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arXiv:1009.4295 · Physical Review B

Landau-Zener-Stückelberg spectroscopy of a superconducting flux qubit

Shuang Xu, Yang Yu, Guozhu Sun

Published Oct 27, 2010• 8 citations
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Abstract

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.

DOI
10.1103/physrevb.82.144526

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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.
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.
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.
Superconducting qubits are artificial solid state quantum systems which present quantized energy level at low temperature and low dissipation. The energy difference between levels can be tuned by external driving electro-magnetic field, leading to avoided level crossings under certain conditions. Recent research has shown Landau-Zener-Stückelberg(LZS) interference can be realized in solid state qubits with such avoided level crossings. This provides a new method for the measurement of energy spectroscopy, the characterization of coupling between quantum system and environment, as well as the realization of quantum logic gates and quantum entanglement.
The device for the Josephson flux qubit can be considered as a solid-state artificial atom with multiple energy levels. When a large-amplitude harmonic excitation is applied to the system, transitions at the energy levels avoided crossings produce visible changes in the qubit population over many driven periods that are accompanied by a rich pattern of interference phenomena. We present a Floquet treatment of the periodically time-dependent Schr\"odinger equation of the strongly driven qubit beyond the standard two-level approach. For low amplitudes, the average probability of a given sign of the persistent current qubit exhibits, as a function of the static flux detuning and the driving amplitude, Landau-Zener-St\"uckelberg (LZS) interference patterns that evolve into complex diamondlike patterns for large amplitudes. In the case of highly coherent flux qubits we show that the higher-order diamonds can not be simply described relying on LZS transitions in each avoided crossing considered separately. In addition we propose a spectroscopic method based on starting the system in the first excited state instead of in the ground state, which can give further information on the energy-level spectrum and dynamics in the case of highly coherent flux qubits. We compare our numerical results with recent experiments that perform amplitude spectroscopy to probe the energy spectrum of the artificial atom.
We report an experimental measurement of Landau-Zener transitions on an individual flux qubit within a multiqubit superconducting chip. The method used isolates a single qubit, tunes its tunneling amplitude $\ensuremath{\Delta}$ into the limit where $\ensuremath{\Delta}$ is much less than both the temperature TTT and the decoherence-induced energy level broadening, and forces it to undergo a Landau-Zener transition. We find that the behavior of the qubit agrees to a high degree of accuracy with theoretical predictions for Landau-Zener transition probabilities for a double-well quantum system coupled to a nonMarkovian 1/f1/f1/f magnetic flux noise.
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.