---
title: "Quantum Node Photon Collection Interactive Lab | Sandbox Physics"
description: "Can a collected photon still miss the receiving mode? Collection probability counts the photon in a channel."
canonical_url: "https://sandboxphysics.com/labs/quantum-node-photon-collection/"
language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/quantum-node-photon-collection/"
---

FR11 · Receive the whole temporal mode

# Quantum Node Photon Collection

**Can a collected photon still miss the receiving mode?** Collection probability counts the photon in a channel. Receiving-mode fidelity also depends on its arrival time, envelope and phase. A frequency-shifted pulse can retain its intensity profile and have a small mode overlap.

Send a shaped single photon toward a receiver. Change its arrival time, bandwidth or phase rotation, and compare how much light is collected with how well its temporal mode matches.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

A controlled one-excitation Markov source emits a hyperbolic-secant envelope. A constant branching efficiency divides it between a collected channel and loss. The source is conditioned on survival at the start of the finite window; its remaining population is retained. Fidelity is the overlap of the saved complex output with a normalized receiving mode in that window. The ideal receiver projects onto that mode; no receiver Hamiltonian or state-transfer process tomography is simulated. The source waveform maps the ideal envelope in Kurpiers et al., arXiv:1712.08593v1, Fig. 2 and Appendix C. It does not reproduce the experiment’s measured efficiencies or noise.

## How much arrives, and how well it fits

Cyan: collected one-photon output. Amber: fixed receiving mode. Violet: real part of the complex output. Curves are simulated amplitudes and intensities.

Intensity and receiving mode $|\xi(t)|^2,\ |u(t)|^2$

> Saved simulated output intensity.

The phase that intensity hides $\operatorname{Re}\xi(t),\ u(t)$

> Computed state probabilities or temporal amplitudes.

Read the saved record

The collected probability and overlap are integrated from the exported complex amplitude. The target mode is renormalized in the finite window. The source population remaining at the window end is reported separately. In the ideal vacuum–one-photon superposition used for heterodyne calibration, the squared mean-field amplitude is one quarter of the single-photon probability flux.

Physics tutorial

## Receiving a photon in one chosen mode

**Background** A single photon occupies a wavepacket extended in time. Its complex amplitude describes both when it can arrive and how its phase changes.

**Why it matters** A receiving system is sensitive to one temporal mode. Counting everything in its input channel can hide a poor match to that mode.

Start with the essentials

- **Focus question**: Can a collected photon still miss the receiving mode?
- **One-sentence intuition**: Intensity loses the phase information needed to evaluate temporal-mode overlap.

### Core mathematical model

#### The output is a complex temporal amplitude

$$
\xi(t)=\sqrt{\eta}\,\phi_\kappa(t-t_c)e^{-i\delta t}/\sqrt{S(0)},\quad \phi_\kappa(t)=\frac{\sqrt\kappa}{2}\operatorname{sech}\frac{\kappa t}{2}
$$

The finite starting time conditions the source on survival. Branching loss changes the amplitude scale; detuning rotates its phase.

#### Separate collection from mode overlap

$$
P=\int_0^T|\xi(t)|^2dt,\qquad F=\frac{|\int_0^T u^*(t)\xi(t)dt|^2}{P},\quad\int_0^T|u(t)|^2dt=1
$$

The receiver mode is normalized inside the observation window. The target-mode probability is the collection probability multiplied by the conditional fidelity.

### Common difficulties

#### Collection and mode matching

**Typical misconception** Identical intensity profiles imply identical photon states.

**Better mental model** A changing temporal phase can reduce the overlap even when every intensity sample stays fixed.

### Run the experiment

1. 01

   #### Change collection alone

   Choose Fewer photons, same mode. Predict which of the first two readouts changes.

   **What to observe:** Collection falls while the conditional mode fidelity stays near one.

2. 02

   #### Keep the intensity

   Choose Same intensity, rotating phase. Compare the intensity and phase-sensitive curves.

   **What to observe:** The intensity keeps its shape; the oscillating real amplitude reduces the overlap with the receiver.

3. 03

   #### Move the arriving packet

   Drag the glowing packet along the channel, then reset.

   **What to observe:** The arrival offset changes continuously, and the overlap is largest when the emitted packet and receiver mode align.

Physical conclusion

Report collection probability and conditional fidelity separately. Their product gives the probability in the chosen target mode.

## Related experiments and articles

Cavity and waveguide quantum light · Reading path

### From one excitation to photon pairs and collected modes

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Receiving a photon also means receiving its mode**](https://sandboxphysics.com/stories/waveguide-qed/collected-temporal-modes/)
2. [Lab **Structured Bath and Output Ports** Can one receiver collect a band-edge tail?](https://sandboxphysics.com/labs/structured-bath-output-ports/)
3. [Article **Connect a temporal mode to a published experiment**](https://sandboxphysics.com/stories/waveguide-qed/kurpiers-photon-interface/)
4. [Article **Turn a scattering picture into a reproducible study**](https://sandboxphysics.com/stories/waveguide-qed/reproducible-waveguide-study/)
5. [Lab **Two-Photon Waveguide Scattering** Write a prediction that the calculation could reject](https://sandboxphysics.com/labs/two-photon-waveguide-scattering/)
6. [Lab **Single-Atom Photon Blockade** Compare cavity output with atomic side fluorescence](https://sandboxphysics.com/labs/single-atom-photon-blockade/)

Quantum & fields · Starter path

## Start from a single measurement

Predict an outcome, then count what the measurements actually give. The path starts with one qubit and moves on to wave packets, bound states and two-photon interference.

[Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare your prediction with the measured frequency over many 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. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/)

[View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)