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Physics of the Solid State

Relaxation dynamics of superconducting Josephson cubits in a strong alternating field

A. I. Gel’man, Сатанин Аркадий Михайлович

Published Nov 1, 2010• 0 citations
Publisher

Abstract

The quantum trajectory method has been applied to study the influence of noise on the level populations of a cubit in separate realizations of the experiment and to follow the transition to the averaged dynamics obtained by multiple measurements of the cubit state. As an example of applying the developed method, the influence of noise on the interference pattern appearing in amplitude spectroscopy due to the Landau-Zener transitions in an alternating field has been analyzed. The influence of the number of repeated measurements and fluctuations in the phase of the exciting pulse during formation of the response of a cubit to the external field has been studied, which made it possible to interpret recent experiments from the viewpoint of single realizations and averaged dynamics.

DOI
10.1134/s106378341011003x

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•Jan 1, 2013•1 citation
The quantum trajectory method has been applied to study the influence of noise on the level populations of a cubit in separate realizations of the experiment and to follow the transition to the averaged dynamics obtained by multiple measurements of the cubit state. As an example of applying the developed method, the influence of noise on the interference pattern appearing in amplitude spectroscopy due to the Landau-Zener transitions in an alternating field has been analyzed. The influence of the number of repeated measurements and fluctuations in the phase of the exciting pulse during formation of the response of a cubit to the external field has been studied, which made it possible to interpret recent experiments from the viewpoint of single realizations and averaged dynamics.
The effect of noise on the populations of the levels of a qubit in individual experimental implementations has been studied by the quantum trajectory method. A transition to the average dynamics obtained by means of multiple measurements of the state of the qubit is analyzed. The developed method is applied to investigate the effect of noise on the interference pattern appearing in the amplitude spectroscopy of the qubit in a strong variable field owing to Landau-Zener transitions. The effect of the number of repeated measurements and the fluctuation of the phase of a pump pulse on the formation of the response of the qubit to the external field has been analyzed. This makes it possible to interpret recent experiments in terms of individual implementations and averaged dynamics.
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.
The populations of energy levels of interacting qubits have been studied as functions of the field amplitude and other control parameters for a constant frequency of the external electromagnetic field. It has been found that the qubit coupling constant strongly affects the quantum-coherent Landau-Zener transitions between the qubit states and the formation of an interference pattern in level populations, depending on the field parameters. It has been demonstrated that it is possible to determine the qubit coupling constant by Landau-Zener interferometry.
The dynamics of a superconducting Josephson qubit coupled to a bosonic bath has been studied by the quantum trajectory method. The excitation of the qubit by Rabi pulses has been considered. Excited state dissipative dynamics interrupted by quantum jumps has been simulated both for each single realization and for an average over the ensemble of realizations. The transition to the averaged behavior, which is characterized by the intervals of longitudinal and transverse relaxation, has been studied. The simulation results qualitatively agree with the recent single-shot measurements of qubits.
The topic of this thesis is superconducting electric circuits. Technical advances have made possible the experimental study of Josephson junction based circuit elements which sustain quantum mechanical properties long enough to be denoted as quantum devices. The quantum state can be controlled with electronic variables and measured using standard electrical setups. The research is motivated by the possibility to examine quantum phenomena in circumstances that can be customized, prospects of new quantum devices, and the development of quantum information processing. This thesis presents theoretical studies on the nonlinear and stochastic driving of a superconducting quantum two-level system (qubit). We first investigate the energy level shifts a single-Cooper-pair transistor under large amplitude driving realized via the inherently nonlinear Josephson energy by using an external magnetic flux. The effective driving field substantially deviates from a circular polarization and linear coupling. The energy level shifts are compared to the cases of a vanishing and a weak driving field, measured as the Stark shift and the generalized Bloch-Siegert shift, respectively. We describe criteria for the natural basis of the analytical and the numerical calculations. In addition to that, we develop a formalism based on the Floquet method for the weak probe measurement of the strongly driven qubit. In the latter part of the thesis research, we study utilization of a stochastic driving field whose time evolution is not regular but follows probabilistic laws. We concentrate on the motional averaging phenomenon and show that it can be measured with an unparalleled accuracy by employing a flux-modulated transmon qubit. As the stochastically modulated qubit is simultaneously measured with a moderate driving field, we develop a theoretical description accounting the possible interference effects between the modulation and the drive. The comparison with experimental results shows good agreement. Motional averaging phenomenon can be applied to estimate the properties of fluctuation processes occurring in qubits, e.g., the quasiparticle tunneling or the photon shot noise. Resting on the motional averaging, we anticipate that the qubit dephasing times can be improved if one can accelerate the dynamics of two-level fluctuators. We apply a semiclassical formalism where the qubit is treated with quantum mechanical concepts whereas the driving fields are classical. In the solution procedure, the numerical results support the main analytical understanding. As the theoretical results are extensively compared to reflection measurements, we construct an explicit connection between the dynamics of the studied quantum devices and the measured reflection coefficient.