Preparation of Topological Floquet States by Quantum Optimal Control Theory

The effective electronic properties of periodically driven quantum materials are conveniently computed via the Floquet formalism. However, in practice the amplitude of the external time-periodic drive is modulated from zero to a targeted value in finite time, breaking the infinite time-periodicity of the ideal Floquet states. In that case, one is interested in how close one may steer the state from the actual time evolution to the ideal Floquet state, as quantified by an appropriate fidelity metric. For the driven quantum well model, we first determine how the fidelity varies as adjustable parameters of elementary ramping functions are varied. Then, we use the gradient ascent in function space (GRAFS) method to assess whether a quantum optimal control theory (QOCT) approach can produce non-elementary ramping functions that further improve the fidelity for a given ramping time. Of particular interest will be characterizing the attainable fidelity when certain classes of topological transitions occur, since the Chern number is provably conserved under unitary time evolution [1]. Our approach may be applied directly to the Floquet graphene antidot lattice that we introduced previously [2,3], and will provide experimentalists with the best-case ramping protocols for preparing Floquet states that are topologically distinct from the corresponding equilibrium system [4].

 

This work was supported by the NSF under grant No. OIA-1921199 and the ARO through US MURI Grant No. W911NF1810218.

 

[1] Dynamical Preparation of Floquet Chern Insulators, L. D’Alessio and M. Rigol, Nat. Commun., 6, 8336, 2015

[2] Floquet Graphene Antidot Lattices, A. Cupo et al., Phys. Rev. B, 104, 174304, 2021

[3] Optical Conductivity Signatures of Floquet Electronic Phases, A. Cupo et al., Phys. Rev. B, 108, 024308, 2023

[4] Light-Induced Anomalous Hall Effect in Graphene, J. McIver et al., Nat. Phys., 16, 38–41, 2020