--- title: "The Matter-Wave Antilaser Interactive Lab | Sandbox Physics" description: "Change the phase. Change what disappears. 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." canonical_url: "https://sandboxphysics.com/labs/coherent-matter-wave-absorber/" language: "en" page_type: "lab" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/labs/coherent-matter-wave-absorber/" last_modified: "2026-10-22" --- 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. > Interactive simulation: open this page in a web browser to change the parameters and run the model. 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 $\tau=0$ Complex phase $-\pi$ $\pi$ Actual survival $100\%$ A schematic chain. Arrows follow the computed probability current. Wave height is square-root probability; crest hue is complex phase. The central amber column marks the local loss, not a measured detector image. 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. 0 0.06 ### 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)](https://pmc.ncbi.nlm.nih.gov/articles/PMC6086614/) These sources establish the physical context. This Lab uses a stated linear model and illustrative parameters, not a reproduction of their experimental data. Physics tutorial ## The Matter-Wave Antilaser **Background** 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. **Why it matters** Learn to distinguish a changing wave shape from the probability that anything remains. 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 misconception** The wave gets brighter, so probability must have been created. **Better mental model** The display scale and conditioning are stated explicitly. The dynamics is passive; total survival never grows. #### Model scope **Typical misconception** This is a calibrated apparatus or an interacting many-body experiment. **Better mental model** 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. ### Run the experiment 1. 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. 2. 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. 3. 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. Physical conclusion 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. Quantum & fields · Starter path ## Start from a single measurement Predict outcomes and collect counts, building from one qubit to wave packets, bound states and two-photon interference. [Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare it with the frequency of acquired shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/) 1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/) 2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/) 3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/) 4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/) 5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/) 6. 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