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arXiv:2603.24067

Towards Schrödinger Cat States in the Second Harmonic Generation

Ranjit Singh, Leonid A. Barinov, Grigori G. Amosov, Anatoly V. Masalov

quant-phphysics.opticsSubmitted Mar 25, 2026• Announced Mar 26, 2026• 0 citations• Revised Apr 1, 2026 (v2)
v1 · Mar 25, 2026v2 · Apr 1, 2026
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Abstract

We investigate the quantum evolution of the pump field in second-harmonic generation under strong pump depletion. Starting from a coherent state, the pump develops a nonclassical phase-space structure resembling a Schrödinger cat state. This behavior originates from phase instability induced by vacuum fluctuations of the harmonic mode. A rigorous quantum analysis has been performed for mean photon numbers up to $\langle \hat n \rangle = 100$ in pump mode. For larger photon numbers, up to $\langle \hat n \rangle = 10^{7}$, the dynamics have been analyzed using a classical trajectory method with sampled initial conditions that reproduces the main features of the quantum evolution. The results indicate that nonlinear frequency conversion can generate macroscopic superposition-like states of the pump field. Although the resulting state is not pure due to correlations with the second-harmonic wave, it remains non-classical with negative zones of Wigner function. These results indicate that strongly nonlinear frequency conversion can provide a scalable route toward macroscopic nonclassical states of light.

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We investigate the quantum evolution of the pump field in second-harmonic generation under strong pump depletion. Starting from a coherent state, the pump develops a nonclassical phase-space structure resembling a Schrödinger cat state. This behavior originates from phase instability induced by vacuum fluctuations of the harmonic mode. A rigorous quantum analysis has been performed for mean photon numbers up to ⟨n^⟩=100\langle \hat n \rangle = 100⟨n^⟩=100 in pump mode. For larger photon numbers, up to ⟨n^⟩=107\langle \hat n \rangle = 10^{7}⟨n^⟩=107, the dynamics have been analyzed using a classical trajectory method with sampled initial conditions that reproduces the main features of the quantum evolution. The results indicate that nonlinear frequency conversion can generate macroscopic superposition-like states of the pump field. Although the resulting state is not pure due to correlations with the second-harmonic wave, it remains non-classical with negative zones of Wigner function. These results indicate that strongly nonlinear frequency conversion can provide a scalable route toward macroscopic nonclassical states of light.
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\mathbb{Z}_{n+1}Zn+1​ phase structure, whereas the full model retains operator-valued nonlinear Kerr phases. For the n=2n=2n=2 intraresonance branch, the four-mode reduced initial-value problem with fixed coherent pump phases has a residual Z3\mathbb{Z}_3Z3​ symmetry and generates cat-like Wigner structures near the interaction length at which the generated-mode population ⟨n1⟩\langle n_1\rangle⟨n1​⟩ is maximal and the pump population ⟨n0⟩\langle n_0\rangle⟨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 an analytical framework for the emergence of nonclassical radiation in strongly laser-driven quantum systems, with a focus on high-order harmonic generation (HHG). Starting from a Pauli-Fierz description, we employ a parametric factorization of the coupled light-matter wavefunction that reduces the dynamics to coupled equations for a field-driven electronic state and a quantized light mode. Within this framework, we identify a simple and predictive mechanism for nonclassicality: it originates from the nonlinear dependence of the electronic dipole response on the light-mode coordinate. An approximately constant dipole yields coherent radiation, a linear dependence produces squeezing, and higher-order nonlinearities give rise to Wigner-function negativity. We illustrate this mechanism for atomic and molecular model systems and analyze its scaling in multi-emitter configurations, indicating routes toward high-photon-number nonclassical radiation in HHG. Our results provide a transparent connection between strong-field dynamics and quantum-optical properties of emitted light, offering a basis for engineering nonclassical states in intense laser-matter interactions.
High-harmonic generation (HHG) provides a powerful platform for exploring the interaction between intense laser fields and matter on ultrafast timescales. Beyond its conventional description in terms of emitted radiation and electron dynamics, a fully quantum treatment of HHG reveals that the nonlinear light-matter interaction can modify the quantum state of the driving field itself, establishing correlations between the fundamental and harmonic modes. This perspective opens new possibilities for using HHG as a tool to engineer and control nonclassical states of light. In this work, we investigate the geometric properties of optical Schroedinger cat states generated in HHG via conditioning and post-selection. By analyzing the coherent-state displacements induced by different structured driving fields, we characterize the resulting phase-space evolution and the associated geometric phases of the generated quantum states. Particular emphasis is placed on how the polarization and spatial-mode structure of the driving light influence the geometry and evolution of displaced coherent states. Our results demonstrate that structured light offers a versatile means of controlling the geometric dynamics of HHG-generated cat states across the parameter space. Furthermore, we discuss the prospects for realizing genuinely topological optical cat states by exploiting more complex structured light configurations.
Schrödinger cat states, representing coherent superpositions of macroscopically distinguishable states, are indispensable nonclassical resources for continuous-variable quantum information processing. Existing generation protocols typically rely on strong nonlinear interactions, complicated control techniques, or engineered dissipation, posing challenges for experimental implementation. Here, we propose a simple measurement-based protocol for generating Schrödinger cat states in a cavity-QED system by combining coherent driving, dispersive atom--cavity interactions, and atomic postselection. The atom--cavity interaction establishes coherent correlations between the atomic and photonic degrees of freedom, while the subsequent atomic postselection projects the cavity field onto a non-Gaussian superposition state with pronounced Wigner negativity. Numerical simulations based on the Lindblad master equation show that the generated Schrödinger cat states remain robust against moderate cavity dissipation. Our results demonstrate that conditional atomic measurements provide an effective and experimentally accessible approach for preparing nonclassical cavity states without relying on strong optical nonlinearities or engineered dissipation.
We investigate the generation of higher-order harmonics from a quantum optics perspective via the interaction of a semiconductor with a coherent pump field focusing on the regime where strong-field intraband excitations dominate. The related Schrödinger equation for the system is solved approximately and the classical and quantum characteristics of the fundamental light mode as well as the higher frequency modes are analyzed. We find intricate but sufficiently mild modifications of the fundamental mode and coherent displacements depending on the position quadrature component of the driving laser field for the harmonic modes within our approximations due to the intricate induced nonlinear interactions. Similar to high-harmonic generation in atoms, all radiation field modes are entangled, allowing for potential novel protocols for quantum information processing with high photon numbers over a large range of frequencies.
Strong laser-atom interactions can produce highly non-classical states of light by using the process of high-harmonic generation in atoms. When the high-harmonic generation is present, the quantum state of the fundamental mode following the interaction is known as the Schrödinger cat state, which is a superposition of the laser’s initial coherent state and the coherent state with a smaller amplitude that results from its interaction with atoms. Here, we demonstrate that new light states with significantly different Wigner function distributions can be produced by combining two separate Schrödinger cat states. Through the engineering of Schrödinger cat states’ parameters, we are able to produce Wigner functions that exhibit high sensitivity in relation to the system parameter. Our research paves the way for the creation of non-classical light by superposing Schrödinger cat states with application in such as quantum sensing.