Light has classical (thermal) fluctuations as well as quantum ones. Well below the Planck peak, the classical fluctuations dominate. They're measurable even a factor of 2 in frequency below the Planck peak--Hanbury Brown's intensity interferometer was able to measure stellar diameters and the separation of close binary stars using the spatial coherence of their classical fluctuations.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
If it had full shot noise before, it has full shot noise afterwards. Interestingly the additional shot noise is anticorrelated between the two photodiodes: if you wire them in parallel you just get the shot noise of the whole beam, as you'd expect.
(Interestingly the same is true of the collector currents of an ideal BJT diff pair--if the tail current has full shot noise, so do the collector currents, irrespective of the splitting ratio.)
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
It's OK for me, I've seen it. They argue that extra noise is injected into the dark port from vacuum fluctuations, and that this extra noise has just the right level to fix the numbers. No explanation of this extraordinary feat. Magic!
Jeroen Belleman
I was thinking about the spectrum of the shot noise. Pure shot has a flat spectrum, but there's nothing stopping one from adding excess noise of some sort. I can certainly modulate a light beam, so some physical phenoms could too.
Would, say, passing through some medium, like a fiber maybe, add more-than-shot noise (beyond the obvious LF mechanical and interferance stuff?)
Shot noise makes jitter in my world.
Is there any optical mechanism that's like the electrical supression of shot noise in metallic conductors? Some medium where photons interact?
-- John Larkin Highland Technology, Inc lunatic fringe electronics
If there was Ligo would use it. I think there is only these squeezed states. This is OK... see fig 4.
I went looking for a tutorial and found this, a bit old (1989)
Saved for later reading.
George H.
No. The zero point (vacuum) is one photon per second per hertz. It's not detectable at DC because the detector is emitting the same amount. I don't know if the fluctuations are detectable.
An actual coherent signal of one photon per second per hertz is detectable at 1 sigma confidence, which is why coherent detectors are as sensitive as ideal photon counters, even working in daylight.
I designed one system that could detect at that level even looking straight into the zenith sun. It's all about having enough LO power. ;)
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
No. Only the lowest order acoustic modes (like an organ pipe) can do that. The higher order modes cause phase shifts across the pupil, which gives rise to components moving in different directions to the main beam. The thermal excitation of those modes is kT/2 each, which for a macroscopic object is pretty darn small.
What a beam splitter _will_ do is generate two beams with anticorrelated shot noise. If you wire the diodes in parallel, it's just like you had no beam splitter and one photodiode, so the shot noise is what it would have been with no beam splitter--in other words, the added noise power cancels out because it's anticorrelated.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
The extra shot noise is white too--it has the same physical origin.
There's an interesting mechanism for turning FM into AM in fibre, even the most perfect fibres with no facet reflections: double Rayleigh scatter. A long fibre, i.e. one whose length is some decent fraction of both the Rayleigh extinction length and the coherence length of the laser light, makes an astounding amount of noise. All those little scatterers make a big distributed Mach-Zehnder interferometer that demodulates the FM noise. It's usually the dominant noise source in long distance fibre links.
Yariv et. al. figured that out.
There are optical analogues of the coulomb blockade, where only one electron can pass at a time. However the angular pattern of a single atom is that of a dipole (2 pi steradians).
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
I was thinking of some really thin long nonlinear fiber that makes photons affect one another.
Suppose you generate some entangled photon pairs, photons going left and right. Detect (and destroy) the lefties. Now you know where and when the right ones are. Send the detection information to some sort of (tm) advancer/retarder to tweak the positions of the photons. Push them together/apart statistically. This would be like beam cooling in a particle accelerator.
So does some nasty quantum effect prevent doing this? Mother Nature sometimes has no sense of humor.
-- John Larkin Highland Technology, Inc picosecond timing precision measurement jlarkin att highlandtechnology dott com http://www.highlandtechnology.com
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Casmir effect.. it would be some tiny fraction of the light pressure force on a mirror/ beamsplitter.
you'll have to rewrite photon/sec/hertz.. it looks like just a photon to me. I audited a 'quantum optics type course' but it was all about electric fields and in-homogeneity in the dielectric constant... semi-classical. I dropped out of the class ~1/3 through.. life got in the way and the class wasn't that good, well it was useful for helping think about X-tal orientation.. I never got to tweak an opa, I only watched.
Local Oscillator? some coherent source, at some optical wavelength? Do I get optical filters and such?
George H.
Jeroen, as a man who is at least sympathetic* with your, 'anti-photon, quantization happens at the detector' view. (Feel free to correct my characterization) I offer this: Photons are squishy. They don't hardly know about time. (which is not something I really understand.) At the beam splitter there's some reflection/ transmission that starts to happen. And is then realized at the detector. All along one path.. there's 'extra' noise/choice, no matter where the detector, so the BS has to be involved.
I think you can mix the two beams back... (the Mach-Zender seems to be quantum optics favorite interferometer.) and the 'extra' noise goes away. Like Phil's two detectors.
mostly confused, George H.
*photons are a useful concept, and often the best way to think about things. Like raising and lower operators in the ideal harmonic oscillator. I would pay money to go to 'quantum optics camp' for a week or two. It would have to be rigorous, like Slac accelerator school.
So a Mach-Zender, (with proper path length adjustment) would have that? (and more...? There's only on photodiode needed then.)
No, you still need two to get rid of the residual AM noise of the laser. The anticorrelation is a little bit subtle. If you think about normal AM, the noise would split just like the carrier, i.e 3 dB down (optical), so that when the beams are summed again, it just goes back where it was.
With the shot noise, the noise power is only 1.5 dB down (optical), so summing the beams should lead to a 1.5 dB (optical) noise increase, but it doesn't, because the vacuum fluctuations are anticorrelated.
Optics is mysterious.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
Parametric downconversion can result in squeezing, but you're usually better off just cranking up the power. Squeezing is very loss-sensitive; if you have a path loss of >3 dB, an arbitrarily squeezed beam goes basically back to the coherent (unsqueezed) state.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
Hmm, I wasn't thinking about noise in the laser.. besides shot noise.
So first without any laser AM noise...(say an LED or laser locked to some atomic line) Won't all the photons going in to a ~zero path length difference, Mach-Zender(M-Z) come out one port, (when the optical phase is set for constructive interference at that port?
And second, I don't see how laser AM noise changes that... unless the AM noise broadens the line such that there is change in the 'in phase' path length. (Does it pay to have a nice tight (small) interferometer?)
Huh, OK. In the photon picture the anti-correlation is obvious. No? The photon goes one way or other.
Right, I think I get that. Resistors divide the noise in half, (given that the thermal noise of the R's is much less than the input voltage noise.)
Hmm again isn't that easy to see in the photon picture?
George H.
It behaves semiclassically, like almost everything in instruments, but when you start having to have correlations between the shot noise in two beams for the simple picture to work, that to me is mysterious.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
OK, (I feel like mostly an idiot in terms of quantum optics.) I did start reading the "Statistical Optics" by Goodman but it's quite a tome! He talks about the semi-classical versus 'full quantum' view of the subject.
I found 'optical coherence and photon statistics' by Glauber online Which is at least shorter. :^)
George H.
If you like. A powerful enough local oscillator beam is all you need. IIRC in that instance it was only 10 mW or so.
Cheers
Phil Hobbs
-- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC / Hobbs ElectroOptics Optics, Electro-optics, Photonics, Analog Electronics Briarcliff Manor NY 10510 http://electrooptical.net http://hobbs-eo.com
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