Engineering Arbitrary Hamiltonians in Phase Space

Abstract

We introduce a general method to engineer arbitrary Hamiltonians in the Floquet phase space of a periodically driven oscillator, based on the non-commutative Fourier transformation (NcFT) 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 well. Our protocol can be realised in a range of experimental platforms for nonclassical states generation and bosonic quantum computation.

arXiv commentMore results and 6 new figures are added in the 2nd version; Figures are updated and typos are corrected in the 3rd version

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Cited by in corpus (8)

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• Entangling Schrödinger's cat states by bridging discrete- and continuous-variable encoding
• Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian
• Engineering Bosonic Codes with Quantum Lattice Gates
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• Single-Period Floquet Control of Bosonic Codes with Quantum Lattice Gates
• Atomic Regional Superfluids in two-dimensional Moiré Time Crystals