An atom reabsorbs its own emission

A Giant Atom Hears Its Echo

What happens when an atom coupled to a waveguide at two distant points meets its own emitted wave again? It can absorb part of it again. The wave emitted at one contact reaches the other only after a delay, so the atom first loses its excitation and later gets some back instead of decaying smoothly. The travel time and the phase picked up between the contacts set how much returns. With equal contacts and the right spacing, part of the excitation stays trapped between them for good.

Connect one artificial atom to two distant points on a waveguide. Watch the emitted wave travel between the two points: it can return its excitation to the atom, or interference can trap it between them.

The model holds one excitation in a lossless chain of resonators coupled to their nearest neighbors. Both connections belong to the same two-level system. The finite-band dispersion and the propagation are solved directly. This is not a calibrated surface-acoustic-wave device or a full electromagnetic circuit. The colored ribbon shows probability; it is not a classical field or the path of a photon.

The emitted wave comes back to the atom

Excitation still in the atom

P_e=0

NOMINAL GROUP DELAY

0

ATOM

0\%

BETWEEN PORTS

0\%

OUTSIDE REGION

0\%

Schematic resonator array. Ribbon height: fixed square-root probability gain; atom glow: excited population. It is a diagnostic over the waveguide, not a mean field or particle path.

Jt=0

01 / Where the excitation goes

Scrub through the whole journey.

Full 401-site model, time increasing downward. Drag vertically or use arrows to select a time. Fixed square-root color scale saturates at probability 0.04 per site; white marks the current snapshot.

$x/a\ \longrightarrow\qquad Jt\ \downarrow$

02 / A return during the decay

The atom brightens again.

Cyan: two-point model. Gray: one connection with the same sum of squared couplings. This reference is computed independently; it is not an exponential fit.

$Jt\ \longrightarrow\qquad P_e(t)$

Each preparation gives one outcome

Find the excitation.

0 / 10000

Each trial starts again in the excited atom, evolves to the selected time, then measures either the atom or one waveguide site. These are ideal independent destructive snapshots, not repeated monitoring of one photon. Fixed seed; every outcome retained.

Recorded atom fraction

\text{—}

95% Wilson interval

\text{—}

Largest norm error

\text{—}

Largest boundary probability

\text{—}

Count the atom and keep every position.

Gold: acquired frequencies. Cyan: integrated model bins, with a separate atom outcome. All 401 sites are included. Square-root vertical scale; tick labels remain probabilities.

Latest 20 records · export all

Trial	Outcome	Site position

The model, units and limits

\frac{H}{\hbar J}=\frac{\Delta}{J}|e\rangle\langle e|-\sum_x(|x+1\rangle\langle x|+\mathrm{h.c.})+\sum_j\frac{g_j}{J}(|e\rangle\langle x_j|+\mathrm{h.c.})

Positive position is rightward along the array. Spacing sets length, nearest-neighbor hopping sets frequency, and its inverse sets time. Frequencies are relative to the array center, not negative absolute photon energies. The atom starts with one excitation, the rotating-wave approximation is used, and the waveguide starts in vacuum. There is no drive after preparation, and there are no counter-rotating terms, loss, disorder or readout backaction before the final snapshot.

401 open sites, fourth-order Runge–Kutta at a time step of 0.01, duration 64. The state is never clipped or renormalized. The displayed norm and the probability in the outer eight sites show any numerical loss and boundary contamination. Sampling normalizes only the cumulative measurement probabilities by the displayed norm.

\tau J=\frac{d/a}{\sqrt{4-(\Delta/J)^2}}\,,\qquad Z_0=\frac{1}{1+(d/2a)(g/J)^2}

The delay is a narrowband group-velocity guide, not an exact arrival threshold in this dispersive lattice. The compact zero mode applies only at zero detuning, equal positive couplings and separations of 2, 6, 10… sites. Its total overlap is the stated weight; its contribution to atomic probability is the weight squared. Other bound and continuum terms remain in the movie.

Primary sources

The acoustic experiments establish delayed self-interaction. This page uses a finite-band resonator lattice to illustrate that mechanism, not their device-specific dispersion or fitted decay.

Start with the essentials

Focus question: What happens when an atom coupled to a waveguide at two distant points meets its own emitted wave again?
One-sentence intuition: Both distant contacts share one atomic amplitude, so the traveling wave can come back and interfere with what the atom emits later.

Core mathematical model

Total probability of the single excitation

P_e(t)+\sum_x|\psi_x(t)|^2=1

In an ideal snapshot readout, finding the excitation in the atom and finding it in the waveguide are mutually exclusive outcomes.

A finite propagation band

\omega(k)-\omega_c=-2J\cos(ka)

The band edges lie two hopping units above and below the band center. The same dispersion drives the animation.

Common difficulties

A cloud is not a trajectory

Typical misconceptionThe excitation splits into many particles that can each be measured on their own.

Better mental modelEach preparation holds exactly one excitation in total. Repeated snapshots show how it is distributed. The ribbon height displays the square root of the probability.

Where the reference curve comes from

Typical misconceptionThe reference curve was reconstructed from the saved samples.

Better mental modelThe model holds one excitation in a lossless chain of resonators coupled to their nearest neighbors. Both connections belong to the same two-level system. The finite-band dispersion and the propagation are solved directly. This is not a calibrated surface-acoustic-wave device or a full electromagnetic circuit. The colored ribbon shows probability; it is not a classical field or the path of a photon.

Run the experiment

01
Watch the propagation first
Restart from the excited atom. Pause and drag the time cursor through the space–time map.
What to observe: The atom loses its excitation, then gets some of it back after the travel delay.
02
Change the conditions
Remove the second connection, then compare separations of 30 and 32 sites.
What to observe: Both the delay and the phase matter. The compact mode needs equal connections and the phase condition stated for it.
03
Sample repeated preparations
Select a time, collect 500 snapshots, pin the experiment and export all records.
What to observe: The gold frequencies come from the acquired samples. Cyan and gray show predictions, each labeled separately.

A Giant Atom Hears Its Echo

Scrub through the whole journey.

The atom brightens again.

Find the excitation.

Count the atom and keep every position.