Non-Gaussian states via pump-depleted SPDC

TL;DR

This work develops a multimode, pump-depleted SPDC model for InGaP microring resonators that incorporates scattering loss via a phantom channel and decomposes the system state into Gaussian and non-Gaussian parts. A Gaussian unitary $U(t)$ evolves the Gaussian sector, while a residual non-Gaussian ket evolves under an effective Hamiltonian $H_{ m eff}(t)$; a reduced supermode basis makes the non-Gaussian dynamics tractable. The authors show that pump depletion yields non-Gaussian features in the residual ket with a Wigner-negativity around 0.18, but in the full ket these features are typically obscured by strong squeezing; applying an inverse Gaussian unitary can reveal them under favorable loss conditions. The framework, validated with realistic InGaP parameters, points toward scalable, on-chip non-Gaussian state sources and highlights the critical role of low scattering loss and high escape efficiency for practical observation of non-Gaussianity.

Abstract

We develop a model for non-Gaussian state generation via spontaneous parametric down-conversion (SPDC) in InGaP microring resonators. The nonlinear Hamiltonian is written in terms of the asymptotic fields for the system, which includes a phantom channel to handle scattering loss. The full ket for the system is written as a Gaussian unitary acting on a residual non-Gaussian ket, which is vacuum initially and evolves according to a non-Gaussian Hamiltonian. We show that for realistic parameters we can access the pump depletion regime, where the Wigner function for the residual non-Gaussian ket has negativity. But we find that the non-Gaussian features for the full ket could be unobservable due to the large amount of squeezing required to lead to pump depletion. We show that a potential solution in the low-loss regime is to implement an inverse Gaussian unitary on the accessible modes to remove most of the squeezing and reveal the non-Gaussian features. This work provides a foundation for modeling pump-depleted SPDC in integrated lossy microring resonators, opening a path toward a scalable on-chip non-Gaussian source.

Figures (11)

• Figure 1: (a) Schematic of a ring resonator point-coupled to an actual waveguide (bottom purple) and phantom waveguide (white). (b) Schematic of the positions of the ring resonances for the SPDC interaction.
• Figure 2: Squeezing (blue) and anti-squeezing (orange) in the actual output channel versus input pump energy for (a) $\eta_S=\eta_I=0.95$ and (b) $\eta_S=\eta_I=0.5$. The squeezing measurement is done at a late time $t_1 = 30/\bar{\Gamma}_P$, where $\bar{\Gamma}_P = 2\pi \times 3.84\,{\rm GHz}$, when the pump pulse has left the ring. We have taken a pump pulse duration of $0.5\,{\rm ns}$, and used $Q_{{\rm int}, S} = Q_{{\rm int}, I} = 10^6$.
• Figure 3: Signal photon number (identical to the idler photon number) versus the initial pump energy for $\eta_S = \eta_I = 0.5$ (green) and $\eta_S = \eta_I = 0.95$ (red), evaluated at $t_1 = 30/\bar{\Gamma}_P$ with $\bar{\Gamma}_P = 2\pi \times 3.84\,{\rm GHz}$. We have taken a pump pulse duration of $0.5\,{\rm ns}$, and used $Q_{{\rm int}, S} = Q_{{\rm int}, I} = 10^6$.
• Figure 4: (a) Conversion efficiency and (b) overlap of the perturbative non-Gaussian ket versus the initial pump energy for $\eta_S = \eta_I = 0.5$ (green) and $\eta_S = \eta_I = 0.95$ (red), evaluated at $t_1 = 30/\bar{\Gamma}_P$ with $\bar{\Gamma}_P = 2\pi \times 3.84\,{\rm GHz}$. We have taken a pump pulse duration of $0.5\,{\rm ns}$, and used $Q_{{\rm int}, S} = Q_{{\rm int}, I} = 10^6$.
• Figure 5: (a) Largest 30 singular values associated with the signal and idler (see Eq. \ref{['eq:joint svd']}) and (b) largest 5 singular values associated with the pump (see Eq. \ref{['eq:L svd']}), for $\eta_S = \eta_I = 0.95$ and a pump energy of $0.09\,{\rm pJ}$, evaluated at $t_1 = 30/\bar{\Gamma}_P$ with $\bar{\Gamma}_P = 2\pi \times 3.84\,{\rm GHz}$. We have taken a pump pulse duration of $0.5\,{\rm ns}$, and used $Q_{{\rm int}, S} = Q_{{\rm int}, I} = 10^6$.