We present a design for a photonic crystal coupled-cavity system to generate entangled two-mode squeezed states of light on-chip and model it with a basis of non-orthogonal leaky quasi-modes to account for scattering loss.
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.
The feasibility of using a parametric down-conversion process to generate squeezed electromagnetic states in three dimensional photonic crystal microcavity structures is investigated for the first time. The spectrum of the squeezed light is theoretically calculated by using an open cavity quantum mechanical formalism. The cavity communicates with two main channels, which model vertical radiation losses and coupling into a single-mode waveguide respectively. The amount of squeezing is determined by the correlation functions relating the field quadratures of light coupled into the waveguide. All of the relevant model parameters are realistically estimated for structures made in Al0.3Ga0.7As, using finite-difference time-domain simulations. Squeezing up to approximately 30% below the shot noise level is predicted for 10 mW average power, 80 MHz repetition, 500 ps excitation pulses using in a [111] oriented wafer.
We investigate theoretically the temporal evolution of a squeezed state in lossy coupled-cavity systems. We present a general formalism based upon the tight-binding approximation and apply this to a two-cavity system as well as to a coupled-resonator optical waveguide in a photonic crystal. We derive analytical expressions for the number of photons and the quadrature noise in each cavity as a function of time when the initial excited state is a squeezed state in one of the cavities. We also analytically evaluate the time-dependent cross correlation between the photons in different cavities to evaluate the degree of quantum entanglement. We demonstrate that loss in such coupled-cavity systems cannot be treated using simple exponential factors. Finally, we also derive approximate analytic expressions for the maximum photon number, maximum squeezing, and maximum entanglement for cavities far from the initially excited cavity in a lossless coupled-resonator optical waveguide.