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arXiv:1707.02537 · Physical Review A

Entanglement and asymmetric steering over two octaves of frequency difference

M. K. Olsen

Published Dec 29, 2017• 31 citations
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Abstract

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.

DOI
10.1103/physreva.96.063839

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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.
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 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.
Asymmetric quantum steering can achieve one-way control, which is different from multipartite quantum steering and can accomplish some work that quantum entanglement cannot complete. The cascaded nonlinear process of spontaneous parametric down-conversion cascaded with double sum-frequency generations can be realized in one optical superlattice by quasi-phase-matching technique. Here the asymmetric quantum steering is investigated in this cascaded nonlinear process and the asymmetry of quantum steering is confirmed in a wide range of the parameters both below and without the oscillation threshold, respectively. The generation of asymmetric quantum steering in present scheme has potential applications in quantum key distribution and continuous variable teleportation.
We have experimentally demonstrated how two beams of light separated by an octave in frequency can become entangled after their interaction in a chi;{(2)} nonlinear medium. The entangler was a nonlinear optical resonator that was strongly driven by coherent light at the fundamental and second-harmonic wavelengths. An interconversion between the fields created quantum correlations in the amplitude and phase quadratures, which were measured by two independent homodyne detectors. Analysis of the resulting correlation matrix revealed a wave function inseparability of 0.74(1)<1, thereby satisfying the criterion of entanglement.
Quantum entanglement is a crucial resource for performing quantum computing and constructing quantum communication networks. The preparation and manipulation of entangled light field are the basic elements of quantum communication. With the development of science and technology, multicolor multipartite entanglement is becoming a kind of special resource for quantum information, quantum networks, and quantum memory. In this paper, we propose a scheme of generating quadripartite entanglement among four output beams from a two-port frequency doubling resonator, in which a type-II phase matching nonlinear crystal is placed. We make two fundamental-frequency pump beams with the same frequency and vertical polarization pass through the nonlinear crystal to produce two frequency-doubling beams. There is a quadripartite entanglement between the frequency-doubling beams, which are output at two ports of the optical resonator, and the incident fundamental beams. Based on the transmission matrix from the coupled wave equation, the self-consistent equations of the intracavity modes and the corresponding noise properties of the output modes can be obtained. Then, the quadripartite entanglement produced from two second harmonic beams and two reflected fundamental-frequency pump beams, is verified by using the positive partial transposition criterion, in a wide range of pumping power and analysis frequency. The setup proposed in this work is compact and experimentally feasible. It is also convenient to separate the four entangled beams spatially, with different wavelengths and polarizations. When the beam wavelengths are matched with 1560 nm (low loss window of fiber) and 780 nm (atomic absorption line of Rb), this scheme can be more useful in both quantum communication and quantum memory.