Floquet Schrieffer-Wolff transform based on Sylvester equations

• URL: http://arxiv.org/abs/2407.08405v4
• Date: Fri, 24 Jan 2025 08:22:42 GMT
• Title: Floquet Schrieffer-Wolff transform based on Sylvester equations
• Authors: Xiao Wang, Fabio Pablo Miguel Méndez-Córdoba, Dieter Jaksch, Frank Schlawin,
• Abstract summary: We present a Floquet Schrieffer Wolff transform (FSWT) to obtain effective Floquet Hamiltonians and micro-motion operators of periodically driven many-body systems. We anticipate this method will be useful for designing Rydberg multi-qubit gates, controlling correlated hopping in quantum simulations in optical lattices, and describing multi-orbital and long-range interacting systems driven in-gap.
• Score: 4.58527340094927
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• Abstract: We present a Floquet Schrieffer Wolff transform (FSWT) to obtain effective Floquet Hamiltonians and micro-motion operators of periodically driven many-body systems for any non-resonant driving frequency. The FSWT perturbatively eliminates the oscillatory components in the driven Hamiltonian by solving operator-valued Sylvester equations with systematic approximations. It goes beyond various high-frequency expansion methods commonly used in Floquet theory, as we demonstrate with the example of the driven Fermi-Hubbard model. In the limit of high driving frequencies, the FSWT Hamiltonian reduces to the widely used Floquet-Magnus result. We anticipate this method will be useful for designing Rydberg multi-qubit gates, controlling correlated hopping in quantum simulations in optical lattices, and describing multi-orbital and long-range interacting systems driven in-gap.

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