Nonlinear Response via Sublinear Optics

• URL: http://arxiv.org/abs/2607.19154v1
• Date: Tue, 21 Jul 2026 14:53:14 GMT
• Title: Nonlinear Response via Sublinear Optics
• Abstract summary: Sublinear optical response lies beyond the conventional perturbative hierarchy of nonlinear optics.<n>We show that such a response can be engineered in a hydrogen atom using tracking control.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Sublinear optical response, in which the emitted field scales as a fractional power of the driving field, lies beyond the conventional perturbative hierarchy of nonlinear optics. Here, we show that such a response can be engineered in a hydrogen atom using tracking control. Rather than prescribing the driving waveform, the field is determined self-consistently from the evolving quantum state to enforce a chosen relation between the optical response and the applied field. We demonstrate accurate tracking for multiple exponents and scaling strengths, establishing that a single atomic system can be driven to realize a family of distinct sublinear responses. The calculations are enabled by a compact wave-packet continuum discretization that treats bound and continuum states on equal footing and is applied here, to the best of our knowledge, for the first time to strong-field optics and quantum control. These results establish tracking control as a general route to engineering optical responses beyond conventional polynomial nonlinearities.

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