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Sandbox Physics

Q031 · Prepare / exchange / read

Cavity Quantum Excitation Exchange

Start with one excited atom. Watch excitation move into the cavity and return; add photons or let them leak away.

Interactive modelCavity Quantum Excitation Exchange
Model excited fraction—\text{—}
Recorded at this time—\text{—}

02 / FOLLOW THE EXCHANGE

Watch the excitation return.

Excited atom0%
Empty cavity0%

Blue line: excited atom. Amber: mean cavity photons, divided by initial total excitation. Dots and 95% Wilson bars: atomic state readings.

Drag across the plot or use the time slider. Playing changes the preview only.

Cavity photons · model

—\text{—}

Leaked photons · integrated model flux

—\text{—}

03 / THE OSCILLATOR

How many photons are inside?

ϵtail=0\epsilon_{\rm tail}=0

04 / KEEP THE EVIDENCE

Fresh preparations at every time

Acquire a comparison to fill the table. It keeps its captured settings when controls change.

ProbeRead / totalExcited
Model and measurement boundaries

Ideal binary state discrimination when available; unread trials are retained. No fluorescence photon arrival stream is simulated. Every trial uses an independent preparation. Model number distributions are not reconstructed from these binary counts.

An initially excited atom couples to a single mode. Poisson mixtures retain photon-number statistics but no optical phase. They reproduce the atomic population collapse and revival of a coherent preparation in this model; they do not reproduce its full state. No driven transmission spectrum or entanglement certification is claimed.

Time uses an arbitrary reference unit. Geometry is schematic, with enlarged atoms and mode envelopes.

Primary sources: Bina · Jaynes–Cummings dynamics

Physics tutorial

Follow a quantum of excitation

BackgroundA two-level system can exchange energy with a quantized oscillator.

Why it mattersChange a preparation, then test the model with independently repeated state readings.

Start with the essentials

Focus question
What changes when the oscillator contains no quanta?
One-sentence intuition
A model curve and a finite collection of observations are different kinds of evidence.

Core mathematical model

One mode and one atom

Hℏ=Δσ+σ−+g(aσ++a†σ−)\frac{H}{\hbar}=\Delta\sigma_+\sigma_-+g(a\sigma_++a^\dagger\sigma_-)

The atom begins excited. The mode starts in a number state or a phase-averaged Poisson mixture. Time and rates use reference units.

Excitation exchange

∣e,n⟩↔∣g,n+1⟩,Ωn=Δ2+4g2(n+1)|e,n\rangle\leftrightarrow|g,n+1\rangle,\quad\Omega_n=\sqrt{\Delta^2+4g^2(n+1)}

More photons increase the exchange frequency. Different number components dephase and may rephase, producing population collapse and revival.

Independent losses

ρ˙=−i[H/ℏ,ρ]+κD[a]ρ+γD[σ−]ρ\dot\rho=-i[H/\hbar,\rho]+\kappa\mathcal D[a]\rho+\gamma\mathcal D[\sigma_-]\rho

Both rates describe population decay. The block solver includes coherent feeding between excitation sectors when a photon leaks; it does not simply damp a plotted sine wave.

Conservation budget

⟨n⟩+Pe+∫0t(κ⟨n⟩+γPe) dt=1+⟨n(0)⟩\langle n\rangle+P_e+\int_0^t(\kappa\langle n\rangle+\gamma P_e)\,dt=1+\langle n(0)\rangle

The lossless limit conserves excitation. Integrated output is a model expectation, separate from the sampled atomic-state records.

What is measured

P^e=NeNread\hat P_e=\frac{N_e}{N_{\rm read}}

Only the atomic state is sampled here. Number distributions and leakage are model diagnostics. Binary counts do not reconstruct the joint density matrix or certify entanglement.

Common difficulties

Readout is not a trajectory

Typical misconceptionThe glowing object shows a single particle path.

Better mental modelThe fixed marker locates the particle; brightness encodes a probability or mean occupation. Only recorded tiles are samples.

Approximation boundary

Typical misconceptionThis is a calibrated apparatus.

Better mental modelThe cavity uses a single mode, rotating-wave coupling and zero-temperature Markov loss. It does not compute driven transmission or preserve the optical phase of a coherent state.

Run the experiment

  1. 01

    Prepare

    Begin with the vacuum, then add four photons.

    What to observe: The contrast changes the entire response curve.
  2. 02

    Probe

    Drag the time cursor and read 200 fresh preparations.

    What to observe: The preview never generates data on its own.
  3. 03

    Compare

    Acquire a time scan, then compare lossless and leaky cases.

    What to observe: Export the raw CSV and reproduce the state frequencies. Saved comparisons keep their original settings.