Photon blockade / One atom in a cavity

Single-Atom Photon Blockade

How can one atom in a cavity keep a second photon out once the first is inside? By making the cavity's energy ladder uneven. Strongly coupled, atom and cavity share their energy, and each rung splits by an amount that grows more slowly than the photon number. A laser tuned to the first rung is off resonance for the second, so a second photon rarely gets in and photons leave one at a time. An empty cavity has evenly spaced rungs and lets photons in at random.

Tune a laser to one of the resonances of the combined atom–cavity system. Compare single-photon blockade, two-photon resonance and an empty cavity, look at the ladder of energy levels, and collect photon-number snapshots from repeated preparations.

A two-level atom sits on resonance with one driven cavity mode, and the system is solved with a zero-temperature Lindblad equation. The cavity's population decay rate sets the units. Each readout is an ideal, independent count of the photons inside the cavity, not a time stamp of a transmitted photon; the conditional output correlation is a separate model prediction. Atomic motion and extra atomic levels are left out, and the apparatus is not calibrated.

A driven cavity holding one quantum emitter

ZERO-DELAY PAIR CORRELATION

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MEAN CAVITY OCCUPATION

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01COHERENT DRIVE

02ATOM / CAVITY

03IDEAL NUMBER READOUT

Schematic geometry. Standing-wave envelope scales with square root of mean occupation; atom glow with excitation. Number snapshots are ideal independent state readouts, not flying photon trajectories.

01 / The dressed-state ladder

The first step is in tune; the second is not.

Dressed energies in the laser rotating frame. Gold is zero energy. A one- or two-excitation level at zero marks the corresponding resonance; line thickness is visual only and does not represent a spectral linewidth.

$E_{n,\pm}/(\hbar\kappa)=-n\Delta/\kappa\pm(g/\kappa)\sqrt n$

02 / After one photon leaves

How quickly can another one follow?

Model output correlation after one photon leaves the cavity, computed with the quantum regression theorem. The dashed Poisson reference is one. The curve is not reconstructed from the independent number snapshots below.

$\kappa\tau\ \longrightarrow\quad g^{(2)}(\tau)$

Each trial starts from a fresh preparation

Count the rare photon pairs.

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Every trial prepares the driven steady state again, then reads the intracavity photon number ideally. No sequential stream, time-tag detector, or destructive real-time counter is claimed. Rare pairs require many preparations; zero observed pairs is not proof of zero probability.

Recorded multiphoton fraction

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95% Wilson interval

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Model multiphoton probability

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Stationary-equation residual

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Single photons get in; pairs are rarer.

Gold: recorded number frequencies. Cyan: the solved photon-number distribution. Gray: an independent Poisson reference at the same mean. Vacuum is retained in all counts. The vertical axis uses a square-root scale to reveal rare outcomes; ticks show probabilities.

Top photon sector

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Trace error

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Latest 20 records · export all

Trial	Setting	Photons

Model, conventions and sources

The atom and bare cavity share a resonance. Detuning is laser minus resonance frequency. Cavity population decay is one, atomic population decay is 0.4. The solver retains photon numbers zero through eleven, evolves from vacuum for 48 cavity decay times, and computes output regression for another 12. No clipping or renormalization is used.

H/\hbar=-\Delta(a^\dagger a+\sigma_+\sigma_-)+g(a^\dagger\sigma_-+a\sigma_+)+\epsilon(a+a^\dagger)

\dot\rho=-i[H/\hbar,\rho]+\kappa\mathcal D[a]\rho+\gamma\mathcal D[\sigma_-]\rho

\mathcal D[L]\rho=L\rho L^\dagger-\tfrac12\{L^\dagger L,\rho\}

g^{(2)}(\tau)=\frac{\operatorname{Tr}[a^\dagger a\,e^{\mathcal L\tau}(a\rho_{\mathrm{ss}}a^\dagger)]}{\langle n\rangle_{\mathrm{ss}}^2}

Single two-level atom, rotating-wave approximation, classical coherent drive, Markov vacuum reservoirs. The 2005 experiment contains additional atomic levels and two polarizations; this page illustrates the ideal Jaynes–Cummings mechanism rather than fitting that apparatus. Equal-time intracavity statistics agree with the normally ordered output of an otherwise vacuum loss port, but independent snapshots do not measure a time correlation.

Start with the essentials

Focus question: How can one atom in a cavity keep a second photon out once the first is inside?
One-sentence intuition: The ladder of excited levels is unevenly spaced, so a second photon at the frequency that let the first one in misses the next step.

Core mathematical model

A measurable signature

g^{(2)}(0)=\frac{\langle n(n-1)\rangle}{\langle n\rangle^2}

The numerator counts ordered pairs of photons; it is not the square of a single-shot count.

Common difficulties

What really causes the effect

Typical misconceptionThe atom works like a classical gate that counts balls as they pass.

Better mental modelCoherent coupling to the atom changes the energy spectrum, and the drive and the loss are solved together.

Model curves versus collected data

Typical misconceptionThe theory curve on screen already counts as measured data.

Better mental modelA two-level atom sits on resonance with one driven cavity mode, and the system is solved with a zero-temperature Lindblad equation. The cavity's population decay rate sets the units. Each readout is an ideal, independent count of the photons inside the cavity, not a time stamp of a transmitted photon; the conditional output correlation is a separate model prediction. Atomic motion and extra atomic levels are left out, and the apparatus is not calibrated.

Run the experiment

01
Predict the difference
At resonance, compare the cavity with the coupled atom against the empty cavity.
What to observe: The empty cavity gives Poisson statistics. Adding the atom changes the probability of finding two photons together.
02
Make the effect disappear
Tune between the one-photon and two-photon resonances.
What to observe: Even when the mean output is weak, the normalized pair correlation can be large.
03
Collect and inspect
Collect trials and pin a run, then change one control and restore it. Export all the records as CSV.
What to observe: The gold data come only from saved simulated records, and the cyan curves are model references.

Single-Atom Photon Blockade

The first step is in tune; the second is not.

How quickly can another one follow?

Count the rare photon pairs.

Single photons get in; pairs are rarer.