TWO WAVES / ONE SINK

The Matter-Wave Antilaser

Launch two coherent matter-wave packets at one lossy lattice site. Make them disappear together, protect them with a phase reversal, then discover why a stronger absorber can reflect more.

Linear single-particle tight-binding model with local Markovian loss. Finite wave packets are evolved explicitly; monochromatic perfect absorption is a separate analytic reference. No interacting condensate, electron-beam apparatus or detector calibration is reproduced.

COHERENCE / ABSORPTION / REFLECTION

ABSORBED BY THIS TIME

0\%

EVOLUTION TIME

\tau=0

EVERY OUTCOME COUNTS

Nothing disappears from the accounting.

Watch the encounter unfold

Time runs down, site number runs right. Drag the white time cursor. Brightness is square-root unconditional site probability, with a fixed scale of zero to 0.06.

00.06

What remains, what was absorbed

Cyan: survival. Amber: absorbed probability. The dashed level is the monochromatic reference, not a fit to these finite packets.

MONOCHROMATIC ABSORPTION

0

MAX LOSS-BALANCE ERROR

0

The probability at this instant

INDEPENDENT SIMULATED PREPARATIONS

Count the survivors. Keep the losses.

Each of 1,024 fresh preparations produces one outcome: lost, or detected at a site. The event grid uses amber for loss and cyan for survival. The histogram counts only those recorded surviving sites.

Ideal loss-or-position readout, with no detector inefficiency. Time and display-scale changes preserve the record. A new preparation clears it. Export includes every loss and every site, plus a separately labelled model reference.

Equations, loss and model boundaries

\tau=Jt/\hbar,\qquad E_*=J

The hopping energy sets the units. Site number increases from left to right in the data plots. The three-dimensional layout is schematic; no physical length or calibrated apparatus is assigned.

\begin{gathered}i\dot\psi_n=-(\psi_{n-1}+\psi_{n+1})\\-i(\gamma/2)\delta_{n0}\psi_n\end{gathered}

Two equally weighted Gaussian packets start forty sites either side of the sink, each with density standard deviation eight. Opposite carrier momenta direct them inward. There are 241 sites; the outer boundary remains negligibly occupied over the displayed interval. The sink removes excitation irreversibly into a vacuum state.

\begin{gathered}v=2\sin q,\quad\alpha=\gamma/2\\A_{\rm mono}=\frac{4v\alpha}{(v+\alpha)^2}\cos^2(\phi/2)\end{gathered}

This reference assumes monochromatic, equally strong coherent inputs. Perfect absorption requires matched loss and equal phase. A finite packet has a bandwidth, so its result need not equal the reference exactly. Atom interactions, nonlinear stability, electron-beam scattering and finite detector efficiency are omitted.

\begin{gathered}S=\sum_n|\psi_n|^2,\quad P_{\rm lost}=1-S\\p_n=|\psi_n|^2,\quad p_{n|\rm survive}=p_n/S\end{gathered}

The propagator uses fourth-order Runge–Kutta with a step no larger than 0.01. It never renormalizes the evolving state. A separately integrated loss rate checks the probability balance. The bright conditional display divides by survival; raw acquisition always includes lost trials. No gain, many-body statistics or continuously observed particle paths are claimed.

Müllers et al. — Coherent perfect absorption of nonlinear matter waves (2018)

These sources establish the physical context. This Lab uses a stated linear model and illustrative parameters, not a reproduction of their experimental data.

Start with the essentials

Focus question: Change the phase. Change what disappears.
One-sentence intuition: A symmetric input can feed the lossy site, while an antisymmetric input has a node there. More loss is not always more absorption.

Core mathematical model

Generator

i\dot\psi_n=-(\psi_{n-1}+\psi_{n+1})-\frac{i\gamma}{2}\delta_{n0}\psi_n

Time is measured in inverse hopping units. The propagation is not renormalized.

A loss balance

\frac{d}{d\tau}\sum_n|\psi_n|^2=-\gamma|\psi_0|^2

Disappearance is accounted for by an integral of the local loss rate.

Common difficulties

Shape is not survival

Typical misconceptionThe wave gets brighter, so probability must have been created.

Better mental modelThe display scale and conditioning are stated explicitly. The dynamics is passive; total survival never grows.

Model scope

Typical misconceptionThis is a calibrated apparatus or an interacting many-body experiment.

Better mental modelLinear single-particle tight-binding model with local Markovian loss. Finite wave packets are evolved explicitly; monochromatic perfect absorption is a separate analytic reference. No interacting condensate, electron-beam apparatus or detector calibration is reproduced.

Run the experiment

01
Make a contrast
Compare the first two presets at the same time.
What to observe: The central loss is unchanged; phase controls whether the incoming waves feed it.
02
Inspect the probability
Switch between all trials and surviving trials. Keep an eye on the survival meter.
What to observe: The conditional shape sums to one even when very few trials survive.
03
Keep every outcome
Acquire 1,024 independent preparations. Export lost outcomes as well as measured sites.
What to observe: A bright conditional image does not increase the number of detected events. The snapshot stays frozen when time moves.