Quantum computing with electrons floating above superfluid helium promises long spin coherence times and a clean substrate free of charge traps. However, until now, a single electron in this system had not been strongly coupled to a microwave field, which is necessary for reading out and manipulating spin states. This work joins recent efforts to integrate electrons on helium with superconducting circuits: control of single electrons and their coupling to resonators had been demonstrated previously, but the strong coupling regime remained out of reach. This work closes that gap by using a compact quantum dot and a high-impedance resonator.
The electron is held in a quantum dot of size 1.4×1.4 μm², formed by electrostatic potentials above superfluid helium in a microfluidic channel. A titanium nitride resonator with high kinetic impedance (Z = 3.8 kΩ) enhances the coupling to the electron's motion by a factor of 20 compared to previous designs. The coupling was measured via resonator transmission spectroscopy: when the electron's motion frequency matched the resonator frequency, vacuum Rabi splitting was observed. Additionally, two-tone spectroscopy was used to directly probe the electron's energy levels and measure the relaxation time T1.
Vacuum Rabi splitting was observed with a coupling strength g/2π = 118 ± 3 MHz, exceeding the resonator linewidth κ/2π = 23 MHz and the electron decoherence rate Γ2/2π = 61 MHz (under optimal conditions). The single-photon cooperativity was C ≈ 32. Voltage control of the electrodes allowed tuning the electron's motion frequency from 5.5 to 10 GHz and reducing decoherence by applying a negative bias. The energy relaxation time T1 reached 0.76 μs and was limited by Purcell emission into the resonator at small detunings. Decoherence Γ2 increased with temperature following a power law $T^0$.5, indicating coupling to low-frequency excitations of the helium surface or fluctuating charges.
This work for the first time brings electrons on helium into the strong coupling regime with a microwave photon, placing this platform on par with semiconductor quantum dots, where this regime has already enabled spin readout. The difference from related works in the archive is the use of a high-impedance resonator and a compact dot, which yielded a record coupling strength for this system. This opens the way to hybridizing charge and spin states via a magnetic field gradient, and thus to reading out spin qubits in microseconds.
The next step will be to introduce a magnetic field gradient to couple the electron's spin state to its motion, and through it, to the resonator. This would enable spin readout and possibly two-qubit operations. It also remains to understand the nature of the residual decoherence and find ways to suppress it, for example by improving shielding from charge fluctuations. In the long term, the architecture could be scaled to arrays of qubits on a shared helium film.
The result will impact the development of quantum computers based on electrons in superfluid helium, as well as fundamental studies of circuit quantum electrodynamics with single particles.
Integrate a magnetic gradient into the device and demonstrate spin-resonator coupling; study decoherence sources at low temperatures.
For the electron-on-helium platform, the key unresolved problem remains reading out the spin state within a time shorter than the decoherence time. This work solves the first half of the problem: strong coupling of charge motion to a photon, but it does not solve the problem of spin control and protection from noise.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
This study reports the first realization of strong coupling between the motion of a single electron on superfluid helium and a microwave photon in a superconducting resonator. A compact quantum dot and a high-impedance titanium nitride resonator were used, achieving a coupling strength of g/2π = 118 MHz, which exceeds both the decoherence rate and the resonator linewidth. Vacuum Rabi splitting, voltage tuning of the electron frequency, and measurement of the relaxation time T1, limited by Purcell emission, were demonstrated.
Where its strength is
Strong coupling in the electron-on-helium system opens a direct path to reading out spin states via the microwave field. The high resonator impedance and compact dot geometry yield record cooperativity for this platform, making hybridization of charge and spin degrees of freedom possible.
Where it could go next
Worth trying
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.56, against a usual 0.64. It looks like few have drilled nearby.
The electron is held above the helium thanks to its image charge: it is repelled from the surface but cannot enter the liquid due to a barrier of about 1 eV. The depth of the potential well for the electron in the dot is approximately 1000 GHz, which is hundreds of times larger than the energy of its motion.