Phys. Rev. Lett. 132, 023602 (2024)

Engineering Arbitrary Hamiltonians in Phase Space

Lingzhe Guo^1,2,*  and Vittorio Peano²

1 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300072, China

2 Max Planck Institute for the Science of Light, Staudtstrasse 2, 91058 Erlangen, Germany

* lingzhen_guo@tju.edu.cn

Abstract

We introduce a general method to engineer arbitrary Hamiltonians in the Floquet phase space of a periodically driven oscillator, based on the noncommutative Fourier transformation technique. We establish the relationship between an arbitrary target Floquet Hamiltonian in phase space and the periodic driving potential in real space. We obtain analytical expressions for the driving potentials in real space that can generate novel Hamiltonians in phase space, e.g., rotational lattices and sharp-boundary wells. Our protocol can be realized in a range of experimental platforms for nonclassical state generation and bosonic quantum computation.