Controlled dc Monitoring of a Superconducting Qubit

A. Kringhøj, T. W. Larsen, B. van Heck, D. Sabonis, O. Erlandsson, I. Petkovic, D. I. Pikulin, P. Krogstrup, K. D. Petersson, and C. M. Marcus

Phys. Rev. Lett. 124, 056801 – Published 5 February 2020

Abstract

Creating a transmon qubit using semiconductor-superconductor hybrid materials not only provides electrostatic control of the qubit frequency, it also allows parts of the circuit to be electrically connected and disconnected in situ by operating a semiconductor region of the device as a field-effect transistor. Here, we exploit this feature to compare in the same device characteristics of the qubit, such as frequency and relaxation time, with related transport properties such as critical supercurrent and normal-state resistance. Gradually opening the field-effect transistor to the monitoring circuit allows the influence of weak-to-strong dc monitoring of a “live” qubit to be measured. A model of this influence yields excellent agreement with experiment, demonstrating a relaxation rate mediated by a gate-controlled environmental coupling.

Received 17 October 2019
Accepted 23 December 2019

DOI:https://doi.org/10.1103/PhysRevLett.124.056801

Physics Subject Headings (PhySH)

Josephson junctions Nanowires Superconducting qubits

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Kringhøj ¹, T. W. Larsen¹, B. van Heck ^2,3, D. Sabonis ¹, O. Erlandsson ¹, I. Petkovic¹, D. I. Pikulin², P. Krogstrup^1,4, K. D. Petersson ¹, and C. M. Marcus ¹

¹Microsoft Quantum Lab Copenhagen and Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
²Microsoft Quantum, Station Q, University of California, Santa Barbara, California 93106-6105, USA
³Microsoft Quantum Lab Delft, Delft University of Technology, 2600 GA Delft, Netherlands
⁴Microsoft Quantum Materials Lab Copenhagen, Kanalvej 7, 2800 Lyngby, Denmark

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Issue

Vol. 124, Iss. 5 — 7 February 2020

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Images

Figure 1
(a) Optical micrograph of the modified gatemon qubit device showing the bottom of the readout resonator capacitively coupled to the qubit island. The island is contacted to a nanowire placed in the highlighted green square. (b) Scanning electron micrograph (SEM) of the nanowire in the green rectangle in (a). Two removed segments of the Al shell form the qubit JJ (125 nm) and the FET (175 nm), controlled by gates $V_{Q}$ and $V_{FET}$ . The bias voltage across the nanowire is indicated $V_{J}$ . (c) Device circuit with FET off for cQED (dashed red box), and FET on allowing transport (dashed blue box). The bias voltage $V_{B}$ refers to the total voltage drop across both the nanowire and line resistance $R_{line}$ . (d) Differential conductance $d I_{B} / d V_{B}$ as a function of bias voltage $V_{B}$ shows the superconducting gap $Δ$ of the qubit JJ, with $V_{FET} = + 4 V$ and $V_{Q} = - 2.9 V$ . (e) Rabi oscillations of the qubit seen in resonator output $V_{H}$ as a function of drive time $τ$ at $V_{FET} = - 3 V$ and $V_{Q} = - 2.5 V$ , with exponentially damped sinusoid (orange).
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Figure 2
(a) Scanning electron micrograph of a gatemon without transport lead. $C_{Q}$ is the capacitance of the qubit island. (b) Same as (a) for gatemon with transport lead, with voltage bias $V_{J}$ . (c) Qubit relaxation times $T_{1}$ of the gatemons as a function of qubit frequency $f_{01}$ . Both leaded (black circle) and nonleaded (red square) devices show similar $T_{1}$ times between $3 - 8 μ s$ , with comparable mean and standard deviation values. Inset: Relaxation time $T_{1}$ (black points) at $f_{01} = 4.6 GHz$ for the leaded device as a function of wait time $τ$ , with exponential fit (orange curve) yielding $T_{1} = 6 μ s$ . Error bars are estimated from fit uncertainties.
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Figure 3
(a) Differential conductance $d I_{B} / d V_{B}$ as a function of FET gate voltage $V_{FET}$ at high bias $V_{B} = 1.0 mV$ , to approximate normal-state resistance. (b) Qubit frequency $f_{01}$ as a function of $V_{FET}$ using two-tone spectroscopy. Insets: Lorentzian fits (orange) to data points in the main panel as indicated by the corresponding markers (blue circle, green square). From each $V_{H}$ we subtract the background and normalize to the maximal value. (c) Similar to (b) relaxation times $T_{1}$ from exponential fits (insets). Error bars are estimated from fit errors.
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Figure 4
Relaxation rate $γ = 1 / T_{1}$ (black circles) as a function of FET voltage $V_{FET}$ , by inverting the experimental data from Fig. 3. Model relaxation rates $γ_{lead}$ due only to the transport lead (blue) and $γ_{tot}$ (orange) including lead and nonlead contributions (see text). The circuit model is sketched in the inset where the qubit is coupled to the environment by an effective impedance, $Z_{env} = i ω L_{FET} + {(1 / R_{F} + i ω C_{F})}^{- 1}$ . The dashed rectangle indicates the environment circuit.
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Figure 5
(a) Differential resistance of the qubit JJ, $d V_{J} / d I_{B}$ , as a function of current bias $I_{B}$ and qubit gate voltage $V_{Q}$ . Switching current $I_{s}$ (blue points) from the edge of the zero-resistance state for increasing sweep at $V_{FET} = + 4 V$ to turn the FET conducting. (b) Qubit frequency $f_{01}$ from two-tone spectroscopy as a function of $V_{Q}$ , acquired at $V_{FET} = - 3 V$ to deplete the FET. The area of missing data at 5.0–5.6 GHz is due to $f_{01}$ crossing the resonator frequency $f_{R}$ . (c) Correlation between transport and cQED data. $f_{01}$ from (b) (red) extracted as in Fig. 3, inset. $f_{01}$ from $I_{c}$ (blue) extracted by applying an RCSJ model to the data in (a) (see text).
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