Geometric quantum drives: Hyperbolically driven quantum systems and beyond

• URL: http://arxiv.org/abs/2503.08242v1
• Date: Tue, 11 Mar 2025 10:05:10 GMT
• Title: Geometric quantum drives: Hyperbolically driven quantum systems and beyond
• Authors: Jihong Wu, Chuan Liu, Daniel Bulmash, Wen Wei Ho,
• Abstract summary: We present a construction of driven quantum systems in which the position of a classical particle is used to steer a quantum Hamiltonian over time.<n>This results in a time-dependent quantum Hamiltonian with a structured temporal profile and properties dependent on the local and global nature of the underlying choice of manifold.<n>We show that fully gapped hyperbolically driven quantum systems in the adiabatic limit are topologically classified by a quantized dynamical response.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a geometrical construction of driven quantum systems, in which the position of a classical particle moving autonomously on a smooth connected manifold is used to steer a quantum Hamiltonian over time. This results in a time-dependent quantum Hamiltonian with a structured temporal profile and properties dependent on the local and global nature of the underlying choice of manifold. We explain how our construction recovers the well-known classes of periodically-driven and quasiperiodically-driven quantum systems, but also unveils fundamentally novel classes of quantum dynamics: by steering a quantum Hamiltonian using a classical particle freely moving on a compact 2d hyperbolic Riemann surface called the Bolza surface, we demonstrate an example of a hyperbolically driven quantum system. We show that fully gapped hyperbolically driven quantum systems in the adiabatic limit are topologically classified by a quantized dynamical response. We propose geometric quantum driving to be a general framework to chart the landscape of time-dependent quantum systems, which can be realized with time-dependent controls available in modern day quantum simulators.

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