双泵浦腔内Kerr微谐振器中的量子泵浦耗尽与多分量薛定谔猫态
Quantum Pump Depletion and Multicomponent Schrödinger-Cat-Like States in Doubly Pumped Intraresonance Kerr Microresonators
AI总结：
本文通过量子化泵浦模式研究双泵浦Kerr微谐振器中的泵浦耗尽和非高斯态生成，揭示了多模动力学产生的Wigner负性和多分量薛定谔猫态。
摘要：
我们研究了在腔内共振模式下运行的双泵浦Kerr微谐振器中的量子泵浦耗尽和非高斯态生成。泵浦模式被量子力学处理，而非作为未耗尽的经典振幅，从而允许泵浦耗尽、反作用、纠缠生成、正交涨落和Wigner函数负性从相同的多模动力学中涌现。从Kerr四波混频选择定则出发，我们将一个有效的共振光子转换模型与包含自相位调制（SPM）、交叉相位调制（XPM）和四波混频（FWM）的完整Kerr哈密顿量区分开来。简化模型隔离了负责离散$\mathbb{Z}_{n+1}$相位结构的光子转换网络，而完整模型保留了算符值的非线性Kerr相位。对于\(n=2\)腔内分支，具有固定相干泵浦相位的四模简化初值问题具有残余的\(\mathbb{Z}_3\)对称性，并在相互作用长度附近生成猫状的Wigner结构，此时生成模布居数\(\langle n_1\rangle\)最大，泵浦模布居数\(\langle n_0\rangle\)强烈耗尽。所得状态不是Dodonov、Malkin和Man'ko的典型偶或奇相干态，而是多分量薛定谔猫态，其特征为Wigner负性、非泊松统计、泵浦模正交压缩和大单模Schmidt数。简化与完整Kerr动力学的比较表明，未补偿的SPM/XPM诱导的相位剪切抑制了最清晰猫状特征所需的干涉条纹和Wigner负性。这些结果将量子耗尽的腔内Kerr动力学确定为Kerr谐振器中对称组织非高斯态的一条途径。
英文摘要：
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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