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.

Third-harmonic entanglement and Einstein-Podolsky-Rosen steering over a frequency range of more than an octave

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.

Entanglement and asymmetric steering over two octaves of frequency difference

Tripartite correlations over two octaves from cascaded harmonic generation

Continuous-variable (CV) entanglement frequency comb can be produced by enhanced Raman scattering in an above-threshold optical oscillator cavity in which a hexagonally-poled LiTaO3 crystal resides as a Raman gain medium. The Stokes and anti-Stokes Raman signals are enhanced by a coupled quasi-phase-matching optical parametric process and the entanglement natures among these Raman signals and pump are demonstrated by applying a sufficient inseparability criterion for CV entanglement. Such entanglement frequency comb source with different frequencies and continuously tunable frequency interval may be very significant for the applications in quantum communication and networks.

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The generation of Continuous-Variable Entanglement Frequency Comb

Continuous variable quantum entanglement at a telecommunication wavelength of 1550 nm is experimentally generated using a single nondegenerate optical parametric amplifier based on a type-II periodically poled KTiOPO4 crystal. The triply resonant of the nondegenerate optical parametric amplifier is adjusted by tuning the crystal temperature and tilting the orientation of the crystal in the optical cavity. Einstein–Podolsky–Rosen-entangled beams with quantum correlations of 8.3 dB for both the amplitude and phase quadratures are experimentally generated. This system can be used for continuous variable fibre-based quantum communication.

Generation of 8.3 dB continuous variable quantum entanglement at a telecommunication wavelength of 1550 nm

Bright three-color continuous-variable (CV) entanglement generated by a cascaded sum-frequency process in an optical cavity is investigated. The second- and fourth-harmonic beams can be generated by two quasi-phase-matched cascaded sum-frequency processes in a quasi-periodic optical superlattice. Quantum correlations among the fundamental and second- and fourth-harmonic beams are calculated and discussed by applying a sufficient and necessary inseparability criterion for CV three-mode entanglement. Strong three-color CV entanglement beams with a double frequency interval can be produced in this simple system. It is experimentally feasible and may be very useful for applications in quantum communication and computation networks.

Bright three-color continuous-variable entanglement generated by a cascaded sum-frequency process in an optical cavity

Three-color entanglement generated by single-pass cascaded sum-frequency processes

Analysis is presented in this paper to directly produce three-color continuous-variable (CV) entanglement by nondegenerate optical parametric oscillator (NOPO) with an injected signal. The quantum entanglement among the pump, signal, and idler beams are calculated by applying sufficient inseparability criteria for CV entanglement which proposed by van Loock and Furusawa [Phys. Rev. A 67, 052315 (2003)]. The results indicates that strong three-color CV entangled beams, i.e. pump, signal, and idler beams, can be generated when the NOPO operating above the threshold. The degree of entanglement dependence on damping rates is also investigated.

Analysis of directly produce pump, signal, and idler three-color continuous-variable entanglement

Quadripartite continuous-variable (CV) entanglement with different optical frequencies can be generated by nondegenerate optical parametric amplification cascaded with a sum-frequency process in only one optical superlattice. Firstly, the idler beam is generated by a different frequency process between pump and signal beams. Then, the sum-frequency beam will be generated by a cascaded sum-frequency process between pump and idler beams in the same optical superlattice. The conversion dynamics of the cascaded nonlinear processes is investigated by using a quantum stochastic method. The quantum correlations among pump, signal, idler and sum-frequency beams are calculated by applying a sufficient inseparability criteria for quadripartite CV entanglement. The results show that quadripartite CV entangled beams can be produced by this single-pass cascaded nonlinear process in one optical superlattice.

Quadripartite continuous-variable entanglement generation by nondegenerate optical parametric amplification cascaded with a sum-frequency process

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