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.
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Notes
It is easy to verify this by differentiating with respect to the time and using the fact that the functions \(e^{-ikz+i\omega(k)t}\) and \(f(z,t)\) and the field \(\hat{\phi}(z,t)\) are solutions of the same Klein–Gordon equation (4).
The authors are grateful to the referee for the statement of this problem.
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Funding
The work was supported by the Theoretical Physics and Mathematics Advancement Foundation “BASIS” (Grant No. 20-1-2-33).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 208, pp. 218-232 https://doi.org/10.4213/tmf10086.
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Kirillov, A.I., Polyachenko, E.V. On the evolution of states of controlled qubits. Theor Math Phys 208, 1038–1050 (2021). https://doi.org/10.1134/S0040577921080043
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DOI: https://doi.org/10.1134/S0040577921080043