Quantum Pump Depletion and Multicomponent Schrödinger-Cat-Like States in Doubly Pumped Intraresonance Kerr Microresonators

• URL: http://arxiv.org/abs/2606.19085v1
• Date: Wed, 17 Jun 2026 13:55:31 GMT
• Title: Quantum Pump Depletion and Multicomponent Schrödinger-Cat-Like States in Doubly Pumped Intraresonance Kerr Microresonators
• Abstract summary: We investigate quantum pump depletion and non-Gaussian state generation in doubly pumped Kerr microresonators.<n>The results identify quantum-depleted intraresonance Kerr dynamics as a route to symmetry-organized non-Gaussian states in Kerr resonators.
• Score: 46.07145155913717
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\mathbb{Z}_{n+1}$ 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 \(\mathbb{Z}_3\) symmetry and generates cat-like Wigner structures near the interaction length at which the generated-mode population \(\langle n_1\rangle\) is maximal and the pump population \(\langle n_0\rangle\) 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.

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