Abstract

Multimode entanglement is an essential resource for quantum information in continuous-variable systems. Light-based quantum technologies will arguably not be built upon table-top bulk setups, but will presumably rather resort to integrated optics. Sequential bulk opticslike proposals based on cascaded integrated interferometers are not scalable with the current state-of-the-art low-loss materials used for continuous variables. We analyze the multimode continuous-variable entanglement capabilities of a compact currently available integrated bulk-optics analog: the array of nonlinear waveguides. We theoretically demonstrate that this simple and compact structure, together with a reconfigurable input pump distribution and multimode coherent detection of the output modes, is a versatile entanglement synthesizer in the spatial domain. We exhibit this versatility through analytical and numerically optimized multimode squeezing, entanglement, and cluster-state generation in different encodings. Our results re-establish spatial encoding as a contender in the game of continuous-variable quantum information processing.

View the article : https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.14.044025

David Barral^1,*, Mattia Walschaers², Kamel Bencheikh¹, Valentina Parigi², Juan Ariel Levenson¹, Nicolas Treps², and Nadia Belabas^1,†

• ¹Centre de Nanosciences et de Nanotechnologies C2N, CNRS, Université Paris-Saclay, 10 boulevard Thomas Gobert, Palaiseau 91120, France
• ²Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 place Jussieu, Paris F-75252, France

Contact C2N :

• nadia.belabas@universite-paris-saclay.fr

Figure

Sketch of our versatile entanglement synthesizer based on an array of nonlinear waveguides (ANWs) made up of five PPLN waveguides working in a SPDC configuration (not at scale). A single laser with a second harmonic generation stage outputs coherent pump and local oscillator (LO) beams. A reconfigurable multimode shaper composed of a $1\times N$ fiber beam splitter (FBS), attenuators (${\mathrm{Att}}_j$) and phase shifters (${\varphi }_j$) at pump frequency inputs the desired profile ($\overrightarrow{\eta },\overrightarrow{\varphi }$) in the array through a $V$-groove array. Bent waveguides conduct the pump modes to the periodically poled ANWs (dashed box) where signal modes are generated and evanescently coupled. The coupling profile $\overrightarrow{f}$, wavevector phase matching and coupling phase matching can be suitably engineered for a specific operation mode. The output light is collected by $V$-groove arrays and directed to a multimode balanced homodyne detector (BHD). The multimode LO shaper is composed of attenuators (${\mathrm{Att}}_j$) and phase shifters (${\theta }_j$). Each independent BHD mixes the LO and SPDC light in a balanced FBS and the result is measured by a pair of photodiodes. The currents yielded by photodiodes are subtracted two by two and the generated electric signals are then electronically mixed (postprocessed) if necessary. Access to the individual mode basis is achieved simply using independent LOs. Access to the supermode bases involves shaping the LO in every single supermode through LO phase ($\overrightarrow{\theta }$) and amplitude profiles (see Secs. 3 and 5)