Cavity QED Simulator: Jaynes-Cummings Model & Vacuum Rabi Oscillations

simulator intermediate ~10 min
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Ω = 141 MHz — strong coupling regime

With g = 50 MHz, κ = 5 MHz, γ = 2.5 MHz and 1 photon, the system is deep in the strong coupling regime. Vacuum Rabi oscillations occur at 141 MHz, much faster than dissipation rates.

Formula

Ω_n = 2g√(n+1) (Rabi frequency for n photons)
C = g²/(κγ) (cooperativity)
E_±(n) = ℏω(n+½) ± ½ℏ√(Δ² + 4g²(n+1))

Atoms Meet Photons

When a single atom is placed inside a high-finesse optical cavity, the atom-photon interaction is enhanced by the cavity's ability to recirculate photons thousands of times. If the coupling rate g exceeds both the cavity decay rate κ and atomic spontaneous emission rate γ, the system enters the strong coupling regime — a cornerstone of quantum optics recognized by the 2012 Nobel Prize awarded to Serge Haroche.

The Jaynes-Cummings Ladder

The Jaynes-Cummings model, the simplest fully quantum model of light-matter interaction, predicts an anharmonic energy ladder. Each rung with n photons splits into two levels separated by 2g√(n+1). This √(n+1) scaling — the hallmark of quantum field theory — means the splitting grows with photon number but not linearly, distinguishing it from any classical model.

Vacuum Rabi Oscillations

Even when no photons are present, an excited atom in a cavity oscillates between emitting and reabsorbing a photon at frequency 2g. These vacuum Rabi oscillations demonstrate that the vacuum itself has structure. Adding photons increases the oscillation frequency as √(n+1), and with many photons, collapses and revivals appear as the different frequency components dephase and rephase.

From Cavities to Circuits

The same physics governs superconducting qubits coupled to microwave resonators in circuit QED — the foundation of modern quantum computing platforms from IBM and Google. The cooperativity C = g²/(κγ) determines gate fidelity, readout contrast, and entanglement generation rates. Understanding cavity QED is essential for designing the next generation of quantum processors.

FAQ

What is cavity QED?

Cavity quantum electrodynamics (cavity QED) studies the interaction between atoms and photons confined in high-finesse optical or microwave cavities. When the atom-photon coupling rate exceeds the dissipation rates, the system enters the strong coupling regime where a single photon can be coherently exchanged between atom and cavity many times.

What is the Jaynes-Cummings model?

The Jaynes-Cummings model describes a two-level atom interacting with a single mode of a quantized electromagnetic field. It predicts vacuum Rabi oscillations, collapse and revival of atomic inversion, and an anharmonic energy ladder with splitting 2g√(n+1) for the n-th rung.

What is vacuum Rabi splitting?

When a single atom is strongly coupled to a cavity, the transmission spectrum splits into two peaks separated by 2g, even with zero photons (vacuum). This vacuum Rabi splitting is a hallmark of quantum strong coupling and has been observed in optical cavities, microwave cavities, and superconducting circuits.

What is the Purcell effect?

In the weak coupling regime, the cavity modifies the spontaneous emission rate of the atom by the Purcell factor Fp = 4g²/(κγ). A high-finesse cavity can enhance emission by orders of magnitude, enabling efficient single-photon sources and faster quantum gates.

Sources

Embed

<iframe src="https://homo-deus.com/lab/quantum-optics/cavity-qed/embed" width="100%" height="400" frameborder="0"></iframe>
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