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arXiv:2103.14285 · Physical Review A

Control of spectroscopic features of multiphoton transitions in two coupled qubits by driving fields

V. O. Munyaev, M. V. Bastrakova

Published Jul 26, 2021• 9 citations
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Abstract

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.

DOI
10.1103/physreva.104.012613

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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.
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.
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 multiphoton spectroscopy of artificial solid-state four-level quantum system. This system is formed by two coupled superconducting flux qubits. When multiple driving frequency of the applied microwaves matches the energy difference between any two levels, the transition to the upper level is induced. We demonstrate two types of the multiphoton transitions: direct transitions between two levels and ladder-type transitions via an intermediate level. Our calculations show, that for the latter transitions, in particular, the inverse population of the excited state with respect to the ground one is realized. These processes can be useful for the control of the level population for the multilevel scalable quantum systems.
Resonant driving enables coherent control of quantum systems, including single and coupled qubits. From a complementary perspective, transitions of a quantum system can be exploited for the detection of microwave photons. In this work, we theoretically investigate resonant multiphoton excitations in a system of qubits. When the energy of K photons matches the energy splitting of the qubit system, the absorption of these photons leads to collective excitation of the qubits. We focus on the case of two coupled qubits and analyze the quantum dynamics of both excitation and relacation processes. In the particular case where only a single qubit is relevant and the remaining qubits can be neglected, the dynamics admits an analytical treatment. We examine multiphoton resonances, the Bloch-Siegert shift, and population inversion, phenomena that are central to both coherent quantum control and microwave photon detection.
We study the effect of a time-dependent driving field with a high amplitude on a system composed of two coupled qubits (two-level systems). Using the rotating-wave approximation (RWA) makes it possible to find simple conditions for resonant excitation of the four-level system. We find that the resonance conditions include the coupling strength between the qubits. Numerical simulations confirm the qualitative conclusions following from the RWA. To reveal the peculiarities of resonant transitions caused by the quasilevel motion and crossing in a periodic driving field, we use Floquet states, which determine the precise intermediate states of the system. Calculating the quasienergy states of the multilevel system makes it possible to find the transition probabilities and build interference patterns for the transition probabilities. The interference patterns demonstrate the possibility of obtaining various pieces of information about the qubits, since the positions of transition-probability maxima depend on various system parameters, including the coupling strength between the qubits.