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Laplace transform approach for the dynamics of N qubits coupled to a resonator

An approach to use the method of Laplace transform for the perturbative solution of the Schr\"{o}dinger equation at any order of the perturbation for a system of \(N\) qubits coupled to a cavity with \(n\) photons is suggested. We investigate the dynamics of a system of \(N\) superconducting qu...

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Bibliographic Details
Published in:arXiv.org 2018-09
Main Authors: Amico, Mirko, Berman, Oleg L, Roman Ya Kezerashvili
Format: Article
Language:English
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Summary:An approach to use the method of Laplace transform for the perturbative solution of the Schr\"{o}dinger equation at any order of the perturbation for a system of \(N\) qubits coupled to a cavity with \(n\) photons is suggested. We investigate the dynamics of a system of \(N\) superconducting qubits coupled to a common resonator with time-dependent coupling. To account for the contribution of the dynamical Lamb effect to the probability of excitation of the qubit, we consider counter-rotating terms in the qubit-photon interaction Hamiltonian. As an example, we illustrate the method for the case of two qubits coupled to a common cavity. The perturbative solutions for the probability of excitation of the qubit show excellent agreement with the numerical calculations.
ISSN:2331-8422
DOI:10.48550/arxiv.1809.02881