Early Experiments on Macroscopic Quantum Tunneling

The Big Idea: When a Giant Ball Jumps a Hill

Imagine you have a heavy bowling ball sitting in a valley between two hills. In the everyday world (classical physics), if you don't push the ball hard enough, it will stay in that valley forever. It simply doesn't have the energy to roll over the hill.

However, in the strange world of quantum mechanics (the physics of the very small), particles like electrons can sometimes do something impossible: they can "tunnel" through the hill and appear on the other side without ever climbing over it. It's like the ball suddenly vanishing from one valley and reappearing in the next, as if it took a secret underground shortcut.

For a long time, scientists thought this "quantum tunneling" only happened to tiny things like atoms or electrons. But in the late 1970s, a group of researchers at Leiden University in the Netherlands asked a crazy question: Can a huge, visible electrical circuit do this too?

This paper is a "look back" by one of the original researchers, Willem den Boer, describing their early attempts to prove that a macroscopic (large-scale) object could perform this quantum magic.

The Experiment: A Tiny, Delicate Loop

The team built a special device called an rf-SQUID. Think of it as a superconducting (electricity flows with zero resistance) metal ring with a tiny gap in it.

The Gap: Instead of a modern, factory-made chip, they used a very old-school method: two blocks of Niobium metal pressed together by a sharp screw. This created a "point contact"—a tiny, fragile bridge where electricity could jump across.
The Goal: They wanted to see if the magnetic "current" flowing in this ring could spontaneously jump from one state to another (like the ball jumping the hill) just by using quantum tunneling, even when the temperature was low but not absolute zero.

The Challenge: Heat vs. The Quantum Shortcut

The researchers faced a major problem: Heat.

Thermal Escape (The Normal Way): If the ring is warm, the atoms vibrate. This vibration is like shaking the table the bowling ball sits on. Eventually, the shaking is so strong that the ball gets enough energy to roll over the hill. This is a normal, classical event.
Quantum Tunneling (The Magic Way): If the ring is cold enough, the shaking stops. If the ball still jumps the hill, it must be doing it via quantum tunneling.

The team cooled their device down to 1 Kelvin (about -272°C). They knew that at higher temperatures (like 4.2 K), the "shaking" (thermal energy) was too strong, and any jumps they saw were just the ball rolling over the hill. But at 1 K, the shaking was very weak.

What They Saw

When they ran the experiment at 4.2 K, the results were messy and depended heavily on the temperature, exactly as expected for normal thermal shaking.

But when they cooled it to 1 K, something strange happened:

The Jumps Continued: The magnetic current still jumped between states.
Temperature Didn't Matter: If they changed the temperature slightly, the rate of these jumps did not change.

This was the smoking gun. If the jumps were caused by heat (thermal shaking), changing the temperature should have changed the jump rate dramatically. Since the rate stayed the same, the team concluded that the "ball" was no longer rolling over the hill; it was taking the quantum shortcut.

The "Maybe" Caveat

The paper is written with a lot of humility. The author admits that back in 1979, they didn't have the perfect tools or the complete theoretical understanding we have today.

Their "bridge" (the point contact) was a bit messy and hard to measure precisely.
They weren't 100% sure if some invisible "noise" or friction was helping the jump.

So, while they believed they had seen Macroscopic Quantum Tunneling (MQT), they phrased their conclusion carefully: "MQT might be playing a role." They knew they had a strong hint, but they didn't have the "definitive proof" that would come later.

The Aftermath and Legacy

The paper notes that in 1985, other scientists (Clarke, Devoret, and Martinis) finally provided the "definitive proof" using better, cleaner technology. That work eventually led to a Nobel Prize in 2025 (according to the paper's future-dated timeline).

The author reflects on how this early, slightly "primitive" experiment was a stepping stone. It helped prove that quantum mechanics isn't just for tiny atoms; it applies to big electrical circuits too. This realization eventually paved the way for superconducting qubits, the building blocks of modern quantum computers.

Summary

The Question: Can a large electrical circuit tunnel through a barrier like a tiny particle?
The Method: They built a delicate metal ring with a screw-contact gap and cooled it to near absolute zero.
The Discovery: At 1 Kelvin, the circuit jumped states in a way that didn't depend on temperature, suggesting it was using quantum tunneling.
The Conclusion: They were likely the first to see this effect, but they couldn't prove it 100% at the time. Their work helped set the stage for the quantum computing revolution that followed.

The author ends with a fun note: while he went on to work on the silicon chips in your TV and phone screens, the quantum circuits he helped study might one day change computing even more than those screens have.

Technical Summary of "Early Experiments on Macroscopic Quantum Tunneling" by Willem den Boer

Problem Statement
Prior to the definitive 1985 confirmation of Macroscopic Quantum Tunneling (MQT) by Clarke, Devoret, and Martinis, the scientific community sought experimental evidence that quantum tunneling could occur in macroscopic electrical circuits, specifically superconducting loops containing Josephson weak links. Theoretical predictions by Ivanchenko and Zil'berman (1969) and Leggett (1978) suggested that the phase difference across a Josephson junction or the magnetic flux in a superconducting loop could tunnel through a potential barrier. However, distinguishing this quantum phenomenon from classical thermal escape was challenging due to the dominance of thermal fluctuations at accessible temperatures and the difficulty in precisely characterizing circuit parameters like capacitance and dissipation.

Methodology
The paper retrospectively analyzes experiments conducted at Leiden University in 1979 using low-capacitance Niobium (Nb) point contacts configured as a radio-frequency Superconducting Quantum Interference Device (rf-SQUID).

Device Fabrication: Unlike modern thin-film tunnel junctions, the samples consisted of two cylindrical Nb blocks separated by a thin foil, with sharpened Nb screws creating point contacts. One contact served as the Josephson junction, while the other was adjustable to close the superconducting loop.
Experimental Setup: Measurements were performed in a cryostat using 4He cooling, achieving temperatures down to approximately 1 K (dilution refrigeration was unavailable for this specific setup). The system was heavily shielded against external noise using copper, lead, and mu-metal shields, along with RF filters.
Measurement Protocol: The researchers applied an external magnetic flux ( $\Phi_x$ ) via a coil and measured the resulting trapped flux ( $\Phi$ ) inside the loop using a commercial rf-SQUID and flux transformer. Current-voltage characteristics were recorded to determine the critical current ( $I_c$ ) and resistance ( $R$ ).
Analysis: The team compared experimental flux curves against theoretical models derived from the "tilted washboard" potential. They calculated escape rates for thermal activation ( $R_{th}$ ) and quantum tunneling ( $R_{tun}$ ) using the WKB approximation, assuming a very small junction capacitance ( $C \approx 1$ fF) based on the geometry of point contacts and high plasma frequencies.

Key Results

Temperature Dependence: At 4.2 K, the flux curves exhibited continuous behavior with strong dependence on temperature variations, consistent with thermal escape being the dominant mechanism.
Low-Temperature Behavior: At 1 K, for specific parameters ( $I_c = 1.2$ µA, $L = 1.1$ nH, $L \approx 4$ ), the flux curves showed no hysteresis. Crucially, the observed escape rates remained nearly constant despite 10% variations in temperature.
Theoretical Comparison: Calculations indicated that at 1 K, the thermal escape rate ( $R_{th}$ ) should be negligible (less than 0.01 s⁻¹) and significantly lower than the tunneling rate ( $R_{tun}$ ) by a factor of $4 \times 10^5$ . The absence of hysteresis and the weak temperature dependence of the escape rates at 1 K were inconsistent with a purely thermal model but aligned with the hypothesis that MQT was driving the flux transitions.
Dissipation Considerations: The authors noted that while dissipation (due to quasi-particle currents) could theoretically suppress tunneling rates, the ring configuration might be less dissipative than current-biased junctions because the junction remains superconducting with only tiny AC voltages. Even with a potential reduction in tunneling rates by four orders of magnitude due to dissipation, tunneling was calculated to remain dominant over thermal escape at 1 K.

Significance and Claims
The paper positions these 1979 Leiden experiments as the first experimental evidence of MQT, although the authors explicitly maintain a modest tone regarding the conclusiveness of their findings.

Historical Context: The authors acknowledge that their original 1979 publication was cautious, stating that MQT "might play a role" rather than definitively proving it, due to uncertainties in dissipation and noise parameters inherent to point contacts.
Contribution: The work provided early qualitative support for Leggett's theoretical predictions, demonstrating that flux transitions in superconducting loops could occur via a mechanism other than thermal activation at temperatures where thermal escape should be negligible.
Limitations: The paper admits that the lack of precise control over capacitance and the primitive nature of point contacts (compared to later tunnel junctions) prevented a rigorous, quantitative proof. The authors state that conclusive evidence, including energy level quantization, was only provided later by the Berkeley group in 1985.
Legacy: The research underscored the validity of quantum mechanics in macroscopic systems and laid the groundwork for the eventual development of superconducting qubits and quantum computing, distinguishing the behavior of closed loops (reversible phase shifts) from current-biased junctions (DC voltage generation).