Gatemonium

Figure

Description

Gatemonium is a hybrid superconductor-semiconductor fluxonium qubit in which both the small Josephson junction and the superinductive shunt array are realized using gate-tunable Al/InAs Josephson junctions on a 2DEG (two-dimensional electron gas) platform. The name reflects its parentage: a gatemon (gate-voltage-tunable transmon) crossed with the fluxonium architecture (small junction shunted by a large superinductance).

The key innovation is that the Josephson energy $E_J$ of the single small junction can be continuously tuned by a gate voltage $V_g$ applied to the semiconductor channel, without requiring magnetic flux bias lines. This enables all-electrical frequency control and allows the device to be tuned between fundamentally different fluxonium operating regimes:

• Light fluxonium ($E_J\lesssim E_L$): Shallow cosine wells atop the parabolic inductive potential. Wavefunctions are delocalized across wells, and the qubit frequency is first-order insensitive to flux near the sweet spot — providing flux noise protection.
• Heavy fluxonium ($E_J\gg E_L$): Deep cosine wells with strongly localized states. Large $E_J/E_C$ ratio suppresses charge dispersion — providing charge noise protection.

The superinductance is achieved using approximately 600 planar Al-InAs Josephson junctions in series, each with large critical current so they behave as linear inductors. The 2DEG platform offers advantages over nanowire-based gatemons, including the ability to fabricate large junction arrays with controlled parameters.

Hamiltonian

$H=4E_C(\hat{n}-n_g{)}^2-E_J(V_g)\cos \hat{\phi }+\frac{1}{2}{E}_L{\hat{\phi }}^2$

where:

• $E_C=e^2/(2C_{\Sigma })$ is the charging energy
• $E_J(V_g)$ is the gate-voltage-tunable Josephson energy of the single junction
• $E_L=({\Phi }_0/2\pi {)}^2/L_{\text{array}}$ is the inductive energy from the superinductive shunt
• $\hat{n}$ is the Cooper pair number operator conjugate to $\hat{\phi }$
• $n_g$ is the offset charge

This is the standard fluxonium Hamiltonian, but with the critical distinction that $E_J$ is a continuously tunable function of the applied gate voltage rather than a fixed fabrication parameter. At half-flux-quantum bias (${\Phi }_{\text{ext}}={\Phi }_0/2$), the full Hamiltonian becomes $H=4E_C(\hat{n}-n_g{)}^2-E_J(V_g)\cos (\hat{\phi }-\pi )+\frac{1}{2}{E}_L{\hat{\phi }}^2$.

The nonsinusoidal current-phase relation of the semiconductor junction introduces corrections beyond the simple $\cos \hat{\phi }$ potential, which are accounted for in spectroscopic fitting.

Motivation

• Enables all-electrical frequency tuning of a fluxonium qubit without magnetic flux bias lines, simplifying wiring and reducing crosstalk at scale.
• Allows in-situ exploration of different fluxonium parameter regimes (light vs. heavy) on the same device by adjusting gate voltage.
• The 2DEG platform supports fabrication of large junction arrays with more uniform parameters than nanowire-based approaches.
• Potential path to enhanced coherence times through hybridization of fluxon and plasmon modes, and through high-plasma-frequency junction arrays.
• Demonstrates the viability of an all-superconductor-semiconductor platform for complex superconducting qubit circuits beyond the simple gatemon.

Experimental Status

First demonstration — Strickland et al. (2024):

• Fabricated gatemonium using ~600 planar Al-InAs Josephson junctions in series for the superinductance.
• Demonstrated electrostatic control of effective Josephson energy via gate voltage on the single junction.
• Performed one- and two-tone spectroscopy revealing the hybrid plasmon-fluxon spectrum.
• Extracted charging and inductive energies by fitting measured spectra with a model accounting for nonsinusoidal current-phase relation.
• Time-domain characterization showed energy relaxation times limited by inductive loss, possibly in the thin aluminum film.

Key Metrics

Metric	Value	Notes	Fidelity reference
Qubit coherence $T_1$	TBD	Early-stage device; limited by inductive loss	Strickland et al. 2024
Qubit coherence $T_2$	TBD	Not yet reported	—
$E_J$ tunability	Gate voltage	No flux bias lines needed	Strickland et al. 2024
Superinductance	~600 JJs in series	Planar Al-InAs array	Strickland et al. 2024
Anharmonicity	Large (fluxonium-like)	$E_L\ll E_J$ regime accessible	—
Operating temperature	10–20 mK	Dilution refrigerator	—

References

Original proposal and demonstration

• W. M. Strickland, B. H. Elfeky, L. Baker, A. Maiani, J. Lee, I. Levy, J. Issokson, A. Vrajitoarea, and J. Shabani, “Gatemonium: A Voltage-Tunable Fluxonium,” arXiv:2406.09002 (2024)

Related fluxonium theory

• V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, “Fluxonium: Single Cooper-Pair Circuit Free of Charge Offsets,” Science 326, 113 (2009)
• A. Somoroff, Q. Ficheux, R. A. Mencia, H. Xiong, R. V. Kuzmin, and V. E. Manucharyan, “Millisecond Coherence in a Superconducting Qubit,” Phys. Rev. Lett. 130, 267001 (2023)

Related gatemon work

• L. Casparis, M. R. Connolly, M. Kjaergaard, N. J. Pearson, A. Kringhøj, T. W. Larsen, F. Kuemmeth, T. Wang, C. Thomas, S. Gronin, G. C. Gardner, M. J. Manfra, C. M. Marcus, and K. D. Petersson, “Superconducting gatemon qubit based on a proximitized two-dimensional electron gas,” Nat. Nanotechnol. 13, 915 (2018)

Linked Papers

• strickland-2024-gatemonium

Related Entries

• gatemon — parent device (gate-tunable transmon, no superinductance)
• fluxonium — inductive shunt ancestor with oxide junctions
• transmon — capacitive shunt cousin
• andreev-spin-qubit — shares the Al/InAs material platform
• cos2phi-qubit — another protected superconducting qubit with superinductance
• flux-qubit — related persistent-current qubit