How did a biased Josephson circuit reveal tunneling and discrete energy levels?
Prepare a current-biased junction
Measure escape under controlled temperature
Apply microwaves
Compare switching and resonance evidence
In Berkeley in 1984–1985, researchers repeatedly prepared a cold electrical circuit in a state with no average voltage and waited for it to switch. Some trials lasted longer than others. Changing temperature, current and microwave illumination changed the switching statistics. Those electrical measurements let John Clarke, Michel Devoret, John Martinis and their collaborators test quantum behavior in a circuit large enough to connect with ordinary wires.
Their circuit contained a Josephson junction: two superconductors separated by a thin insulating barrier. The superconducting state has a collective phase, a position in an oscillation cycle shared by many electrons. The difference between the phases on the two sides can have its own quantum energy levels and undergo tunneling. This is a collective circuit variable, distinct from the passage of a single electron through the barrier. The 2025 prize recognized macroscopic quantum tunneling and energy quantization in an electric circuit, established through this connected series of experiments.
To picture the circuit’s energy, imagine a ball resting in a hollow on a corrugated slope. The ball represents the phase difference. Increasing the bias current tilts the slope more steeply and lowers the barrier ahead. Below the ideal critical current, hollows remain: the phase can stay near a minimum, giving a zero-voltage state. After escape, a junction with weak enough damping can keep running down the slope and develop a measurable voltage.
This tilted cosine energy is called the washboard potential. Josephson current depends on phase; voltage depends on how fast phase changes. The junction capacitance gives the phase an effective inertia. Together these circuit relations produce the ball-like dynamics. The energy drawing is a mathematical representation of the junction, with capacitance, critical current and frequency-dependent damping as physical inputs.
The scale of the potential is the Josephson energy, equal to reduced Planck’s constant times critical current divided by twice the elementary charge. Relative bias means applied current divided by critical current. Phase and relative bias are dimensionless; the potential itself is an energy. These definitions connect the drawing to quantities that can be measured electrically.
Even at a fixed bias, the state is metastable: it can remain for a while and then escape. A simple rate description treats its survival as the exponential of minus the escape rate accumulated over time. The rate has units of inverse seconds. This description also applies when bias changes during a ramp, linking fixed-current lifetime measurements with switching-current histograms.
A histogram of switching currents therefore depends on the ramp speed as well as on the underlying escape process. A faster ramp leaves less time for escape at each bias. Comparing distributions without accounting for that timing can create an apparent change in physics. The original experiments used controlled electrical preparation and repeated measurements to infer rates. The observable was an electrical transition out of a prepared state; the mechanism had to be identified by comparing how those rates depended on temperature, bias and microwave excitation.
At higher temperature, thermal fluctuations can supply enough energy for the phase to pass over the barrier. The escape rate is then exponentially sensitive to barrier height divided by thermal energy, with a prefactor that also depends on the circuit. Cooling strongly suppresses this mechanism. Quantum tunneling offers another route: a state can decay through a finite barrier even when ordinary thermal activation is negligible.
A plateau on cooling also had a classical explanation to exclude. Noise arriving from warmer parts of the apparatus could keep exciting the junction; poor thermal anchoring could likewise leave it warmer than the refrigerator thermometer suggested. The 2025 scientific background emphasizes this difficulty. Interpreting the plateau required noise isolation and independent measurements of the potential and damping, so that both thermal and quantum predictions could be compared with the escape rates.
Devoret, Martinis, Daniel Esteve and Clarke studied resonant activation under conditions dominated by thermal activation in 1984. A weak microwave perturbation enhanced escape when its frequency approached the junction’s natural plasma resonance. This established a practical way to characterize the small oscillations inside a potential minimum. Thermal activation governed this experiment. The later search for discrete quantum levels needed a further spectroscopic test.
The resonance frequency constrained the well dynamics, its width helped characterize damping, and other measurements constrained critical current. The relevant impedance included the current and voltage leads at microwave frequencies. In the 1985 tunneling experiment, the junction was underdamped, meaning oscillation lost relatively little energy per cycle. Measuring the inputs under thermal-activation conditions let the later low-temperature calculation make a prediction with independently determined parameters.
The 1985 escape paper reports a quality factor of about thirty. This dimensionless number describes how slowly an oscillation loses energy; a larger value means weaker damping. Dissipation changes the escape prediction, which made the effective microwave impedance of the leads an important measured input.
Martinis, Devoret and Clarke then used escape-rate spectroscopy to look for discrete energy levels in the zero-voltage state. At a suitable frequency, a microwave photon could lift the phase system into an excited state. That state escaped more readily, so an increased switching probability revealed the transition. Electrical escape acted as the detector for an energy change inside the well.
The inferred level positions agreed quantitatively with a quantum calculation using parameters measured under classical operating conditions. The well is anharmonic, so its level spacings differ instead of repeating a single equally spaced ladder. Resolving that structure supplied information beyond a classical oscillator’s natural frequency. The 1984 thermal resonance calibrated the dynamics; the 1985 experiment tested the discrete levels within the metastable well.
A five-gigahertz transition has an energy equivalent to about twenty-four hundredths of a kelvin. At a few tens of millikelvin, thermal excitation across that gap can be strongly suppressed if the device thermalizes and the well supports the relevant levels. In the formula, E with subscripts one and zero are the upper and lower energies, h is Planck’s constant and f is the transition frequency. This is an energy conversion, useful for deciding how cold the device must be.
The same comparison explains why warm microwave noise was dangerous. A low refrigerator temperature does not remove photons arriving through electrical leads. The Berkeley apparatus used extensive filtering and thermal anchoring, and characterized the electromagnetic environment at relevant frequencies. The later low-temperature escape results agreed with the independently parameterized tunneling prediction. That combination of controlled environment, classical calibration, escape statistics and level spectroscopy was substantially stronger than a temperature plateau alone.
The achievement made a collective electrical coordinate a quantitatively testable quantum system. Classical calibration established the well dynamics, low-temperature escape tested barrier penetration, and microwave spectroscopy resolved discrete states within the well. Isolation from the environment connected these measurements. Ordinary wires could lead to an experiment in which a variable shared by many electrons answered quantum questions.
Bias, escape-rate measurements, microwave resonances and the circuit’s electromagnetic environment.
Official attribution and award year. The observation or theoretical paper may be much earlier.
Thermal-regime microwave activation calibrates plasma resonance and damping; it is not itself discrete-level evidence.
Escape-rate spectroscopy resolves transitions of the collective phase using parameters measured in the classical regime.
Underdamped-junction escape with in-situ parameter and microwave-impedance measurements; the low-temperature comparison has no adjustable parameters.
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Each experiment from this article that another series also uses, followed by the articles there.