On the evolution of states of controlled qubits

A. I. Kirillov^a, E. V. Polyachenko<sup>b

a</sup> Laboratory of infinite-Dimensional Analysis and Mathematical Physics, Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
^b Institute of Astronomy, RAS, Moscow, Russia

Abstract: We describe the interaction between the qubit and the electromagnetic field in a waveguide in accordance with the Lee model using the fact that photons in the waveguide are quanta of a massive scalar neutral field. We study the case where the energy of the excited state of the qubit is larger than the photon mass. We find the stationary state of the "qubit $+$ electromagnetic field " system. We describe the evolution of nonstationary states under initial conditions of the general form. We present results of numerical calculations under the initial conditions of two types: 1 the qubit is in the excited state, and there is no photon; 2) the qubit is in the ground state, and the photon is present. The study is related to the consistent quantum theory of the qubit control with the goal to force qubits to make transitions from one state to another.

Keywords: qubit, electromagnetic field in the waveguide, qubit control.

Received: 01.03.2021
Revised: 19.04.2021

DOI: 10.4213/tmf10086

 English version: Theoretical and Mathematical Physics, 2021, 208:2, 1038–1050

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