© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1003.2025

Landau-Zener-Stuckelberg interferometry in multilevel superconducting flux qubit

Xueda Wen, Yiwen Wang, Shanhua Cong, Guozhu Sun, Jian Chen, Lin Kang, Weiwei Xu, Yang Yu, Peiheng Wu, Siyuan Han

Published Mar 10, 2010• 2 citations

Abstract

Landau-Zener-Stuckelberg interferometry has been extensively investigated in quantum two-level systems, with particular interests on artificial system such as superconducting flux qubits. With increasing the driving field amplitude, more energy levels will be involved into the quantum evolution, which results in population inversion and many interesting interference patterns. These interference patterns can be used to obtain the parameters characterizing the system and probe dephasing mechanisms of the qubit. Most recently, experiments have been extended to the regime with higher-frequency and larger-amplitude driving field, in which the interference pattern exhibited more complicated characteristics. In this article, we give a universal description of the characteristics observed in both low-frequency and high-frequency regimes. Besides explaining the already observed experimental results, our theoretical model predicted many interesting phenomenon, which can be demonstrated by future experiments.

DOI: 10.48550/arxiv.1003.2025

Related papers

Play building blocks on population distribution of multilevel superconducting flux qubit with quantum interference

Xueda Wen, Yiwen Wang, Yu, Yang

Recent experiments on Landau-Zener interference in multilevel superconducting flux qubits revealed various interesting characteristics, which have been studied theoretically in our recent work by simply using rate equation method [PRB 79, 094529, (2009)]. In this note we extend this method to the same system but with larger driving amplitude and higher driving frequency. The results show various anomalous characteristics, some of which have been observed in a recent work.

arXiv:0912.0881•Dec 4, 2009•1 citation

Landau–Zener–Stückelberg Interference in Nonlinear Regime*

Tong Wu, Yuxuan Zhou, Yuan Xu +2 more

Landau–Zener–Stückelberg (LZS) interference has drawn renewed attention to quantum information processing research because it is not only an effective tool for characterizing two-level quantum systems but also a powerful approach to manipulate quantum states. Superconducting quantum circuits, due to their versatile tunability and degrees of control, are ideal platforms for studying LZS interference phenomena. We use a superconducting Xmon qubit to study LZS interference by parametrically modulating the qubit transition frequency nonlinearly. For dc flux biasing of the qubit slightly far away from the optimal flux point, the qubit excited state population shows an interference pattern that is very similar to the standard LZS interference in linear regime, except that all bands shift towards lower frequencies when increasing the rf modulation amplitude. For dc flux biasing close to the optimal flux point, the negative sidebands and the positive sidebands behave differently, resulting in an asymmetric interference pattern. The experimental results are also in good agreement with our analytical and numerical simulations.

Chinese Physics Letters•Dec 1, 2019•5 citations

Landau-Zener interference in multilevel superconducting flux qubits driven by large-amplitude fields

Xueda Wen, Yang Yu

We proposed an analytical model to analyze the Landau-Zener interference in a multilevel superconducting flux qubit driven by large-amplitude external fields. Our analytical results agree remarkably well with those of Berns et al. [Nature (London) 455, 51 (2008)]. Moreover, we studied the effect of driving frequency and dephasing rate on the interference. The dephasing generally destroys the interference, while increasing frequency rebuilds the interference at large dephasing rate. At a certain driving frequency and dephasing rate, the interference shows some anomalous features, as observed in recent experiments.

arXiv:0906.4620•Physical Review B•Mar 31, 2009•22 citations

Dynamic transition in Landau-Zener-Stückelberg interferometry of dissipative systems: The case of the flux qubit

Alejandro Ferrón, Daniel Domı́nguez, María José Sánchez

We study Landau-Zener-St\"uckelberg (LZS) interferometry in multilevel systems coupled to an Ohmic quantum bath. We consider the case of superconducting flux qubits driven by a dc+ac magnetic fields, but our results can apply to other similar systems. We find a dynamic transition manifested by a symmetry change in the structure of the LZS interference pattern, plotted as a function of ac amplitude and dc detuning. The dynamic transition is from an LZS pattern with nearly symmetric multiphoton resonances to antisymmetric multiphoton resonances at long times (above the relaxation time). We also show that the presence of a resonant mode in the quantum bath can impede the dynamic transition when the resonant frequency is of the order of the qubit gap. Our results are obtained by a numerical calculation of the finite time and the asymptotic stationary population of the qubit states, using the Floquet-Markov approach to solve a realistic model of the flux qubit considering up to ten energy levels.

arXiv:1511.09400•Physical review. B./Physical review. B•Feb 29, 2016•20 citations

Noise effects on Landau-Zener-Stückelberg interferometry in multilevel artificial atoms

Lingjie Du, Yang Yu

We have developed a comprehensive theory of Landau-Zener-St\"uckelberg interferometry in a strongly driven multilevel superconducting flux qubit interacting with the environment bath. It is found that not only the dephasing but also the intrawell relaxation make important contribution to the interference fringes. We propose that Fourier-transform-based phase tomography can be used to determine the intrawell relaxation rate as well as the type of the low-frequency noise, besides dephasing rate. The quantitative agreement between our theory and the experimental results indicates that Landau-Zener-St\"uckelberg interferometry provides a useful tool to analyze the noise source of solid-state qubits.

Physical Review B•Oct 25, 2010•16 citations

Revealing the system-bath coupling via Landau-Zener-Stückelberg interferometry in superconducting qubits

Ana Laura Gramajo, Daniel Domı́nguez, María José Sánchez

In this work we propose a way to unveil the type of environmental noise in strongly driven superconducting flux qubits through the analysis of the Landau-Zener-St\"uckelberg (LZS) interferometry. We study both the two-level and multilevel dynamics of the flux qubit driven by a $\mathrm{dc}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\mathrm{ac}$ magnetic field. We find that the LZS interference patterns exhibit well-defined multiphoton resonances whose shape strongly depends on the timescale and the type of coupling to a quantum bath. For the case of transverse system-bath coupling, the $n$-photon resonances are narrow and nearly symmetric with respect to the dc magnetic field for almost all timescales, while in the case of longitudinal coupling they exhibit a change from a wide symmetric to an antisymmetric shape for times of the order of the relaxation time. We find this dynamic behavior relevant for the interpretation of several LZS interferometry experiments in which the stationary regime is not completely reached.

arXiv:1906.03514•Physical review. B./Physical review. B•Aug 5, 2019•6 citations

Landau-Zener-Stuckelberg interferometry has been extensively investigated in quantum two-level systems, with particular interests on artificial system such as superconducting flux qubits. With increasing the driving field amplitude, more energy levels will be involved into the quantum evolution, which results in population inversion and many interesting interference patterns. These interference patterns can be used to obtain the parameters characterizing the system and probe dephasing mechanisms of the qubit. Most recently, experiments have been extended to the regime with higher-frequency and larger-amplitude driving field, in which the interference pattern exhibited more complicated characteristics. In this article, we give a universal description of the characteristics observed in both low-frequency and high-frequency regimes. Besides explaining the already observed experimental results, our theoretical model predicted many interesting phenomenon, which can be demonstrated by future experiments.

Landau–Zener–Stückelberg (LZS) interference has drawn renewed attention to quantum information processing research because it is not only an effective tool for characterizing two-level quantum systems but also a powerful approach to manipulate quantum states. Superconducting quantum circuits, due to their versatile tunability and degrees of control, are ideal platforms for studying LZS interference phenomena. We use a superconducting Xmon qubit to study LZS interference by parametrically modulating the qubit transition frequency nonlinearly. For dc flux biasing of the qubit slightly far away from the optimal flux point, the qubit excited state population shows an interference pattern that is very similar to the standard LZS interference in linear regime, except that all bands shift towards lower frequencies when increasing the rf modulation amplitude. For dc flux biasing close to the optimal flux point, the negative sidebands and the positive sidebands behave differently, resulting in an asymmetric interference pattern. The experimental results are also in good agreement with our analytical and numerical simulations.

We proposed an analytical model to analyze the Landau-Zener interference in a multilevel superconducting flux qubit driven by large-amplitude external fields. Our analytical results agree remarkably well with those of Berns et al. [Nature (London) 455, 51 (2008)]. Moreover, we studied the effect of driving frequency and dephasing rate on the interference. The dephasing generally destroys the interference, while increasing frequency rebuilds the interference at large dephasing rate. At a certain driving frequency and dephasing rate, the interference shows some anomalous features, as observed in recent experiments.

We study Landau-Zener-St\"uckelberg (LZS) interferometry in multilevel systems coupled to an Ohmic quantum bath. We consider the case of superconducting flux qubits driven by a dc+ac magnetic fields, but our results can apply to other similar systems. We find a dynamic transition manifested by a symmetry change in the structure of the LZS interference pattern, plotted as a function of ac amplitude and dc detuning. The dynamic transition is from an LZS pattern with nearly symmetric multiphoton resonances to antisymmetric multiphoton resonances at long times (above the relaxation time). We also show that the presence of a resonant mode in the quantum bath can impede the dynamic transition when the resonant frequency is of the order of the qubit gap. Our results are obtained by a numerical calculation of the finite time and the asymptotic stationary population of the qubit states, using the Floquet-Markov approach to solve a realistic model of the flux qubit considering up to ten energy levels.

We have developed a comprehensive theory of Landau-Zener-St\"uckelberg interferometry in a strongly driven multilevel superconducting flux qubit interacting with the environment bath. It is found that not only the dephasing but also the intrawell relaxation make important contribution to the interference fringes. We propose that Fourier-transform-based phase tomography can be used to determine the intrawell relaxation rate as well as the type of the low-frequency noise, besides dephasing rate. The quantitative agreement between our theory and the experimental results indicates that Landau-Zener-St\"uckelberg interferometry provides a useful tool to analyze the noise source of solid-state qubits.

In this work we propose a way to unveil the type of environmental noise in strongly driven superconducting flux qubits through the analysis of the Landau-Zener-St\"uckelberg (LZS) interferometry. We study both the two-level and multilevel dynamics of the flux qubit driven by a

\mathrm{dc}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\mathrm{ac}

magnetic field. We find that the LZS interference patterns exhibit well-defined multiphoton resonances whose shape strongly depends on the timescale and the type of coupling to a quantum bath. For the case of transverse system-bath coupling, the

n

-photon resonances are narrow and nearly symmetric with respect to the dc magnetic field for almost all timescales, while in the case of longitudinal coupling they exhibit a change from a wide symmetric to an antisymmetric shape for times of the order of the relaxation time. We find this dynamic behavior relevant for the interpretation of several LZS interferometry experiments in which the stationary regime is not completely reached.