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.

Collected probability $.770$

Conditional mode fidelity $1.00$

Target-mode probability $.770$

Source population at window end $8.32\times10^{-7}$

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

The phase that intensity hides

\operatorname{Re}\xi(t),\ u(t)

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.

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 misconceptionIdentical intensity profiles imply identical photon states.

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

Run the experiment

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.
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.
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.

Quantum Node Photon Collection

How much arrives, and how well it fits

Receiving a photon in one chosen mode

Core mathematical model

The output is a complex temporal amplitude

Separate collection from mode overlap

Common difficulties

Collection and mode matching

Run the experiment

Change collection alone

Keep the intensity

Move the arriving packet

Related experiments and articles

From one excitation to photon pairs and collected modes