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🕳️ Jaynes–Cummings Model — Vacuum Rabi Oscillations

Interactive Jaynes–Cummings simulator: watch vacuum Rabi oscillations of a single atom coupled to a cavity photon mode, plus quantum collapse and revival for coherent light.

Quantum Physics2DAdvanced60 FPS

About the Jaynes–Cummings Model

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.

Frequently Asked Questions

What is the Jaynes–Cummings model?

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).

Why does the atom still oscillate when n = 0 (the vacuum)?

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.

What causes the collapse-and-revival pattern in coherent-state mode?

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.

Where is this physics used in real experiments?

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.

⚙ Under the hood

Interactive Jaynes–Cummings simulator: watch vacuum Rabi oscillations of a single atom coupled to a cavity photon mode, plus quantum collapse and revival for coherent light.

Canvas 2DQuantum OpticsRabi OscillationsCavity QEDCollapse and Revival

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install