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arXiv:1711.09483 · Physical Review A

Quantum correlations across two octaves from combined up- and down-conversion

Jingyan Li, M. K. Olsen

Published Apr 24, 2018• 22 citations
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Abstract

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.

DOI
10.1103/physreva.97.043856

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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.
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.
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.
We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO present two χ^2 level oscillation thresholds that are therefore remarkably lower than for a χ^3 OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a χ^2 cascaded device also has potential applications in frequency conversion to far infra-red regimes. But, most importantly, it can generate novel multi-partite quantum correlations in the output radiation, which represent a step beyond squeezed or entangled light. The output can be highly non-Gaussian, and therefore not describable by any semi-classical model.
We analyze an optical parametric oscillator (OPO) in which cascaded down-conversion occurs inside a cavity resonant for all modes but the initial pump. Due to the resonant cascade design, the OPO presents two ${\ensuremath{\chi}}^{(2)}$-level oscillation thresholds that are therefore much lower than for a ${\ensuremath{\chi}}^{(3)}$ OPO. This is promising for reaching the regime of an effective third-order nonlinearity well above both thresholds. Such a ${\ensuremath{\chi}}^{(2)}$ cascaded device also has potential applications in frequency conversion to far-infrared regimes. But, most importantly, it can generate novel multipartite quantum correlations in the output radiation, which represent a step beyond squeezed or entangled light. The output can be highly non-Gaussian and therefore not describable by any semiclassical model. In this paper, we derive quantum stochastic equations in the positive-PPP representation and undertake an analysis of steady-state and dynamical properties of this 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.