2023/04/26 by Xu Xiao, Jayameenakshi Venkatraman, Xiao, Xu +7 · 4 citations
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena
paper · pdf · doi:10.48550/arxiv.2304.13656
openalex publication_date 2023/04/26 · openalex created_date 2023/04/28 · openalex updated_date 2026/07/28
In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a direct correspondence between the diagram and algebra. Each diagram corresponds to a Hamiltonian term, the prefactor of which, like those in Feynman diagrams, involves a simple counting of topologically equivalent diagrams. Leveraging the algorithmic simplicity of our diagrammatic method, we provide a readily available computer program that generates the effective Hamiltonian to arbitrary order. We show the consistency of our schemes with existing perturbation methods such as the Schrieffer-Wolff method. Furthermore, we recover the classical harmonic balance scheme from our result in the limit of ℏ→0. Our method contributes to the understanding of dynamic control within quantum systems and achieves precision essential for advancing future quantum information processors. To demonstrate its value and versatility, we analyze five examples from the field of superconducting circuits. These include an experimental proposal for the Hamiltonian stabilization of a three-legged Schrödinger cat, modeling of energy renormalization phenomena in superconducting circuits experiments, a comprehensive characterization of multiphoton resonances in a driven transmon, a proposal for an inductively shunted transmon circuit, and a characterization of classical ultra-subharmonic bifurcation in driven oscillators. Lastly, we benchmark the performance of our method by comparing it with experimental data and exact Floquet numerical diagonalization.