⚛️ quantum physics

Quantum Coherence in Superconducting Vortex States

This paper demonstrates that vortices trapped in granular superconducting films can function as coherent two-level systems with microsecond-range quantum coherence, enabling their manipulation and readout via circuit quantum electrodynamics for potential applications in quantum information and sensing.

Original authors: Ameya Nambisan, Simon Günzler, Dennis Rieger, Nicolas Gosling, Simon Geisert, Victor Carpentier, Nicolas Zapata, Mitchell Field, Milorad V. Milošević, Carlos A. Diaz Lopez, Ciprian Padurariu, Björn Ku

Published 2026-06-23

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Ameya Nambisan, Simon Günzler, Dennis Rieger, Nicolas Gosling, Simon Geisert, Victor Carpentier, Nicolas Zapata, Mitchell Field, Milorad V. Milošević, Carlos A. Diaz Lopez, Ciprian Padurariu, Björn Kubala, Joachim Ankerhold, Wolfgang Wernsdorfer, Martin Spiecker, Ioan M. Pop

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

Imagine a superconductor as a perfectly smooth, frictionless highway where electricity flows without losing any energy. Usually, if you push a magnet near this highway, it creates "traffic jams" called vortices. In normal superconductors, these traffic jams are messy, dissipative (they lose energy like a car with a flat tire), and behave like semi-classical objects. They are generally considered bad news for delicate quantum machines.

However, this paper reports a surprising discovery: in a specific type of "rough" superconductor made of tiny aluminum grains (like a road made of pebbles instead of smooth asphalt), these traffic jams can actually behave like quantum bits (qubits).

Here is the breakdown of what the researchers found, using simple analogies:

1. The Setup: A Rough Road

The scientists used a special film made of granular aluminum. Think of this not as a solid sheet, but as a mosaic of tiny islands (grains) separated by thin, insulating gaps.

The Experiment: They cooled this film down to near absolute zero (colder than outer space) while applying a magnetic field.
The Result: Instead of the magnetic field just pushing the vortices out or making them chaotic, the vortices got "stuck" (trapped) between the aluminum grains.

2. The Discovery: The Vortex as a Quantum Switch

Usually, a trapped vortex is a messy, energy-leaking entity. But here, the trapped vortex acted like a two-level system.

The Analogy: Imagine a ball sitting in a valley with two hills on either side. In a normal world, the ball rolls down and loses energy. In this quantum world, the ball can exist in a "superposition"—it is effectively in both valleys at the same time, or it can "tunnel" (teleport) from one side to the other without climbing the hill.
The "Qubit": The researchers found that these trapped vortices could be flipped between two states (like a light switch being On or Off) using microwave pulses. They call this a Vortex Qubit.

3. The "Sweet Spot" and Coherence

The researchers found a specific magnetic field strength (a "sweet spot") where the vortex is perfectly balanced between two pinning sites.

Stability: Once trapped, these vortices stayed stable for weeks.
Coherence: They could keep their quantum "memory" (coherence) for microseconds. In the world of quantum physics, this is a very long time—long enough to perform calculations.
- Relaxation Time ( $T_1$ ): The time it takes for the vortex to naturally fall back to its resting state was about 186 microseconds.
- Coherence Time ( $T_2$ ): The time it could stay in a quantum superposition was about 440 nanoseconds (extending to 1.2 microseconds with special echo techniques).

4. How They Read It

To see what the vortex was doing, they connected it to a microwave resonator (a tiny circuit that vibrates at a specific frequency, like a tuning fork).

The Interaction: When the vortex changed its state, it slightly shifted the frequency of the resonator.
The Measurement: By listening to this shift, they could tell if the vortex was in the "ground state" (resting) or the "excited state" (flipped) without destroying the quantum state. This is called Quantum Non-Demolition readout.

5. Why This Happens (The Theory)

The paper suggests that because the aluminum film is made of grains, the vortex gets trapped in a "double-well potential."

The Metaphor: Imagine the vortex is a marble rolling in a bowl that has been split into two separate dips by a small ridge. The magnetic field controls how deep each dip is. At the "sweet spot," the dips are equal depth, allowing the marble to quantum-tunnel back and forth between them.
The Model: The behavior fits a mathematical model called the Asymmetric Quantum Rabi Model, which describes how a quantum two-level system interacts with a wave (the resonator).

Summary of Claims

Vortices can be qubits: Contrary to the idea that vortices are always destructive, trapped vortices in granular aluminum act as stable quantum bits.
Long lifetimes: These vortex qubits have coherence times in the microsecond range, comparable to some engineered superconducting qubits.
Control: The team successfully manipulated these states (flipped them) and read them out using standard quantum electronics tools.
Mechanism: The behavior is likely caused by the vortex tunneling between pinning sites (traps) in the granular material, creating a double-well energy landscape.

The paper does not claim these are ready for commercial computers or medical devices yet; it simply establishes that these natural quantum states exist, can be controlled, and have surprisingly long lifetimes.

Technical Summary: Quantum Coherence in Superconducting Vortex States

Problem Statement
Traditionally, Abrikosov vortices in type-II superconductors are viewed as dissipative, semi-classical entities where the superconducting gap is completely suppressed in the core. Their dynamics are generally considered detrimental to applications, causing heating, flux noise, and magnetic hysteresis. While pinned vortices can enhance critical currents or improve resonator quality factors, they are typically modeled within semi-classical frameworks. Although quantum tunneling of vortices has been observed in long Josephson junctions and thin films, and zero-point motion of pinned vortices has been noted, a direct measurement of quantum coherence in superconducting vortex states has remained elusive. Recent theoretical models suggest that in granular superconductors, where the coherence length is comparable to the grain size, vortex cores might remain gapped and dissipationless, potentially behaving as quantum two-level systems.

Methodology
The authors investigated this hypothesis using a granular aluminum (grAl) micro-stripline resonator. The grAl film, with a resistivity of 3600 µΩcm, consists of 3–4 nm aluminum grains separated by amorphous AlOx barriers, creating a system near the superconducting-to-insulating transition. The resonator (3 µm wide, 400 µm long) was placed in a dilution cryostat at 20 mK and measured in reflection.

Vortices were introduced via field cooling in a perpendicular magnetic field ( $B_{cd} = 820$ µT), a regime chosen to ensure a stable configuration of 1 to 3 vortices per square without triggering complex buckling transitions. The system was probed using circuit quantum electrodynamics (cQED) techniques. The authors performed:

Two-tone spectroscopy: To map the vortex mode frequency ( $f_q$ ) and identify avoided level crossings indicating coupling to the resonator.
Quantum Non-Demolition (QND) Readout: Measuring the resonator's phase response ( $S_{11}$ ) to distinguish between the ground ( $|g\rangle$ ) and excited ( $|e\rangle$ ) vortex states.
Coherent Manipulation: Applying microwave drives at the vortex frequency to implement $\pi$ -pulses and induce Rabi oscillations.
Time-Domain Measurements: Conducting free decay, Ramsey fringe, and Hahn echo experiments to quantify energy relaxation ( $T_1$ ) and coherence times ( $T_2^*$ and $T_2^{echo}$ ).

Key Contributions and Results

Observation of Vortex Qubits (VQs): The study demonstrates that vortices trapped in grAl resonators behave as effective spins (qubits) with microsecond-range coherence. The system exhibits strong coupling to the readout resonator with a coupling strength of $g/2\pi = 92.5$ MHz.
Dispersive Coupling and Modeling: The interaction between the vortex and the resonator is described by an asymmetric quantum Rabi model (AQRM). This model successfully captures the non-monotonic dependence of the dispersive shift ( $\chi$ ) on the magnetic field, a feature that symmetric models fail to reproduce. The measured coupling and frequency dispersion are consistent with a double-well potential formed between pinning sites, modulated by the Gibbs energy in a magnetic field.
Coherence Metrics:
- Energy Relaxation ( $T_1$ ): The vortex qubit exhibits an energy relaxation time of $T_1 = 186$ µs (ranging from 40–300 µs across cycles). This is comparable to engineered superconducting qubits and qualitatively distinct from the expected dissipation of Abrikosov vortices.
- Coherence Times: Ramsey measurements yielded a coherence time of $T_2^* = 440$ ns. Hahn echo measurements extended this to $T_2^{echo} = 1.2$ µs, indicating that low-frequency noise is a dominant dephasing source.
- State Readout: The system allows for single-shot state discrimination with an effective qubit temperature of approximately 74 mK.
Physical Mechanism: The authors propose that the VQ arises from a vortex tunneling between pinning sites within the granular network. The double-well potential is formed by the interplay of the vortex Gibbs energy and random pinning potentials inherent to the disordered grAl structure. The "sweet spot" ( $B_0 = 128$ µT) corresponds to a degenerate double-well where the vortex delocalizes into symmetric and antisymmetric superpositions.

Significance and Claims
The paper claims that these findings provide direct evidence that superconducting vortices can harbor quantum coherence on microsecond timescales, challenging the semi-classical view of vortex dynamics. The results support the theoretical modeling of granular superconductors as networks of tunnel junctions capable of hosting "gapped vortices."

The significance of this work lies in:

Fundamental Physics: It validates the existence of gapped vortex states and demonstrates that vortex dynamics in granular systems can be described by quantum two-level systems rather than dissipative classical objects.
Technological Potential: The authors suggest that these VQs offer a new direction for quantum information processing, materials characterization at the microscopic level, and nanoscale sensing.
Future Outlook: While the current results are consistent with single-vortex tunneling, the authors note that distinguishing between single- and multi-vortex dynamics remains an open question requiring further investigation (e.g., via imaging or geometry shaping). They posit that engineering the pinning landscape and noise environment could enhance coherence, potentially leading to a vortex-based quantum information platform.

The paper concludes that the observation of quantum coherence in vortex states, combined with the relative technological simplicity of the grAl system, opens new avenues for exploring the physics near the superconductor-to-insulator transition and utilizing disordered superconductors as embedded tools for material characterization.