Probing individual tunneling fluctuators with coherently controlled tunneling systems

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Probing individual tunneling fluctuators with coherently controlled tunneling systems

Saskia M. Meißner, Arnold Seiler, Jürgen Lisenfeld, Alexey V. Ustinov, and Georg Weiss

Phys. Rev. B 97, 180505(R) – Published 25 May 2018

Abstract

Josephson junctions made from aluminum and its oxide are the most commonly used functional elements for superconducting circuits and qubits. It is generally known that the disordered thin film ${AlO}_{x}$ contains atomic tunneling systems. Coherent tunneling systems may couple strongly to a qubit via their electric dipole moment, giving rise to spectral level repulsion. In addition, slowly fluctuating tunneling systems are observable when they are located close to coherent ones and distort their potentials. This interaction causes telegraphic switching of the coherent tunneling systems' energy splitting. Here, we measure such switching induced by individual fluctuators on timescales from hours to minutes using a superconducting qubit as a detector. Moreover, we extend the range of measurable switching times to millisecond scales by employing a highly sensitive single-photon qubit swap spectroscopy and statistical analysis of the measured qubit states.

Received 5 December 2017
Revised 22 December 2017

DOI:https://doi.org/10.1103/PhysRevB.97.180505

Physics Subject Headings (PhySH)

Point defects

Disordered systems

Josephson junctions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Saskia M. Meißner¹, Arnold Seiler¹, Jürgen Lisenfeld¹, Alexey V. Ustinov^1,2, and Georg Weiss¹

¹Physikalisches Institut, Karlsruher Institut für Technologie (KIT), D-76128 Karlsruhe, Germany
²Russian Quantum Center, National University of Science and Technology MISIS, Moscow 119049, Russia

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Issue

Vol. 97, Iss. 18 — 1 May 2018

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Images

Figure 1
Energy fluctuation of a TS resonance $f_{TS}$ due to a TLF. (a) The TS resonances are measured by application of a long microwave pulse $f_{μ w}$ observing the qubit population $P (|1〉)$ after aswap pulse as shown in the pulse sequence (b). Each data point comprises 1000 single measurements within 0.7 s. (c) Random telegraphic noise of the TS resonance measured at 40 mK. (d) Histograms of the population probabilities of the TLF's $|L〉$ and $|R〉$ states.
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Figure 2
Strain dependence of TS resonance frequencies: (a) Dark traces correspond to a reduced qubit population indicating that the qubit lost its excitation to a coherent TS. Particular attention is owed to the two parallel TS traces in the middle of the plot with a smooth transition from $E_{1}$ to $E_{2}$ continued as gray and black hyperbolas. The sketches show the suggested TLF energy $E_{TLF}$ (magenta, energy not to scale) and three variations of its double-well potential. (b) Protocol for single-photon swap spectroscopy. The qubit is excited by a $π$ pulse and subsequently tuned to a range of frequencies $f_{q}$ to find TSs. (c) Occupation number $N_{TLF}$ and (d) in energy basis $N_{g / e}$ as a function of strain at 40 mK with continuous lines obeying Eqs. (2) and (3).
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Figure 3
(a) 100 out of $50 000$ single measurements of the readout dc-SQUID's switching current $I_{SQ}$ (black line, left axis) and the associated qubit states $|0〉$ and $|1〉$ (gray line, right axis). (b) Qubit population probability $P (|1〉)$ for resonant excitation when it was tuned to different resonance frequencies $f_{q}$ . The dip at $f_{q} = 6.72$ GHz indicates a resonant interaction with a coherent TS. (c) and (d) show the abundancies $ln [N (m)]$ of measuring $m$ successive times the same qubit state $P (|0〉)$ (green) or $P (|1〉)$ (orange), taken either for the isolated qubit (c) or the qubit in resonance with the TS (d). For the latter case, the qubit is found with a larger probability of $P^{*} |0〉$ in its ground state. Continuous and dashed lines are fits to Eq. (4). Deviations from the unity of the sum of probabilities are due to statistical uncertainty using a finite number of measurements.
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Figure 4
(a) Two parallel TS traces as a function of mechanical deformation. (b) Line cut along the frequency axis (orange line) of (a) near the symmetry point of the TLF with two highlighted data points marked with (c) and (d) according to the following plots. (c) Statistic analysis using $50 000$ single-qubit measurements and simulation of the qubit without perturbation: The abundance $N (m)$ of measuring $m$ times the same qubit state results in two histograms for the qubit's ground $|0〉$ (green) and excited $|1〉$ state (orange), and black dashed lines are fits with Eq. (4). (d) Analysis of a coherent TS which is disturbed by an incoherent TLF: The switching probability $P_{TLF}$ is determined by comparison of the simulation with the experimental data (black lines are only guides to the eye).
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