The Jaynes–Cummings model (1963) describes the simplest possible quantum light–matter interaction: a single two-level atom coupled with strength g to one quantized mode of an electromagnetic cavity. It is the theoretical backbone of cavity quantum electrodynamics (cavity QED) and, today, of circuit QED with superconducting qubits — the same physics used in leading quantum-computing hardware. This simulator lets you drive the atom-cavity system in two regimes: a definite photon-number (Fock) state, and a coherent state resembling a small laser pulse trapped in the cavity.
Fock state: P_e(t) = cos²(g·t·√(n+1))
Coherent state: P_e(t) = ½ + ½·Σₙ Pois(n;n̄)·cos(2g·t·√(n+1))
Poisson weight: Pois(n;n̄) = e−n̄·n̄ⁿ/n!
Revival time: t_revival ≈ 2π√n̄ / g
Even with zero photons (n = 0, the electromagnetic vacuum) the excited atom still oscillates — at rate g — because it can emit a photon and reabsorb it from the vacuum fluctuations themselves. This "vacuum Rabi oscillation" has no classical analogue at all. The collapse-and-revival pattern was first observed experimentally by Rempe, Walther and Klein in 1987, and Serge Haroche later won the 2012 Nobel Prize in Physics for related cavity-QED experiments trapping and probing single photons.
The Jaynes–Cummings model, published by Edwin Jaynes and Fred Cummings in 1963, is the simplest fully quantum description of light interacting with matter: one two-level atom coupled with strength g to a single mode of a quantized electromagnetic field inside a cavity. When the cavity starts with an exact number of photons n and the atom is excited, the excited-state probability P_e(t) oscillates as a perfect cosine-squared curve at the "vacuum Rabi frequency" g√(n+1) — remarkably, this oscillation persists even at n = 0, driven by vacuum fluctuations of the electromagnetic field alone, a purely quantum effect with no classical counterpart.
Switch to the coherent-state mode to see richer behaviour: a coherent state is a Poisson-weighted superposition of many photon numbers, each oscillating at its own slightly different Rabi frequency. These components quickly fall out of step, causing the oscillation envelope to "collapse" to near-flat, then — because the frequencies are approximately commensurate near the mean photon number n̄ — drift back into phase and "revive" the oscillation. This collapse-and-revival signature, first measured by Rempe, Walther and Klein in 1987, is a hallmark of cavity quantum electrodynamics and underlies modern circuit-QED architectures used in superconducting quantum computers.
It is the simplest exactly solvable model of a single two-level atom coupled to a single quantized mode of light in a cavity, with coupling strength g. It captures the fully quantum exchange of a single excitation between atom and field, and is the foundation of cavity and circuit quantum electrodynamics (QED).
Even an empty cavity is not truly "nothing" quantum-mechanically — the electromagnetic vacuum has zero-point fluctuations. An excited atom can emit a photon into these fluctuations and reabsorb it, producing a genuine oscillation at rate g even with zero photons present. This "vacuum Rabi oscillation" has no analogue in classical physics.
A coherent state contains a spread of photon numbers with Poisson weights around the mean n̄. Each photon-number component Rabi-oscillates at its own frequency 2g√(n+1). Because these many frequencies are close but not identical, they quickly dephase (collapse), then, since √(n+1) varies smoothly and nearly linearly near n̄, they periodically drift back into phase and the oscillation reappears (revival), roughly every t_revival ≈ 2π√n̄/g.
Cavity QED experiments by Serge Haroche's group trapped microwave photons between superconducting mirrors and observed exactly this collapse-and-revival behaviour, work recognised by the 2012 Nobel Prize in Physics. The same Jaynes–Cummings coupling now describes superconducting qubits coupled to microwave resonators in circuit QED, the leading architecture behind many of today's quantum computers.