🔬 mesoscale physics

Towards a micromechanical qubit based on quantized oscillations in superfluid helium

The paper proposes a novel micromechanical qubit design utilizing quantized oscillations in superfluid helium, which leverages charge-neutral Josephson tunneling to achieve discrete energy levels and millisecond-scale coherence times at millikelvin temperatures.

Original authors: Priya Sharma, Jens Koch, Eran Ginossar

Published 2026-08-18

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CC BY 4.0

Original authors: Priya Sharma, Jens Koch, Eran Ginossar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quest to build machines that can solve problems beyond the reach of ordinary computers, scientists are constantly searching for new ways to store and process information. The most successful attempts so far rely on superconducting circuits, materials that conduct electricity without any resistance. These circuits act as tiny switches that can exist in two states at once, a property known as superposition, which forms the basis of a quantum bit, or qubit. However, these electronic systems are sensitive to electrical noise and require complex shielding. A new proposal suggests looking at a different kind of fluid to achieve the same goal. This approach turns to superfluid helium, a state of matter that flows without friction and has no electrical charge. By treating this frictionless liquid not as a substance to be pumped, but as a mechanical system that can vibrate in specific, quantized steps, researchers have outlined a path toward a new type of quantum computer component that is immune to the electrical interference that plagues current designs.

The researchers, working from institutions in the United Kingdom and the United States, have proposed a specific device they call a Superfluid Helium Oscillator Quantum, or SHOQ. The core of this device is a small, cylindrical cell filled with superfluid helium-3, a rare isotope of helium that becomes superfluid at temperatures just above absolute zero. One end of this cell is sealed not by a rigid wall, but by a flexible, elastic plate, similar to a drumhead. Inside the cell, a tiny opening connects the fluid to a larger reservoir of the same liquid. This opening acts as a "weak link," a narrow passage where the fluid's behavior changes in a way that allows it to tunnel through, much like particles passing through a barrier they shouldn't be able to cross. When the fluid flows through this weak link, it creates a pressure difference that pushes against the flexible plate, causing it to move. As the plate moves, it changes the pressure, which in turn alters the flow through the link. This creates a continuous, self-sustaining oscillation where the fluid sloshes back and forth and the plate vibrates up and down.

The breakthrough in this work is the realization that these vibrations are not continuous and smooth like a wave on a pond, but are instead made of discrete, distinct steps. Just as a guitar string can only vibrate at specific notes, the superfluid in this device can only oscillate at specific energy levels. The researchers calculated that at the extremely cold temperatures required to keep the helium in its superfluid state, these energy steps are large enough to be clearly distinguished from one another. This distinctness is crucial because it allows the device to function as a qubit, where the lowest energy state represents a zero and the next energy level represents a one. The team showed that by carefully engineering the size of the weak link and the stiffness of the elastic plate, they could create a system where these energy levels are separated enough to be controlled, yet close enough to be manipulated by external signals.

A significant advantage of this design is its neutrality. Unlike the electronic circuits used in current quantum computers, which rely on the movement of charged particles, this device uses a neutral fluid. This means it is naturally shielded from the electrical noise and magnetic fluctuations that often cause errors in existing systems. The researchers found that the primary source of energy loss in their proposed device comes from a specific quantum effect involving single particles tunneling through the weak link. Even with this loss, their calculations suggest the device could maintain its quantum state for milliseconds, a duration long enough to perform complex calculations. To make the device useful, they proposed connecting it to a standard superconducting circuit, acting as a bridge that allows the neutral fluid system to be read and controlled by conventional electronic equipment.

The study provides a detailed blueprint for building these devices, offering several specific designs with different sizes for the weak link and the vibrating plate. They calculated that for a plate with a radius of about five micrometers and a weak link roughly ten nanometers wide, the system would oscillate at a frequency of about fourteen million cycles per second. At a temperature of 0.3 millikelvin, the device would be stable enough to operate as a qubit. The researchers also explored how to introduce the necessary nonlinearity to make the device behave like a true qubit rather than a simple oscillator, finding that by adjusting the physical dimensions of the components, they could create the right conditions for quantum control. While the paper does not claim to have built the device yet, it demonstrates that the physics required to make it work is sound and that the necessary conditions are within the reach of current experimental technology. This work opens a new door for quantum engineering, suggesting that the pristine, frictionless world of superfluids could host the next generation of quantum information processors.

Technical Summary: Towards a Micromechanical Qubit Based on Quantized Oscillations in Superfluid Helium

Problem Statement

The pursuit of scalable quantum information processing hardware has led to the exploration of diverse systems, including superconducting circuits, trapped ions, and photons. While superconducting qubits have achieved significant success through the use of Josephson junctions to provide necessary anharmonicity, they operate using charged Cooper pairs, making them susceptible to charge and flux noise. The authors propose an alternative architecture based on superfluid $^3$ He, a charge-neutral system. The central challenge addressed is whether a superfluid system, which lacks the direct electromagnetic coupling of superconductors, can be engineered to exhibit quantized energy levels, sufficient anharmonicity for qubit functionality, and long coherence times comparable to state-of-the-art superconducting qubits. Specifically, the paper investigates the feasibility of a "Superfluid Helium Oscillator Quantum" (SHOQ) device that couples superfluid Josephson dynamics with mechanical oscillations.

Methodology

The authors propose a theoretical framework for a hybrid electromechanical device consisting of a cylindrical cell containing superfluid $^3$ He-B, coupled to a reservoir via a nanoaperture acting as a Josephson weak link. One surface of the cell is a flexible elastic plate (membrane) that displaces in response to pressure changes.

The methodology involves:

Theoretical Modeling: Deriving the Lagrangian and Hamiltonian for the system by mapping superfluid quantities to their superconducting circuit analogues.
- The superfluid phase difference ( $\phi$ ) across the weak link is treated as the dynamical variable.
- The elastic plate acts as a "fluidic capacitor," storing potential energy, while the superfluid mass current provides the kinetic energy.
- The system is quantized using canonical quantization procedures similar to those used for superconducting transmon qubits.
Parameter Estimation: Calculating operating frequencies ( $\omega_p$ ), anharmonicity ( $\alpha$ ), and energy scales ( $E_C$ , $E_J$ ) for specific device geometries (plate radius, aperture size, stiffness $k$ ) at hydrostatic pressures of 21 bar and temperatures below 1 mK.
Dissipation Analysis: Estimating the quality factor ( $Q$ ) and coherence times ( $T_1$ ) by evaluating various dissipation channels, including viscous damping, the mechanocaloric effect, substrate two-level systems, and single quasiparticle tunneling.
Coupling Scheme: Proposing a hybrid coupling architecture where the neutral SHOQ device interacts with a conventional superconducting transmon qubit via a gate capacitance ( $C_g$ ) modulated by the plate's motion, enabling readout and control.

Key Contributions

Proposal of the SHOQ Device: The paper introduces a novel quantum device architecture that utilizes the charge-neutral nature of superfluid $^3$ He. It posits that the combination of a Josephson weak link and a mechanical oscillator creates a quantized system where the "charging energy" analogue is derived from the mechanical stiffness of the plate.
Superfluid-Superconducting Dictionary: The authors establish a rigorous mapping (Table I) between superfluid variables (chemical potential, mass current, circulation) and superconducting circuit variables (voltage, electrical current, flux). This allows the application of established circuit QED theory to superfluid mechanics.
Quantization of Mechanical-Superfluid Oscillations: The work demonstrates that the discrete energy levels of the SHOQ device are resolvable at millikelvin temperatures. It derives the Hamiltonian $H = 2km^2/(\rho^2 A^2) n^2 - (\hbar/2m)I_c \cos(2\pi K/\kappa_0)$ , showing the system behaves as a quantum anharmonic oscillator.
Hybrid Readout Mechanism: The paper proposes a specific coupling scheme where the motion of the superfluid-driven plate induces a "motional gate charge" on a superconducting qubit, allowing the neutral SHOQ state to be measured via the dispersive shift of the superconducting qubit.

Results

Quantum Regime Attainability: For a device with a 5 $\mu$ m radius plate, stiffness $k \approx 10^7$ N/m, and a 10 nm $\times$ 10 nm aperture, the authors calculate an oscillator frequency $\omega_p/2\pi \approx 14.25$ MHz. This frequency is well below the superfluid gap ( $\Delta/h \approx 87.47$ MHz), ensuring the system operates within the superfluid state.
Anharmonicity: The calculated anharmonicity ( $\alpha \approx 99.62$ kHz) allows for the resolution of the ground and first excited states. While the relative anharmonicity is small ( $\alpha_r \approx 0.007$ ), the authors note that specific design variations (e.g., Design #5 and #6 in Table II) can achieve sufficient anharmonicity to confine state occupation to the lowest two levels, a prerequisite for qubit operation.
Coherence Times: The analysis identifies single quasiparticle tunneling through the weak link as the dominant dissipation channel at low temperatures. For optimized designs (e.g., Design #5), the estimated coherence time ( $T_{sqt}$ ) is approximately 25.96 ms. This rivals or exceeds the coherence times of current state-of-the-art fluxonium and transmon qubits.
Coupling Strength: The estimated coupling strength between the SHOQ device and a superconducting qubit is $\sim 0.18$ MHz. This is deemed sufficient for dispersive readout and state tomography, provided the detuning is managed appropriately.
Design Space: The paper provides a range of design parameters (Table II) showing that varying the plate radius, aperture area, and stiffness allows tuning of the operating frequency and anharmonicity to meet qubit criteria.

Significance and Claims

The paper claims to present the first proposal for a quantum device in a charge-neutral condensed matter environment. Its significance is framed around several key points:

Noise Immunity: By utilizing charge-neutral superfluids, the device theoretically avoids the flux and charge noise challenges inherent to superconducting circuits.
Exotic Physics Platform: The SHOQ device offers a potential testbed for exploring the rich order parameter structure of superfluid $^3$ He, including topological phases, Majorana states, and half-quantum vortices, which are difficult to probe in bulk superfluids.
Scalability and Engineering: The authors argue that the quantum regime is within reach for micron-sized devices using existing fabrication techniques for mesoscopic superfluid experiments.
Future Potential: While the current proposal focuses on $^3$ He, the authors suggest that if Josephson physics can be realized in superfluid $^4$ He (which has a higher transition temperature), it could lead to SHOQ bits operating at more experimentally feasible temperatures, though this requires further development.

The authors remain modest regarding the immediate realization of the device, acknowledging that the proposed designs rely on idealized assumptions (e.g., smooth textures, pristine surfaces) and that the fabrication of micron-scale devices in superfluid helium remains at the frontier of cryogenic technology. They emphasize that the work provides a theoretical foundation and a design roadmap rather than a completed experimental demonstration.