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25 April (2023)
Follows a thread on our recent paper «Two-photon correlations in detuned resonance fluorescence» doi.org/10.1088/1402-4⊠via @ioppublishing
September last year, Masters et al. from the Humboldt University of Berlin asked on the arXiv whether a single two-level atom can simultaneously scatter two photons arxiv.org/abs/2209.02547
They asked in the wake of an old paper by Dalibard and Reynaud [J. Phys. France, 44:1337, 1983] that explains in a simple and compelling way various mysterious features of detuned resonance fluorescence (@MaxSchemmer, an author, writes about it here )
One mysterious feature is that the emission is a triplet: a very intense central peak, with narrow linewidth, flanked by two weak fluorescent peaks, as shown (I put an â on top of the central peak, to highlight its Dirac ÎŽ character: it is the most intense peak)
This triplet wasâeven in this low (Heitler) driving & detuned regimeâalready known by Mollow, who attached his name to the high-driving resonant case. But *why* one sees a triplet is most clear from the following diagram by Dalibard & Reynaud:
The central peak is Rayleigh scattering. It is sharp and bright as it scatters elastically the laser photons ÏL. The fluorescent peaks involve two laser photons and a virtual state (green) that helps bring the system to the atomic transition (red) as shown on the right diagram.
Now since this is a two-level system (2LS), the photon statistics should be antibunched and gâœÂČâŸ(0)=0. And it is. Can multiphoton emission (green, red and blue) photons be that of a 2LS, i.e., a single-photon emitter (gâœÂČâŸ(0)=0)? That's the question of Masters et al.
The answerâYesâwas already given by Dalibard & Reynaud, who explain it in terms of the celebrated interference of probability amplitudes of the various processes. Despite having multiphotons producing triplet peaks, what you detect in terms of coincidences are single photons!
What Masters et al. did is to check this "Yes" experimentally, by disturbing this interference. Namely, they filtered out the Rayleigh peak. Classically, removing photons from a single-photon source should not make those that pass through be bunched (come together)!
Still, they found that the more they remove the central-peak photons, the more those from the sides come together! A beautiful counter-intuitive effect that, I am sure, will eventually become as famous as other quantum-mechanical mindfuckeries.
This has been at the heart of our interest for years: what photons look like when they are detected [PRL 109:183601 2012; NJP 15:033036 2013; Laser Phot. Rev. 11:1700090 2017] especially when disturbing their interferences [Laser Phot. Rev. 14:1900279 2020;PRA 101:063824 2020]...
Experimentalists have even already shown the exact same effect but at resonance, and, another but, removing the fluorescent peak instead of the Rayleigh one, with a transition from antibunching to uncorrelated-coherent-light, i.e., that of the laser [PRL 125:043603 & 170402 2020]
In this case, we have shown that it is possible to restore the antibunching spoilt by detection (or frequency filtering, which is fundamentally the same thing) by balancing out the excess Rayleigh peak, giving rise to a new type of single-photon source: dx.doi.org/10.1088/2058-9âŠ
What we like with Masters et al.'s configuration is how clean it is: the coherent & fluorescent contributions are neatly split by detuning. When we had considered detuning, this was still for antibunching [J. Phys. B.: At. Mol. Phys., 52:035504 2019] dx.doi.org/10.1088/1361-6âŠ
So now focusing on bunching, we had a look at their clean & neat approach and removed the central peak. But not by filtering, like them. Instead, by coherently homodyning it out, making the interference more salient, we think. The transition is beautiful:
They basically see the same thing except that they filter out while we destructively interfere, what I would sketch as follows:
You would think it's the same, and so did we. Because we are also masters at frequency-filtering (no pun intended with our Humboldt colleagues, cf. journals.aps.org/prl/abstract/1âŠ), we also combined this homodyning with correlating the side peaks (interposing filters before detection).
This is something which, *without homodyning*, has been considered by many & many times [PRL 45:617 1980; PRA 45:8045 1992, PRA 47:510 1993; Nature Photon., 6:238 2012, Laser Photon. Rev., 11:1700090, 2017...] That gives what Eduardo shows on his slide 30, for various parameters:
But if, and that is the novelty, you consider bothâboth homodyning (removing coherently the Rayleigh peak) and filteringâalthough you might expect to see basically the same thing because filtering already removes the Rayleigh peak in the first place, instead you see this:
Excuse the botched animation, which merely overlaps our Figs. 3 & 4 of the paper. In fact if I get enough likes to this tweet we might consider making a real, smooth transition :)
So anyway, what we see is a (surprising) complete transformation of the correlations: observe the magnitudes (y-axis) going from 10â” to 10Âčâ°. See how nasty oscillations get suppressed completely. Note how everything that was jammed together before now splits and breathes...
In fact, what we have is basically an ideal two-photon cascade: one heralds the other, with no extraneous effects. The laser, although very much filtered out, if not properly or in the right amount, still manages to badly spoil the two-photon dynamics.
If you're in the business of making quantum light, you might be interested in paying attention to such a careful balance and admixing of the coherent and quantum components of a quantum emitter.
And what's more: it's only scratching the surface! We have been looking above at the peaks emission. One photon only of these peaks is virtual. Many other things happen worthy of experimentalists' attention when *all* the photons are virtual, and not only two of them.
But I see that I hit the limit of maximum tweets. So I'll conclude with Reynaud himself, commenting to Eduardo about the many things indeed that happen in the things that we call landscapes.
23 April (2023)
Replying to @UtterlyInterest and @DannyDutch
Like my tweets.
22 April (2023)
Replying to @LagorioValentin
IntĂ©ressant... j'espĂšre qu'on aura la rĂ©ponse! Au fond de ma mĂ©moire ne raisonne qu'un lointain "oĂč est la planche Ă pain?" Je ne suis mĂȘme pas sĂ»r de son usage, mais je suis sĂ»r d'avoir jouĂ© avec ça Ă©tant gamin.
Replying to @LagorioValentin
n'est-ce pas pour transférer les baguettes depuis les planches (avant cuisson) sur le tapis du four?
Elena singing about what you see just around the corner between Balmeanach and Dhiseig
youtube.com/watch?v=stCAaHâŠ
youtube.com/watch?v=stCAaHâŠ
21 April (2023)
Replying to @DrNicSwann
Congratulations. That is an extremely demanding offering but is of huge and long-term benefit to children.
Thank you indeed @DrKhechara. You deserve your reputation. I have actually learned a couple of non-trivial things (quinine fluorescing, axing your head with a hammer, ...) That was brilliant. Would have loved to see some of the experiments repeated. Won't try them myself, though.
20 April (2023)
Maybe the last lecture I'll attend.
19 April (2023)
Replying to @sdeliberato
Indeed. One of the leitmotivs of this course is that "a real mathematical proof covering all the cases is not that straightforward". The permutation of partial derivatives is used to illustrate that. That's why the "for Physics" is important.
Just off the press indeed: yesterday (picture) & today (doi) iopscience.iop.org/article/10.108⊠- will write a little summary of what we see here later.
The grown-up version of every function can be decomposed as the sum of an odd and even functions (top in the list of deep/simple-to-prove theorems of my mathematics for physics course).
18 April (2023)
Why there is a circle of antibunching in two-photon spectra...
Homodyning cascaded emission: towards perfect heralded SPS.
Polaritons and Jaynes Cumming as seen by two photons.
16 April (2023)