Illustrated Physics
physics, drawn
Concept

Charging energy — where it appears

The energy needed to add one electron to a small conductor, e²/2C, which grows as the conductor shrinks. When it exceeds the thermal energy, electrons enter one at a time and current is blocked between steps, the Coulomb blockade single-electron transistors use.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

A pendulum with unequal steps. The potential −EJ cos φ of the junction against its phase, at EJ/EC = 50, with the lowest 4 levels of the circuit drawn across the well between their classical turning points, in units of the charging energy. The transitions are 18.94, 17.79, 16.50, each smaller than the one below it; a harmonic well of the same curvature would space them all at the square root of 8·EJ·EC, 20.00. The spacing shrinks because the cosine is flatter than a parabola away from its bottom, and the shrinking is what lets a microwave pulse tuned to the lowest transition leave the next one alone.

The circuit that forgets its charge

A tiny superconducting island joined to its surroundings through a Josephson junction has discrete energy levels, and two of them make a quantum bit. The first such circuits were ruined by stray charges on nearby surfaces, which moved their levels and scrambled any superposition within a nanosecond. The cure was to make the junction's energy fifty times the charging energy. That makes the levels exponentially insensitive to charge while costing only a power-law loss in the unequal spacing that lets one transition be driven alone.

electromagnetism · Superconductivity The diamonds where the island's charge is fixed. The stability diagram of a single-electron island with identical junctions: bias voltage (units of e/CΣ) against the charge the gate induces (units of e). Inside each shaded diamond, labelled with the number of extra electrons the island holds, every possible tunnelling step costs energy and no current flows; outside, at least one step pays for itself and electrons pass one at a time. The diamonds repeat every time the gate charge rises by one electron, and touch at gate charges of e/2, 3e/2, … where two charge states cost the same and the island conducts at any bias. Their height is e/CΣ in each direction. Probing the model at three points outside the diamonds gives currents of 0.60, 0.25, 0.53; inside them, nothing.

The island that takes electrons one at a time

A capacitor holds charge in proportion to its voltage, and the proportion is a property of its shape — on any piece of metal large enough to see. Make the metal small enough and cold enough, and joined to the world only by tunnel junctions, and the proportion breaks into steps: one electron's charge costs more energy than the heat or the battery can supply, so no current flows at all until it can, and then the electrons cross one by one. A charge of a single electron becomes something a voltmeter can see.

electromagnetism · Conductors

Named alongside it

The objects these essays reach for when they reach for this one.

TunnellingAnharmonicityCapacitanceCharge dispersionCooper-pairCoulomb blockadeDecoherenceElectrometerJosephson effectMacroscopic quantum stateMetrologyQuantisation

All concepts