Khalid24a

This page is among our 'okay articles'. It should be further expanded but we hope that it will still be useful in its present stage.Perfect single-photon sources. S. Khalid and F. P. Laussy in Sci. Rep. 14:2684 (2024).   What the paper says!?

In this paper, with Sana Khalid, I show that if a light source has a compact support of exactly zero auto-correlations—thereby implementing a perfect single-photon source resilient to detectors time uncertainty—then it develops oscillations as a result of the high ordering of the photons in a stream of successive heralders.

We provide a closed-form expression for the Glauber $g^{(2)}$ that ensues (Eq. (4)): $$g^{(2)}(\tau) = (1+\gamma t_\mathrm{G})e^{-\gamma(|\tau|-t_\mathrm{G})}\sum^{\infty}_{n = 0} \frac{\big[\gamma\big(|\tau| - (n+1)t_\mathrm{G}\big)e^{\gamma t_\mathrm{G}}\big] ^{n}}{n!}\mathbb{1}_{[(n+1)t_\mathrm{G}, \infty [} (|\tau|)\,.$$

Copy-paste the following in a Mathematica notebook to plot it:

Ind[t1_, t2_, t_] := If[t1 <= t <= t2, 1, 0] (* Indicator function *)

imax = 20; (* number of peaks - increase until converged *)
max\[Tau] = 75; (* max autocorrelation time *)
\[Gamma] = 
 1/5; tG = 10; (* source radiative lifetime and temporal gap *)

Plot[(\[Gamma] tG + 1) Exp[-\[Gamma] (Abs[t] - tG)] \!\(
\*SubsuperscriptBox[\(\[Sum]\), \(n = 0\), \(imax\)]\(
\*FractionBox[\(
\*SuperscriptBox[\((\[Gamma]\ \((Abs[t] - 
          n\ tG)\) Exp[\[Gamma]\ tG])\), \(n - 
       1\)]\(\ \)\), \(\((n - 1)\)!\)] Ind[n*tG, \[Infinity], 
     Abs[t]]\)\), {t, 0, max\[Tau]},
 PlotStyle -> {{Red, Thick, Opacity[.75]}}, PlotPoints -> 1000, 
 PlotRange -> {-.1, 2}, Filling -> Axis]

This paper was the first in a series studying such types of quantum light. It is discussed in this Springer Nature blog post as well as in several Blog posts on this web, namely on the pair correlation function and on a mechanism for implementing such a perfect single-photon source. It is also discussed in various threads on 𝕏:

• The Monty Hall Problem in Quantum Optics:
  • Part I: What people know already — follow Ariadne's thread into the Twitter maze.
  • Part II: Removing photons from a coherent state — where you meet the Minotaur.
• Correlations in circular cascades.