EMIT / RETURN / REABSORB

A Giant Atom Hears Its Echo

Connect one artificial atom to two distant points on a waveguide. Watch the emitted wave travel between them, return excitation to the atom, or become trapped by interference.

One excitation in a lossless nearest-neighbor resonator chain. Both connections belong to one two-level system. Finite-band dispersion and propagation are solved explicitly; this is not a calibrated surface-acoustic-wave device or a full electromagnetic circuit. The colored ribbon is a probability diagnostic, not a classical field or a photon trajectory.

THE WAVEGUIDE REMEMBERS

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 IN 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.

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

ONE PREPARATION. 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. 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. One initial atomic excitation, rotating-wave approximation, vacuum waveguide. No drive after preparation, 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. No state clipping or renormalization. The displayed norm and outer-eight-site probability audit 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: An atom can meet its own emission again.
One-sentence intuition: Both distant contacts share one atomic amplitude. The traveling wave can return and interfere with a later emission.

Core mathematical model

One excitation, one probability budget

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

Atom and waveguide are mutually exclusive outcomes of the ideal snapshot readout.

A finite propagation band

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

The band edges are two hopping units above and below its center. The same dispersion governs the movie.

Common difficulties

A cloud is not a trajectory

Typical misconceptionThe excitation splits into many independently measurable particles.

Better mental modelEach preparation has one total excitation. Repeated snapshots reveal its distribution; the ribbon height is a square-root probability display.

Do not overclaim the reference

Typical misconceptionThe reference curve was reconstructed from saved samples.

Better mental modelOne excitation in a lossless nearest-neighbor resonator chain. Both connections belong to one two-level system. Finite-band dispersion and propagation are solved explicitly; this is not a calibrated surface-acoustic-wave device or a full electromagnetic circuit. The colored ribbon is a probability diagnostic, not a classical field or a photon trajectory.

Run the experiment

01
Start with the movie
Restart from the excited atom. Pause and drag the time cursor through the space–time map.
What to observe: The atom loses excitation, then gains some back after the propagation delay.
02
Break the condition
Remove the second connection, then compare separations of 30 and 32 sites.
What to observe: Delay and phase both matter. The compact mode requires equal connections and its stated phase condition.
03
Read independent preparations
Select a time, collect 500 snapshots, pin the experiment and export all records.
What to observe: Gold frequencies are acquired samples. Cyan and gray are separately labeled predictions.