We theoretically investigate the generation of non-Gaussian quantum states, specifically Schrödinger cat-like states (SCLSs), via degenerate dual-pump spontaneous four-wave mixing in a
χ(3)-based microring resonator. By introducing a unitary transformation that exactly decouples the self-phase modulation (SPM) and cross-phase modulation (XPM) terms, we reduce the full nonlinear Hamiltonian to an effective three-mode interaction. The resulting dynamics (decoupled and full Hamiltonians) are studied using the Lindblad master equation, accounting for cavity losses. Unlike semiclassical or parametric approximations, our full quantum mechanical approach explicitly includes quantum pump depletion, which enables the emergence and observation of non-Gaussian features. We compute the Wigner function, photon number distributions, quadrature variances, Fano factor, Schmidt number, and fidelity to characterize the generated states. For the non-dissipative case, we find that the signal mode
b^3 or
a^3 exhibits clear non-Gaussian features with a structured Wigner function and even-dominated photon number distribution, characteristic of an even coherent state. In the presence of dissipation (
γj=0.2), the interference fringes become faint, odd photon numbers appear, and the fidelity with the ideal state remains high (
>0.9), indicating robustness. The pump mode
b^1 or
a^1 remains Gaussian, while both modes display super-Poissonian statistics and entanglement (
>2). Our results demonstrate that degenerate dual-pump spontaneous four-wave mixing in microring resonators is a promising platform for generating and controlling cat-like states under dissipative conditions.
The intensity buildup of light inside a lossy microring resonator can be used to enhance the generation of squeezed states via spontaneous parametric downconversion (SPDC). In this work, we model the generation of squeezed light in a microring resonator that is pumped with a Gaussian pulse via a side-coupled channel waveguide. We theoretically determine the optimum pump pulse duration and ring-to-channel coupling constant to minimize the quadrature noise (maximize the squeezing) in the ring for a fixed input pump energy. We derive approximate analytic expressions for the optimal coupling and pump pulse duration as a function of scattering loss in the ring. These results will enable researchers to easily determine the optimal design of microring resonator systems for the generation of quadrature-squeezed states.
We explore how III-V semiconductor microring resonators can efficiently generate photon pairs and squeezed vacuum states via spontaneous parametric down-conversion by utilizing their built-in quasi-phase-matching and modal dispersion. We present an analytic expression for the biphoton wave function of photon pairs generated by weak pump pulses and characterize the squeezed states that result under stronger pumping conditions. Our model includes loss and captures the statistics of the scattered photons. A detailed sample calculation shows that for low pump power conversion efficiencies of ${10}^{\ensuremath{-}5}$, corresponding to a rate of 39 MHz for a pump power of $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{W}$, are attainable for rudimentary structures such as a simple microring coupled to a waveguide, in both the continuous-wave and pulsed-excitation regimes. Our results suggest that high levels of squeezing and pump depletion are attainable, possibly leading to the deterministic generation of non-Gaussian states.
We investigate quantum pump depletion and non-Gaussian state generation in doubly pumped Kerr microresonators operating in the intraresonance regime. The pump modes are treated quantum mechanically rather than as undepleted classical amplitudes, allowing pump depletion, back-action, entanglement generation, quadrature fluctuations, and Wigner-function negativity to emerge from the same multimode dynamics. Starting from the Kerr four-wave-mixing selection rule, we distinguish an effective resonant photon-conversion model from the full Kerr Hamiltonian containing self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM). The reduced model isolates the photon-conversion network responsible for the discrete
Zn+1 phase structure, whereas the full model retains operator-valued nonlinear Kerr phases. For the
n=2 intraresonance branch, the four-mode reduced initial-value problem with fixed coherent pump phases has a residual
Z3 symmetry and generates cat-like Wigner structures near the interaction length at which the generated-mode population
⟨n1⟩ is maximal and the pump population
⟨n0⟩ is strongly depleted. The resulting states are not the canonical even or odd coherent states of Dodonov, Malkin, and Man'ko, but multicomponent Schrödinger-cat-like states characterized by Wigner negativity, non-Poissonian statistics, pump-mode quadrature squeezing, and large single-mode Schmidt numbers. Comparison of the reduced and full Kerr dynamics shows that uncompensated SPM/XPM-induced phase shearing suppresses the interference fringes and Wigner negativity responsible for the clearest cat-like signatures. These results identify quantum-depleted intraresonance Kerr dynamics as a route to symmetry-organized non-Gaussian states in Kerr resonators.
We present a multimode theory of squeezed-state generation in resonant systems valid for arbitrary pump power and including pump depletion. The Hamiltonian is written in terms of asymptotic-in and -out fields from scattering theory, capable of describing a general interaction. As an example we consider the lossy generation of a highly squeezed state by an effective second-order interaction in a silicon nitride ring resonator point coupled to a waveguide. We calculate the photon number, the Schmidt number, and the second-order correlation function of the generated state in the waveguide. The treatment we present provides a path forward to study the deterministic generation of non-Gaussian states in resonant systems.
Two-mode squeezed states have potential applications in quantum teleportation, quantum computation, and quantum information. Spontaneous parametric down conversion (SPDC) is one of the processes that can be used to generate two-mode squeezed optical states, both in bulk and integrated systems. In this work, we theoretically model SPDC in a vertically-pumped, lossy, coupled-resonator optical waveguide (CROW), shown in Fig. 1(a), to generate counterpropagating continuous variable (CV) entangled states. For a CROW in which the cavities are identical, using the nearest neighbour TB approximation, the CROW mode dispersion is given by ω̃Fk≈ ω̃F[1+ β̃1cos(kD)] ≡ ωFk-iγFk,, where ω̃Fis the individual-cavity complex mode frequency, β̃1is the complex coupling parameter, D is the periodicity of the CROW, and k is the Bloch vector. We consider the case of a pump that is Gaussian in time and space, with spatial and temporal full width at half maxima of ΔrFMHM= 2 √{l n2}/σ+and ΔtFMHM= 2 √{l n2}/τ/(σ_D), respectively, where σ+and σ_ are the k-space width parameters (see below), and τ = Re {1 / (ω̃Fβ̃1)} is the minimum time for the light to propagate one period.