Physics of Wave Processes and Radio SystemsPhysics of Wave Processes and Radio Systems1810-31892782-294XPovolzhskiy State University of Telecommunications and Informatics1014310.18469/1810-3189.2022.25.1.7-15UnknownEntanglement of two superconducting qubits induced by a thermal noise of a cavity with Kerr medium taking into account the atomic coherenceBashkirovEvgeny K.<p>Doctor of Physical and Mathematical Sciences, professor of the Department of General and Theoretical Physics</p>bash@samsu.ruhttps://orcid.org/0000-0003-2569-1322Samara National Research University2903202225171529032022Copyright © 2022, Bashkirov E.2022<p>The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence o</p>
<p><em>Abstract </em>The system consisting of two identical artificial atoms (qubits), resonantly interacting with the mode of quantum field of an ideal microwave cavity in the presence of Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.</p>
<p>f Kerr nonlinearity, is considered. For the considered model, an exact solution of the quantum Liouville equation for the full density matrix of the system two qubits + resonator field mode is obtained. To solve the quantum equation of evolution, the representation of dressed states, that is, the eigenfunctions of the Hamiltonian, was used. A complete set of dressed states of the considered model is found. With its help, the solution of the evolution equation was initially found for coherent initial states of qubits and Fock states of the field, that is, states with a certain number of photons in the resonator mode. Then, the above solution was generalized to the case of the thermal state of the resonator field. A reduced density matrix of two qubits is found by averaging over the field variables. The two-qubit density matrix is used to calculate the parameter of qubit entanglement in the analytical form. Concurrence was chosen as a quantitative criterion for qubit entanglement. A numerical simulation of the time dependence of the consistency of qubits for various parameters of the model and the initial states of qubits was carried out. The most interesting result seems to be that taking into account the initial coherence of qubits in the model with Kerr nonlinearity leads to a significant increase in the maximum degree of entanglement of qubits induced by the thermal field, even in the case of high intensities of the resonator field.</p>superconducting qubitsmicrowave coplanar resonatorthermal noiseKerr nonlinearityentanglementnegativityinitial qubits coherenceсверхпроводящие кубитымикроволновй копланарный резонатортепловой шумкерровская нелинейностьперепутываниеотрицательностьначальная когерентность кубитов[Dutra S.M. Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box. Hoboken: John Wiley & Sons, 2005, 389 p. DOI: https://doi.org/10.1002/0471713465][Buluta I., Ashab S., Nori F. Neutral and artificial atoms for quantum computation. Rep. 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