arXiv subjects

Alexander E. Teretenkov

Publications and source records attributed to Alexander E. Teretenkov.

3 recordsLinked to original sources

arXiv2026

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

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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arXiv2026

Generation of Schrödinger cat-like states via degenerate dual pump spontaneous four-wave mixing in a $χ^{(3)}$ microring resonator

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 $\hat{b}_3$ or $\hat{a}_3$ 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 ($γ_j = 0.2$), 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 $\hat{b}_1$ or $\hat{a}_1$ 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.

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arXiv2026

The formation of entangled Schrödinger cat-like states in the process of spontaneous parametric down-conversion

We investigate entangled Schrödinger cat-like states (SCLSs) in degenerate and non-degenerate spontaneous parametric down-conversion (SPDC) with a fully quantized, depleted pump. Our fully quantum treatment, visualized via Wigner functions, reveals non-Gaussian features and interference patterns absent in semiclassical models. For degenerate SPDC, we demonstrate significant squeezing (up to $4.04\,\mathrm{dB}$) and robust super-Poissonian statistics in both non-dissipative and dissipative regimes. Extending to non-degenerate SPDC, we confirm that pump quantization also generates non-Gaussian states in all modes and yields a higher-dimensional entanglement structure, evidenced by a larger Schmidt number ($K^{(\mathrm{ND})} \approx 10.38$) compared to the degenerate case ($K \approx 1.93$). Our approach captures critical dynamics like energy exchange and phase-dependent evolution. These entangled SCLSs, non-Gaussian states realizable in $χ^{(2)}$ media at moderate intensities and offering advantages over $χ^{(3)}$-based schemes, are promising resources for quantum sensing and information processing.

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