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arXiv:2607.21248

Tailoring optical Schrödinger cat states via orientation-dependent high-harmonic generation in $\rm{H}_2^+$

Ziyang Gan, Wei-Chao Jiang, Ahai Chen, Yuhai Jiang

quant-phphysics.atom-phphysics.comp-phphysics.opticsSubmitted Jul 23, 2026• Announced Jul 24, 2026• 0 citations
v1 · Jul 23, 2026v2 · Aug 31, 2026v3 · Sep 3, 2026
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Abstract

We theoretically demonstrate that the molecular orientation angle $θ$ provides a structurally intrinsic, continuously tunable control parameter for engineering optical Schrödinger cat states via high-harmonic generation (HHG) in H$_2^+$. Coupling time-dependent Schrödinger equation simulations to the fully quantized HHG framework, we evaluate the Wigner functions of the post-selected harmonic-mode states under two complementary conditioning strategies. Conditioning on resonance-enhanced low-order harmonics exploits the complementary dipole selection rules of the $1σ_g\to1σ_u$ and $1σ_g\to1π_u$ transitions, driving a kitten-cat crossover whose direction is opposite in the two channels as $θ$ is varied. Conditioning on plateau harmonics instead exploits two-center destructive interference, producing a reentrant cat$\to$kitten$\to$cat transition controlled by the order-dependent interference angle $θ^*(q)$. In both cases the crossover is decoupled from the laser intensity, focal geometry, and molecular density, offering a degree of control with no counterpart in atomic targets.

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8 pages, 4 figures

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Tailoring optical Schrödinger cat states via orientation-dependent high-harmonic generation in H2+\rm{H}_2^+H2+​
We theoretically demonstrate that the molecular orientation angle θθθ provides a structurally intrinsic, continuously tunable control parameter for engineering optical Schrödinger cat states via high-harmonic generation (HHG) in H2+_2^+2+​. Coupling time-dependent Schrödinger equation simulations to the fully quantized HHG framework, we evaluate the Wigner functions of the post-selected harmonic-mode states under two complementary conditioning strategies. Conditioning on resonance-enhanced low-order harmonics exploits the complementary dipole selection rules of the 1σg→1σu1σ_g\to1σ_u1σg​→1σu​ and 1σg→1πu1σ_g\to1π_u1σg​→1πu​ transitions, driving a kitten-cat crossover whose direction is opposite in the two channels as θθθ is varied. Conditioning on plateau harmonics instead exploits two-center destructive interference, producing a reentrant cat→\to→kitten→\to→cat transition controlled by the order-dependent interference angle θ∗(q)θ^*(q)θ∗(q). In both cases the crossover is decoupled from the laser intensity, focal geometry, and molecular density, offering a degree of control with no counterpart in atomic targets.
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.
High-harmonic generation (HHG) involves the up-conversion of a high-intensity driving field into its harmonic orders. This process is intrinsically non-classical, requiring from quantum mechanics for a complete explanation as, under suitable conditions, involves phenomena such as particle tunneling through a potential barrier. When exposed to a high-intensity, low-frequency laser field, bound electrons ionize via tunneling, accelerate under the driving field, and recombine with the parent ion, emitting high-harmonic radiation. However, electrons can follow two distinct pathways -- short and long trajectories -- during these steps. In this work, we evaluate the signatures left by these trajectories on the quantum optical state after HHG, and observe that they lead to entanglement between the driving field and the generated harmonics. By leveraging these correlations, we use harmonic generation to herald the creation of optical Schrödinger cat-like states in the driving field. Additionally, using an ab-initio approach, we examine how propagation effects, which spatially separate the harmonic contributions from short and long trajectories, influence the non-classical characteristics of the emitted light.
High-harmonic generation (HHG) involves the up-conversion of a high-intensity driving field into its harmonic orders. This process is intrinsically nonclassical, requiring from quantum mechanics for a complete explanation as, under suitable conditions, involves phenomena such as particle tunneling through a potential barrier. When exposed to a high-intensity, low-frequency laser field, bound electrons ionize via tunneling, accelerate under the driving field, and recombine with the parent ion, emitting high-harmonic radiation. However, electrons can follow two distinct pathways, short and long trajectories, during these steps. In this work, we evaluate the signatures left by these trajectories on the quantum-optical state after HHG, and observe that they lead to entanglement between the driving field and the generated harmonics. By leveraging these correlations, we use harmonic generation to herald the creation of optical Schr\"odinger-cat-like states in the driving field. Additionally, using an ab initio approach, we examine how propagation effects, which spatially separate the harmonic contributions from short and long trajectories, influence the nonclassical characteristics of the emitted light.
High-order harmonic generation from molecules is highly sensitive to molecular geometry and strong-field electron dynamics, providing a powerful route for probing and controlling ultrafast processes in extended systems. In this work, we systematically investigate the influence of molecular chain length on HHG from linear carbon-chain molecules C2_22​H2_22​, C6_66​H2_22​, and C10_{10}10​H2_22​ driven by an 800 nm linearly polarized laser field. To isolate the molecular-size effect from the influence of different ionization potentials, the laser intensities are adjusted to maintain the same Keldysh parameter for different molecules. Real-time time-dependent density functional theory simulations are performed with the molecular axis aligned parallel to the laser polarization direction. The results show that increasing the molecular chain length significantly enhances the harmonic yield and tends to extend the cutoff region. In particular, C10_{10}10​H2_22​ exhibits much stronger plateau harmonics than C2_22​H2_22​, while the intermediate molecule C6_66​H2_22​ shows harmonic intensities between those of C2_22​H2_22​ and C10_{10}10​H2_22​. Time-frequency analysis and charge-density evolution reveal that the enhanced HHG emission in longer chains originates from the enlarged electron acceleration distance and increased probability of multi-center recollision, especially near the terminal carbon atoms. These findings demonstrate that molecular-size engineering offers an effective strategy for controlling harmonic emission and optimizing attosecond light sources in extended molecular systems.
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.
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.