The barrier raised a question beyond the energy gap
Giaever’s junctions showed that a thin insulator could serve as a spectroscopic window onto a superconductor. Josephson asked what else the coupling between two superconductors should do. If each electrode possesses a coherent paired state, transferring an ordinary quasiparticle is not the only possible electrical process. The collective states on the two sides can also couple directly.
In 1962 he predicted a supercurrent governed by their relative phase, including a current at zero voltage. That sounded surprising because an insulating barrier is usually associated with resistance and energy loss. The prediction concerned a weak link between ordered quantum systems, however, rather than an ordinary resistor. Understanding the new current requires distinguishing the amplitude of superconducting order, which describes its strength, from its phase, which determines how the two ordered states combine.
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Relative phase controls the coupling energy
A complex superconducting order parameter has both magnitude and phase. The absolute phase assigned to one isolated electrode is not an independently measurable knob. What matters at a junction is a gauge-invariant relative phase, including the electromagnetic field along the connection. Interference experiments make that relative quantity observable.
In the simplest conventional tunnel junction, the coupling energy changes approximately as the cosine of the phase difference. Current is related to how that energy changes when the phase changes, giving a sine-shaped current–phase relation. The critical current sets the largest stationary supercurrent in this ideal description. Its value depends on the junction and temperature. The sinusoidal relation is a useful low-transparency limit, not a universal shape for every possible weak link. This distinction lets one use a simple formula without hiding the material physics inside its adjustable current scale.
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Zero voltage and steady voltage lead to different motion
The displayed Josephson relation makes the supercurrent proportional to the sine of the phase difference. Critical current is the amplitude, measured in amperes; the phase difference is an angle in radians. A second Josephson relation makes the rate of phase change proportional to voltage, with twice the elementary charge divided by reduced Planck’s constant as the proportionality. Zero voltage allows phase to stay fixed and a stationary supercurrent to persist below the critical value.
A constant nonzero voltage has a very different consequence: phase advances steadily. The supercurrent therefore oscillates even though the applied voltage is constant. This is the ac Josephson effect. It does not imply that every experimental junction emits a clean microwave tone automatically. The surrounding circuit, damping and coupling to a detector determine what radiation or electrical signature can be observed. The relations describe a local quantum constraint; the complete apparatus still has to turn it into a measurement.
A zero-voltage supercurrent is also compatible with energy conservation. The stationary junction does not dissipate power like a resistor, but a circuit that continuously supplies energy to an external load still needs an energy source or stored energy. Persistence of current and the continuous delivery of useful power are different physical statements.
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Microwaves supplied a numerical test
An external microwave drive can synchronize the junction’s phase evolution. On a synchronized step, the average voltage equals an integer times Planck’s constant times drive frequency, divided by twice the elementary charge. The integer labels the step and frequency is measured in cycles per second. At ten gigahertz, adjacent ideal steps are separated by about twenty-one microvolts. The spacing is fixed by frequency and fundamental constants.
Shapiro’s 1963 microwave experiment supplied an important test of this voltage–frequency relationship. The experimental signature is stronger than a vaguely oscillating current: changing the applied frequency predicts how the voltage spacing must move. Material properties still control whether steps exist over a convenient current range and how large their operating margins are. The special feature is that, once the junction is correctly locked, the step voltage follows the frequency relation.
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Current at zero voltage needed more than a continuity check
A metallic short across a faulty insulating film can also carry current with a small measured voltage. Establishing a Josephson weak link therefore requires more than checking that the circuit conducts. Magnetic-field dependence, temperature dependence and microwave response provide additional tests. They ask whether the current follows coherent superconducting coupling rather than a hidden normal conducting path.
The current–voltage curve also depends on junction capacitance and damping. An underdamped junction can switch abruptly to a voltage state and return at a different current. That hysteresis belongs to the dynamics of the circuit, not simply to the static sine relation. Thermal noise can cause switching before the ideal critical current. Reading the measured switching current as the intrinsic critical current without a dynamical model can therefore bias the interpretation. These practical complications explain why a compact phase relation did not eliminate the need for careful experiments.
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A loop converted flux into an interference signal
A superconducting loop with two junctions constrains their relative phases through the enclosed magnetic flux. The two supercurrent paths can reinforce or oppose each other, so the maximum current changes periodically with flux. This is the basis of a dc SQUID. Its flux period involves a flux quantum equal to Planck’s constant divided by twice the elementary charge, approximately two thousandths of a picoweber.
As an ideal geometric example, a loop with an effective area of one hundred square micrometres changes by one flux quantum when a uniform perpendicular field changes by about twenty-one microtesla. Effective area, field focusing and inductance must be considered in a real device, so that estimate is not a calibration. Junction asymmetry prevents perfectly equal path amplitudes, and appreciable self-induced flux changes the simple interference pattern. The loop is thus a new apparatus built from the same phase coupling, not another name for a single junction’s energy spectrum.
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From phase locking to voltage measurement
The Josephson relation links a voltage to a frequency that can be measured very accurately. NIST’s account describes tests across different superconducting materials and the later development of series arrays, which raised the output from a single-junction scale to useful laboratory voltages. Cryogenic and microwave engineering were necessary to make thousands of junctions operate reliably together.
That practical history illustrates what a fundamental relation does and does not guarantee. A correct step relation does not by itself ensure that the device is on the intended step, that leads introduce no offset or that a voltmeter reads the array correctly. Independent comparisons and uncertainty analysis remain necessary. The enduring achievement was to give those measurements a reproducible quantum reference. It transformed relative phase from an apparently abstract variable into a route from controlled microwave frequency to electrical voltage.
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One phase relation connects current, flux and frequency
Josephson coupling connects the relative phase of two superconductors with measurable current and voltage. Closing a loop lets flux control interference; an external microwave frequency can set synchronized voltage steps. Different circuits turn the same coherent relation into different measurements, making weak links central to precision magnetometry, voltage standards and quantum circuits.
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