paper

Copycat process in the early stages of einselection

arXiv:2105.14032 · doi:10.1103/PhysRevResearch.5.023188

Abstract

We identify and describe unique early time behavior of a quantum system initially in a superposition, interacting with its environment. This behavior -- the copycat process -- occurs after the system begins to decohere, but before complete einselection. To illustrate this behavior analytic solutions for the system density matrix, its eigenvalues, and eigenstates a short time after system-environment interactions begin are provided. Features of the solutions and their connection to observables are discussed, including predictions for the continued evolution of the eigenstates towards einselection, time dependence of spin expectation values, and an estimate of the system's decoherence time. In particular we explore which aspects of the early stages of decoherence exhibit quadratic evolution to leading order, and which aspects exhibit more rapid linear behavior. Many features of our early time perturbative solutions are agnostic of the spectrum of the environment. We also extend our work beyond short time perturbation theory to compare with numerical work from a companion paper.

arXiv comment13 pages, 5 figures, 1 appendix. V2: Final version accepted for publication in Phys. Rev. Research. Some edits have been made to improve the clarity of our discussion. Our results and conclusions are unchanged. Additional material has been added to the end of Appendix A (including a new figure) providing results for the SHO with a three wavepacket initial state to compare with the qutrit analysis

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