditions, but the system behaves totally different at the threshold. The effect of the ratio of loss rates of the three modes on the quantum correlations is also investigated. It is shown that the symmetric property of the quantum EPR steering is controlled by these ratios. This system is flexible to be adjusted and controlled, which potentially provides a significant resource for quantum correlations over a large bandwidth.
We propose and analyze a cascaded optical parametric system which involves three interacting modes across two octaves of frequency difference. Our system, combining degenerate optical parametric oscillation (OPO) with second harmonic generation (SHG), promises to be a useful source of squeezed and entangled light at three differing frequencies. We show how changes in damping rates and the ratio of the two concurrent nonlinearities affect the quantum correlations in the output fields. We analyze the threshold behavior, showing how the normal OPO threshold is changed by the addition of the SHG interactions. We also find that the inclusion of the OPO interaction removes the self-pulsing behavior found in normal SHG. Finally, we show how the Einstein-Podolsky-Rosen correlations can be controlled by the injection of a coherent seed field at the lower frequency.
In this paper, a cascaded optical parametric system combing degenerate optical parametric oscillation (OPO) and second harmonic generation (SHG) is investigated. By using the positive-P representation and standard input-output relations, and using quantum trajectory numerical simulation, we can analyse the quantum correlation behavior of the system above or below threshold. By injecting a small coherent signal in the lowest field mode, the threshold of the system can be changed. More importantly, the symmetry property of the EPR steering can also easily be controlled. Without signal injection, the EPR steering only occurs between two higher field modes below threshold, but it will disappear with injection. For EPR steering of other two pair bipartition is formerly not existent, while they occur with injection. Meanwhile, the steering property of the lowest mode and the highest mode becomes asymmetric by changing the value of the signal. The injection of the coherent signal allows for a simple means of control over the EPR steering properties of the system.
The development of quantum technologies which use quantum states of the light field interacting with other systems creates a demand for such states over wide frequency ranges. In this work we compare the bipartite entanglement and Einstein-Podolsky-Rosen (EPR) -steering properties of the two different parametric schemes which produce third-harmonic optical fields from an input field at the fundamental frequency. The first scheme uses second harmonic cascaded with sum-frequency generation, while the second uses triply degenerate four- wave mixing, also known as direct third-harmonic generation. We find that both schemes produce continuous-variable bipartite entanglement and EPR steering over a frequency range which has previously been unobtainable. The direct scheme produces a greater degree of EPR steering, while the cascaded scheme allows for greater flexibility in having three available bipartitions, thus allowing for greater flexibility in the tailoring of light matter interfaces. There are also parameter regimes in both for which classical mean-field analyses fail to predict the mean-field solutions. Both schemes may be very useful for applications in quantum communication and computation networks, as well as providing for quantum interfaces between a wider range of light and atomic ensembles than is presently practicable.
The development of quantum technologies which use quantum states of the light field interacting with other systems creates a demand for entangled states spanning wide frequency ranges. In this work we analyze a parametric scheme of cascaded harmonic generation which promises to deliver bipartite entangled states in which the two modes are separated by two octaves in frequency. This scheme is potentially very useful for applications in quantum communication and computation networks as well as providing for quantum interfaces between a wider range of light and atomic ensembles than is presently practicable. It doubles the frequency range over which entanglement is presently available.
Einstein-Podolsky-Rosen (EPR) steering, that is, an intermediate form of quantum correlations with asymmetry in between entanglement and Bell nonlocality, plays an essential role in quantum information processing, such as one-sided device-independent quantum cryptography tasks. Here we theoretically study the direct generation of EPR steering in ${\ensuremath{\chi}}^{(2)}$ nonlinear optical processes with cascaded crystals in a self-phase-locked optical parametric oscillator. Based on a standard linearization method, we analyze different conditions for generating EPR steering in Gaussian states with vanishing or nonzero mean fields, and also show bistable regions for different types of EPR steering. In particular, such system can intrinsically generate asymmetry one-way EPR steering, without introducing any postoperation. Our results suggest that the self-phase-locked optical parametric oscillator is a good candidate to generate different types of EPR steering at will by varying the cavity detunings, photon loss, or input pump power.
Einstein-Podolsky-Rosen (EPR) steering has potential applications in quantum information processing. Here the genuine tripartite EPR steering is investigated in cascaded nonlinear process of spontaneous parametric down-conversion cascaded with a sum-frequency generation in an optical cavity for a wide range of the nonlinear parameters. The threshold properties of the cascaded nonlinear precess are also analyzed both below and without threshold regime, respectively. The genuine tripartite EPR steering is demonstrated based on the criteria for genuine multipartite EPR steering. Our scheme of the generation of genuine tripartite EPR steering can be used as a suggestion for the potential experiments and the applications in quantum communication and computation.