Multimode Entangled Squeezed Light Generation and Propagation in a Coupled-Cavity Photonic Crystal

TL;DR

This work tackles the challenge of generating and preserving entangled multimode squeezed light in integrated nanophotonic platforms. It introduces a four-step theoretical framework to efficiently model nonlinear generation and propagation in lossy, multimode photonic-crystal coupled cavities, scalable to hundreds of modes. Applied to a three-mode resonant structure coupled to three CROWs in silicon, the approach demonstrates on-chip generation of a two-mode squeezed thermal state and tracks its evolution through the full device, revealing strong RS squeezing but partial entanglement degradation in the output channels. The study highlights the importance of quasi-mode bases, non-orthogonality, and pump dynamics for accurate modeling and points to design optimizations and extensions toward larger entangled resources and on-chip quantum information processing.

Abstract

Entangled multi-mode squeezed states of light have a wide variety of applications in quantum information systems, particularly in the generation of non-Gaussian states of light, which are central to continuous-variable quantum computing. Although theoretical approaches exist to model the nonlinear generation of one- and two-mode entangled states of light in ring resonator systems, these approaches are difficult to implement in modeling more complicated many-cavity systems. In this work, we present an efficient and accurate theoretical approach to modeling the generation and propagation of quantum states of light in lossy coupled-cavity systems containing a two- or three-mode nonlinear resonant structure. Our approach is general and computationally viable even in systems with hundreds of modes. We apply our method to the design and modeling of a multimode photonic crystal coupled-cavity system for the generation of entangled squeezed states of light on-chip. The system consists of a three-mode resonant structure coupled to three coupled-resonator optical waveguides (CROWs) in a square lattice silicon photonic crystal slab. The computational speed of the method allows us to efficiently optimize the system such that the signal and idler light in the two output CROWs remains entangled even after propagating tens of cavities down the CROWs.

Figures (13)

• Figure 1: Schematic of the designed photonic crystal coupled-cavity system in the vicinity of the resonant structure (outlined by the purple box) with key features highlighted. White regions indicate air holes etched into the silicon slab (pale blue). A pump pulse is injected via the pump CROW (green, left of RS), and the generated light leaves the RS via the signal (blue, lower-right of RS) and idler (red, right of RS) CROWs in spatially separated pulses. The numbers below the three CROWS, indicate the cavity labeling convention that will be used in Sec. \ref{['sec:IV']}. Note that the three CROWs used in the simulation are much longer than shown here, with each containing over 50 coupled cavities.
• Figure 2: Procedure flowchart for the four-step analysis used to calculate the quantum state of light in the output CROWS.
• Figure 3: Plot of $|C_{j,x}(x,y,0)|^2$ for the three RS QMs. The area of each subfigure is enclosed by the purple rectangle in Fig. \ref{['fig:PCCCS']}. The complex frequency for each of the QMs (when the CROWs are absent) are given below each plot.
• Figure 4: Dispersion for the CROW bands as calculated in the nearest-neighbor tight-binding approximation (see Appendix \ref{['AppA']}). Idler, pump, and signal CROW bands are shown in red, green, and blue, respectively, with corresponding RS QM frequencies displayed as dashed lines intersecting their corresponding CROW band.
• Figure 5: Absolute values of the QM overlaps $O_{\mu ,\nu}$ for the full system as a function of the absolute value of frequency difference between the $\mu$ and $\nu$ QMs.