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Vestnik of Lobachevsky State University of Nizhni Novgorod Series Social Sciences

Квантовые скачки при спонтанной релаксации сверхпроводящего кубита под действием сильного высокочастотного поля

Гельман Александр Иосифович, Сатанин Аркадий Михайлович

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

The impact of the spontaneous relaxation rate on level populations of a superconducting Josephson qubit driven by a strong RF field in single realizations of the experiment has been studied using the quantum-trajectory approach. The transformation has been traced to the averaged dynamics obtained by multiple determinations of the qubit state in recent experiments.

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The impact of the spontaneous relaxation rate on level populations of a superconducting Josephson qubit driven by a strong RF field in single realizations of the experiment has been studied using the quantum-trajectory approach. The transformation has been traced to the averaged dynamics obtained by multiple determinations of the qubit state in recent experiments.
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 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.
Two basic physical models, a two-level system and a harmonic oscillator, are realized on the mesoscopic scale as coupled qubit and resonator. The realistic system includes moreover the electronics for controlling the distance between the qubit energy levels and their populations and to read out the resonator’s state, as well as the unavoidable dissipative environment. Such rich system is interesting both for the study of fundamental quantum phenomena on the mesoscopic scale and as a promising system for future electronic devices. We present recent results for the driven superconducting qubit–resonator system, where the resonator can be realized as an LC circuit or a nanomechanical resonator. Most of the results can be described by the semiclassical theory, where a qubit is treated as a quantum two-level system coupled to the classical driving field and the classical resonator. Application of this theory allows to describe many phenomena for the single and two coupled superconducting qubits, among which are the following: the equilibrium-state and weak-driving spectroscopy, Sisyphus damping and amplification, Landau–Zener–Stückelberg interferometry, the multiphoton transitions of both direct and ladder-type character, and creation of the inverse population for lasing.
The dynamics of a weakly anharmonic superconducting qubit in a complex electromagnetic environment is generally well described by an effective multimode Kerr Hamiltonian at sufficiently weak excitation. This Hamiltonian can be embedded in a master equation with losses determined by the details of the electromagnetic environment. Recent experiments indicate, however, that when a superconducting circuit is driven with microwave signals populating the system with sufficiently high excitations, the observed relaxation rates appear to be substantially different from expectations based on the electromagnetic environment of the qubit alone. This issue is a limiting factor in the optimization of superconducting qubit readout schemes. We claim here that an effective master equation with drive-power-dependent parameters is an efficient approach to model such quantum dynamics. In this sequence of papers, we derive effective master equations, whose parameters exhibit nonlinear dependence on the excitation level of the circuit as well as the electromagnetic environment of the qubit. We show that the number nonconserving terms in the qubit nonlinearity generally lead to a renormalization of dissipative parameters of the effective master equation, while the number conserving terms give rise to a renormalization of the system frequencies. Here, in Paper I, we consider the excitation-relaxation dynamics of a transmon qubit that is prepared in a certain initial state, but is not driven otherwise. A unitary transformation technique is introduced to study the renormalization of (i) qubit relaxation due to coupling to a generic bath and (ii) Purcell decay. Analytic expressions are provided for the dependence of the nonlinear dissipative terms on the details of the electromagnetic environment of the qubit. The perturbation technique based on unitary transformations developed here is generalized to the continuously driven case in Paper II [A. Petrescu et al., Phys. Rev. B 101, 134510 (2020)].
Recent experiments in superconducting qubit systems have shown an unexpectedly strong dependence of the qubit relaxation rate on the readout drive power. This phenomenon limits the maximum measurement strength and thus the achievable readout speed and fidelity. We address this problem here and provide a plausible mechanism for drive-power dependence of relaxation rates. To this end we introduce a two-parameter perturbative expansion in qubit anharmonicity and the drive amplitude through a unitary transformation technique introduced in Part I. This approach naturally reveals number-nonconserving terms in the Josephson potential as a fundamental mechanism through which applied microwave drives can activate additional relaxation mechanisms. We present our results in terms of an effective master equation with renormalized state- and drive-dependent transition frequency and relaxation rates. Comparison of numerical results from this effective master equation to those obtained from a Lindblad master equation which only includes number-conserving terms (i.e., Kerr interactions) shows that number-nonconserving terms can lead to significant drive-power dependence of the relaxation rates. The systematic expansion technique introduced here is of general applicability to obtaining effective master equations for driven-dissipative quantum systems that contain weakly nonlinear degrees of freedom.