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arXiv:2003.00322 · Physical review. B./Physical review. B

Landau-Zener-Stückelberg-Majorana interferometry of a superconducting qubit in front of a mirror

P. Y. Wen, O. V. Ivakhnenko, M. A. Nakonechnyi, Baladitya Suri, Jia Jhan Lin, Wei-Ju Lin, Jung-Chieh Chen, Sergey N Shevchenko, Franco Nori, I.-C. Hoi

Published Aug 31, 2020• 32 citations
arXivHTMLPDF

Abstract

We investigate the Landau-Zener-St\"uckelberg-Majorana interferometry of a superconducting qubit in a semi-infinite transmission line terminated by a mirror. The transmon-type qubit is at the node of the resonant electromagnetic (EM) field, ``hiding'' from the EM field. We modulate the resonant frequency of the qubit by applying a sinusoidal flux pump. We perform spectroscopy by measuring the reflection coefficient of a weak probe in the system. Remarkable interference patterns emerge in the spectrum, which can be interpreted as multiphoton resonances in the dressed qubit. Our calculations agree well with the experiments.

DOI
10.1103/physrevb.102.075448

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We investigate the Landau-Zener-St"uckelberg-Majorana interferometry of a superconducting qubit in a semi-infinite transmission line terminated by a mirror. The transmon-type qubit is at the node of the resonant electromagnetic (EM) field, ``hiding'' from the EM field. We modulate the resonant frequency of the qubit by applying a sinusoidal flux pump. We perform spectroscopy by measuring the reflection coefficient of a weak probe in the system. Remarkable interference patterns emerge in the spectrum, which can be interpreted as multiphoton resonances in the dressed qubit. Our calculations agree well with the experiments.
We consider the dynamics and stationary regime of a capacitively shunted transmon-type qubit in front of a mirror. The qubit is affected by probe and dressing signals. By varying the parameters of these signals and then analyzing the probe signal (reflected by the ``atom plus mirror'' system), it is possible to explore the system dynamics, which can be described by the Bloch equation. The obtained time-dependent occupation probabilities are related to the experimentally measured reflection coefficient. The study of this type of dynamics opens up new horizons for better understanding the ``qubit plus mirror'' circuit properties and the underlying physical processes, such as Landau-Zener-St\"uckelberg-Majorana transitions.
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 dc+ac\mathrm{dc}\phantom{\rule{0.16em}{0ex}}+\phantom{\rule{0.16em}{0ex}}\mathrm{ac}dc+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 nnn-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.
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.
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.
We demonstrate amplification (and attenuation) of a probe signal by a driven two-level quantum system in the Landau-Zener-St\"uckelberg-Majorana regime by means of an experiment, in which a superconducting qubit was strongly coupled to a microwave cavity, in a conventional arrangement of circuit quantum electrodynamics. Two different types of flux qubit, specifically a conventional Josephson junctions qubit and a phase-slip qubit, show similar results, namely, lasing at the working points where amplification takes place. The experimental data are explained by the interaction of the probe signal with Rabi-like oscillations. The latter are created by constructive interference of Landau-Zener-St\"uckelberg-Majorana (LZSM) transitions during the driving period of the qubit. A detailed description of the occurrence of these oscillations and a comparison of obtained data with both analytic and numerical calculations are given.
We proposed a different method to measure the energy spectrum of a superconducting flux qubit. Different from the conventional frequency spectroscopy, a linear triangle pulse was used to drive the qubit through the anticrossing and to generate Landau-Zener-St\"uckelberg interference patterns, from which the information of the energy spectrum can be extracted. This method facilitates the spectroscopy in regimes of very large energies. Moreover, without installing microwaves lines one can simplify the experimental setup and reduce the unwanted effects of noise. The idea can be applied to other quantum systems as well, opening the possibility of calibrating and manipulating qubits with linear pulses.