Minimum resources for versatile continuous-variable entanglement in integrated nonlinear waveguides

Abstract

In a recent paper [Phys. Rev. A 96, 053822 (2017)], we proposed a strategy to generate bipartite and quadripartite continuous-variable entanglement of bright quantum states based on degenerate down-conversion in a pair of evanescently coupled nonlinear χ (2) waveguides. Here, we show that the resources needed for obtaining these features can be optimized by exploiting the regime of second harmonic generation: the combination of depletion and coupling among pump beams indeed supplies all necessary wavelengths and appropriate phase mismatch along propagation. Our device thus entangles the two fundamental classical input fields without the participation of any harmonic ancilla. Depending on the propagation distance, the generated harmonics are entangled in bright or vacuum modes. We also evidence two-color bipartite and quadripartite entanglement over the interacting modes. The proposed device represents a boost in continuous-variable integrated quantum optics since it enables a broad range of quantum effects in a very simple scheme, which optimizes the resources and can be easily realized with current technology.

Coupling quasi-phase-matching: Entanglement buildup in χ(2) nonlinear-waveguide arrays

“…A detailed analysis will be presented elsewhere. Finally, note that this scheme also applies to second harmonic generation, where entanglement of the generated signal fields has been predicted [27].…”

“…Note that for long distances and/or high input power, the undepleted pump approximation is no longer valid. In such case the depletion of the pump has to be taken into account [14,27]. Thus we conclude that C-QPM is the best option available as of today in terms of compactness and efficiency to generate quantum correlations in cw-PPLN directional couplers.…”

“…A state-of-the-art value for signal field losses is γ s ≈ 0.14 dB cm −1 in reverse-exchange PPLN waveguides [9]. The influence of linear losses, like scattering or absorption, on the fields quadratures can be easily included in our analysis by inserting in Equations ( 6) fictitious beam splitters with effective transmittivities proportional to the losses corresponding to each mode [27]. Our simulations point out that the noise squeezing and entanglement buildup produced by C-QPM is quite robust under these values of losses.…”

“…The production of CV entangled states in a perfectly phase-matched NDC has been theoretically studied in refs. [13,14,27]. These works demonstrated that in the technologically available range of CW-PPLN directional couplers -where linear coupling dominating over nonlinear coupling and sample lengths are a few centimeters-the entanglement between the two signal output fields is maximized for equal input pump powers and phases, showing an oscillatory evolution which periodically shifts between a maximum and zero values [28].…”

Quantum state engineering in arrays of nonlinear waveguides

“…Remarkably, for even number of waveguides and a parabolic coupling profile (not shown), there are propagation distances where destructive interference destroys all the SPDC generated light due to a evolving phase mismatch that periodically switches the system from downconversion to upconversion. Recently, bipartite entanglement between non-coupled pump fields has been demonstrated through this effect for two waveguides in the optical parametric amplification and second harmonic generation regimes [54,59]. Thus, this effect can also produce multipartite entanglement between non-interacting fields.…”