Gatemonium: A Voltage-Tunable Fluxonium

TL;DR

The paper introduces gatemonium, a voltage-tunable fluxonium qubit realized with a planar Al-InAs JJ array to achieve a large inductive energy $E_L$ and gate-tunable $E_J^{eff}$. The authors formulate a circuit QED model with a nonsinusoidal current-phase relation to describe plasmon and fluxon modes, and validate it with one- and two-tone spectroscopy that maps the spectrum across heavy, intermediate, and light regimes. Time-domain measurements on plasmon modes demonstrate coherent control with $T_1$ and $T_2^{\mathrm{Rabi}}$ in the tens of nanoseconds, with inductive loss identified as the dominant decoherence path and an estimated $Q_L \sim 6.3\times 10^2$. They outline future directions for higher plasma frequencies, larger impedance JJ arrays, and voltage-tunable superinductances to enable improved coherence and scalability in voltage-tunable superconducting quantum circuits.

Abstract

We present a new style of fluxonium qubit, gatemonium, based on an all superconductorsemiconductor hybrid platform. The linear inductance is achieved using six hundred planar Al-InAs Josephson junctions (JJs) in series. By tuning the single junction with a gate voltage, we demonstrate electrostatic control of the effective Josephson energy, tuning the weight of the fictitious phase particle. One and two-tone spectroscopy of the gatemonium transitions further reveal details of the hybrid plasmon-fluxon spectrum. Accounting for the nonsinusoidal current-phase relation of the single junction, we fit the measured spectra to extract charging and inductive energies. We conduct time domain characterization of the plasmon modes in a second gatemonium device with different charging energy and JJ array inductance. We discuss future directions for this platform in gate voltage-tunable, high plasma frequency, enhanced impedance junction arrays, and enhanced coherence times for voltage tunable architectures.

Figures (11)

• Figure 1: $E_J$ tuning in the gatemonium qubit: (a) Wavefunctions of the lowest levels of the gatemonium qubit in the heavy regime with $E_J/h$ = 17.0 GHz, $E_L/h$ = 2.8 GHz and $E_C/h$ = 0.8 GHz. The external applied flux is $\Phi/\Phi_0 = 0.48$. (b) Qubit frequencies $f_{01}$ and anharmonicities $\alpha$ at zero and half flux. For large values of $E_J$, the qubit frequency at half flux is seen to approach zero and the anharmonicity $\alpha$ becomes greater than 5 GHz. As $E_J$ decreases, moving to the light regime, the spectrum becomes harmonic, as the anharmonicity goes to zero, and the qubit frequency becomes unchanged with flux and approaches $\sqrt{8E_LE_C}/h$. (c) Landscape of fluxonium devices in terms of the relative capacitive, inductive and Josephson energies. We plot the charge number transition matrix element $\langle 0| \hat{n} | 1\rangle$ at $\Phi/\Phi_0 = 0.45$ in blue color and the derivative of the qubit transition frequency with respect to flux $\partial f_{01}/\partial \Phi$ at $\Phi/\Phi_0 = 0.25$ in red. Relative energies for Fluxonium, Heavy fluxonium, and Blochnium are taken from Refs. nguyen2019, earnest2018_heavy, and Pechenezhskiy2020 respectively. The parameter ranges of two gatemonium qubits studied in this paper are also shown in yellow stars from fits to a sinusoidal current-phase relation.
• Figure 2: Device A optical image and circuit diagram: False-colored optical image of the gatemonium qubit is shown in (a) consisting of a shunt capacitor with charging energy $E_C$ (purple), a planar JJ with Josephson energy $E_J$ (yellow), and a linear inductance, implemented in the form of a series of planar JJs with inductive energy $E_L$ (blue). The inset shows an equivalent circuit diagram. Input and output transmission lines are inductively coupled to a readout resonator, which is capacitively coupled to the gatemonium. A zoomed in scanning electron micrograph (SEM) is shown in (b) of the JJ array, with aluminum islands (blue) connected via Josephson coupling through InAs weak-links (green). An SEM image of the single junction before gate deposition is shown in (c) with aluminum leads (yellow) separated by an InAs weak link (green) and the top gate placement (red).
• Figure 3: Resonator spectroscopy of Device A: Transmission across the feedline $|S_{21}|$ is shown as a function of applied external magnetic flux $\Phi/\Phi_0$ at different gate voltages. (a) The gatemonium is in the heavy regime and the dressed resonator frequency tunes periodically with flux due to coupling with the plasmon mode. Zooming in to the half flux (inset), one can see multiple crossings with the qubit $f_{01}$ and $f_{02}$. (b) In the intermediate regime the fluxon and plasmon modes become hybridized and we see $f_{02}$ cross with the readout resonator near half flux. (c) In the light regime, the detuning of the gatemonium mode with the resonator increases, leading to a less pronounced flux dependence.
• Figure 4: Two-tone spectroscopy of Device A: (a) In the heavy regime $E_{J}^\mathrm{eff}/h = 50G Hz$ the plasmon is weakly flux tunable and exhibits multiple avoided crossings near half flux. (b) Zooming in to near half flux, one can see the linearly dispersing fluxon mode, as well as various other transitions, which are labelled. (c) For $E_{J}^\mathrm{eff}/h$ = 18 GHz the fluxon and plasmon modes are hybridized with $f_{01}$ reaching near 1.0G Hz at half flux and 6.2G Hz at zero flux. (f) As $E_{J1}$ decreases, the gatemonium spectrum becomes harmonic and weakly flux tunable, as seen by the sinusoidal behavior of $f_{01}$ with flux, centered around a value of $\sqrt{8E_LE_C}$. Asymmetry with respect to flux can be attributed to drift in the qubit frequency over the course of the measurement (see Appendix F).
• Figure 5: Time domain measurements of Device B in the plasmon regime: Rabi oscillations as a function of drive frequency and drive power are shown in (a) and (b) respectively. A linecut as a function of pulse width $\tau_\mathrm{Rabi}$ for a fixed drive frequency of 6.45 GHz is shown in the inset (blue points), with a fit to the decaying sinusoid shown (yellow solid line with black dotted line the decay envelope) yielding $T_2^\mathrm{Rabi} = 102n s$.