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arXiv:1305.4800 · Physical Review B

Amplitude and phase effects in Josephson qubits driven by a biharmonic electromagnetic field

Сатанин Аркадий Михайлович, M. V. Denisenko, A. I. Gelman, Franco Nori

Published Sep 22, 2014• 27 citations
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Abstract

We investigate the amplitude and phase effects of qubit dynamics and excited-state population under the influence of a biharmonic control field. It is demonstrated that the biharmonic driving field can have a significant effect on the behavior of quasienergy level crossing as well as on multiphoton transitions. Also, the interference pattern for the populations of qubit excited states is sensitive to the signal parameters. We discuss the possibility of using these effects for manipulating qubit states and calibrating nanosecond pulses.

DOI
10.1103/physrevb.90.104516

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We investigate the amplitude and phase effects of qubit dynamics and excited-state population under the influence of a biharmonic control field. It is demonstrated that the biharmonic driving field can have a significant effect on the behavior of quasienergy level crossing as well as on multiphoton transitions. Also, the interference pattern for the populations of qubit excited states is sensitive to the signal parameters. We discuss the possibility of using these effects for manipulating qubit states and calibrating nanosecond pulses.
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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.
Fluctuations of the population of a Josephson qubit in an alternating field, which is a superposition of electromagnetic pulses with large amplitudes, are studied. It is shown that the relative phase of pulses is responsible for the rate of Landau–Zener transitions and, correspondingly, for the frequency of transitions between adiabatic states. The durations of pulses incident on the qubit are controlled with an accuracy of the field period, which results in strong mesoscopic fluctuations of the population of the qubit. Similar to the magnetic field in mesoscopic physics, the relative phase of pulses can destroy the interference pattern of the population of the qubit. The influence of the duration of the pulse and noise on the revealed fluctuation effects is studied.
We investigate the effect of broken time reversal symmetry in flux qubits driven by a biharmonic magnetic flux signal with a phase lag. In the regime of large relaxation times, we explicitly compute the transition rate between the ground and the excited state, accounting for decoherence as a classical noise. Through a direct analogy between interference effects at the avoided level crossing and scattering events in weakly disordered electronic mesoscopic systems, the transition rate plays the role of an effective transmittance while the phase lag acts as a time reversal control parameter. Clear signatures of both weak localization and conductance fluctuations-like effects are predicted. Their behavior is studied as a function of the coherence rate, and a comparison with recent experimental results is performed. Our study shows that it is decoherence, and not the driving protocol, what limits the experimental detection of weak localization effects.