Laser-Dressed States on Riemannian Manifolds: A Generalization of the Kramers-Henneberger Transformation

• URL: http://arxiv.org/abs/2402.10572v1
• Date: Fri, 16 Feb 2024 10:57:34 GMT
• Title: Laser-Dressed States on Riemannian Manifolds: A Generalization of the Kramers-Henneberger Transformation
• Authors: Hannah Bendin, Benjamin Schwager, Jamal Berakdar
• Abstract summary: We analytically study the laser-driven nonlinear dynamics of a quantum particle. The geometry of space results in a potential-like term that supports bound states on the manifold. We deduce a Schr"odinger-like equation in the Kramers-Henneberger frame.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum particles under geometric constraints are sensitive to the geometry and topology of the underlying space. We analytically study the laser-driven nonlinear dynamics of a quantum particle whose motion is constrained to a two-dimensional Riemannian manifold embedded in a three-dimensional hyperspace. The geometry of space results in a potential-like term that supports bound states on the manifold. In the presence of a laser field, we derive expressions for a generalized Kramers-Henneberger-type unitary transformation which is shown to be generally space- and time-dependent, and deduce a Schr\"odinger-like equation in the Kramers-Henneberger frame. Compared to a flat (geometrically trivial) space, new time-averaged coefficients of differential operators and operator-valued perturbation terms appear which determine the geometry-dependent laser-dressed states on Riemannian manifolds.

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