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International Conference on Information Technology and Nanotechnology (ITNT)

Control of entanglement of two coupled flux qubits by a non-resonant driving field

M. V. Bastrakova, V. O. Munyaev

Published Sep 20, 2021• 0 citations
Publisher

Abstract

We study entanglement and multiphoton transitions in a system of coupled superconducting flux qubits under the action of an alternating drving field (the frequency of the external field is much higher than the frequency of qubit transitions). The positions of multiphoton transitions are found within the framework of the quasi-energy representation and the Floquet perturbation theory. It is shown that by tuning the external control field, it is possible to control the positions of the resonances and the measure of entanglement in the system. The influence of dissipation processes on multiphoton interference effects is studied.

DOI
10.1109/itnt52450.2021.9649227

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We study entanglement and multiphoton transitions in a system of coupled superconducting flux qubits under the action of an alternating drving field (the frequency of the external field is much higher than the frequency of qubit transitions). The positions of multiphoton transitions are found within the framework of the quasi-energy representation and the Floquet perturbation theory. It is shown that by tuning the external control field, it is possible to control the positions of the resonances and the measure of entanglement in the system. The influence of dissipation processes on multiphoton interference effects is studied.
The quantum level population behavior of two coupled flux qubits depending on the external driving field characteristics is studied. Explicit expressions for the multiphoton transition probabilities at an arbitrary control field amplitude are obtained for the case of small tunnel splitting energies. We describe the controllable features of their formation and thereby the creation or destruction of entanglement on the direct interlevel transition and during the transition through intermediate states by system bias tuning. We found a feature of the qubit population inversion that results in the independence of the resonance positions from the qubit coupling strength. Using the Floquet-Markov equation, we numerically demonstrate that the positions of multiphoton resonances are stable to dissipative processes.
An analytical theory to calculate the dissipatively stable concurrence in the system of two coupled flux superconducting qubits in the strong driving field is developed. The conditions for the entanglement state generation and destruction during the formation of the multiphoton transitions regions due to the interference of Landau--Zener--Stückelberg--Majorana are found. Based on the solution of the Floquet--Markov equation, the technique is proposed to adjust the amplitudes of dc- and ac-fields for effective control of the entanglement between qubit states while taking into account the effects of the decoherence.
We study the manipulation of quantum entanglement by periodic external fields. As an entanglement measure we compute numerically the concurrence of two flux qubits coupled inductively and/or capacitively, both driven by a dc+ac magnetic flux. Also we find an analytical lower bound for the concurrence, where the dominant terms correspond to the concurrence in the Floquet states. We show that it is possible to create or destroy entanglement in a controlled way by tuning the system at or near multiphoton resonances. We find that when the driving term of the Hamiltonian does not commute with the qubit-qubit interaction term, the control of the entanglement induced by the driving field is more robust in parameter space. This implies that capacitively coupled two flux qubits are more convenient for controlling entanglement through ac driving fluxes.
We control the transition frequency of a superconducting flux qubit coupled to a frequency-tunable resonator comprising a direct current superconducting quantum interference device (dc SQUID) by microwave driving. The dc SQUID mediates the coupling between microwave photons in the resonator and a flux qubit. The polarity of the frequency shift depends on the sign of the flux bias for the qubit and can be both positive and negative. The absolute value of the frequency shift becomes larger by increasing the photon number in the resonator. These behaviors are reproduced by a model considering the magnetic interaction between the flux qubit and dc SQUID. The tuning range of the transition frequency of the flux qubit reaches $\ensuremath{\approx}1.9\phantom{\rule{0.16em}{0ex}}\mathrm{GHz}$. The effect of photon number fluctuation in the resonator to the dephasing rate of the flux qubit is also discussed.
We present a Floquet treatment of multiphoton quantum interference in a strongly driven superconducting flux qubit. The periodically time-dependent Schr\"odinger equation can be reduced to an equivalent time-independent infinite-dimensional Floquet matrix eigenvalue problem. For resonant or nearly resonant multiphoton transitions, we extend the generalized Van Vleck (GVV) nearly degenerate high-order perturbation theory for the treatment of the Floquet Hamiltonian, allowing the reduction of the infinite-dimensional Floquet matrix to an $N\ifmmode\times\else\texttimes\fi{}N$ effective Hamiltonian, where NNN is the number of eigenstates under consideration. The GVV approach allows accurate treatment of ac Stark shift, power broadening, time-dependent and time-averaged transition probability, etc., well beyond the rotating wave approximation. We extend the Floquet and GVV approaches for numerical and analytical studies of the multiphoton resonance processes and quantum interference phenomena for the superconducting flux qubit system (N=2)(N=2)(N=2) driven by intense ac fields.