Beam splitter noise

So this would have been OT except for the spate of noise stuff. Beam splitter noise is, just shot noise cut in half. And really nothing new. Except the source of the noise was first reported/ explained by Caves (1980,81)* And I just read about it.

So you take a beam with N photons per second. The noise is sqrt(N). You split the beam in half and each arm gets N/2 photons with sqrt(N/2) noise. And that's more noise than you started with! by sqrt(2).. And Caves said, yeah the extra noise is quantum vacuum fluctuations that come in through the 'other' port of the beam splitter.

Which is just cool, and given me pause.

George H.

  • formatting link
    formatting link

Sorry paywalls, but you can read the abstracts. I've done a few searches but found no good links.

This is some how related to Casimir effect,

formatting link

dang hard to measure. But maybe easier with a big scary laser making lots of photons.

Reply to
George Herold
Loading thread data ...

Ouch I should have posted some link.. read the first few pages of this,

formatting link

GH

Reply to
George Herold

Yup. The squeezed state guys were all over it back then.

What I want to know is, when you make an amplitude-squeezed diode laser by driving a very efficient diode with a way-sub-Poissonian current source, where to the vacuum fluctuations go?

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
 Click to see the full signature
Reply to
Phil Hobbs

[...]

Doesn't that problem go away if you accept that light is a wave, and only the interaction with the detector is quantized?

Jeroen Belleman

Reply to
Jeroen Belleman

That 'semiclassical' theory is almost universally applicable in instruments

--photocurrents have full shot noise and there are no correlations between the shot noise of different photocurrents.

You can certainly construct situations where that isn't true, but it doesn' t happen by accident.

The question is, where does the extra noise come from? Coherent detection o f vacuum fluctuations fits the semiclassical result but also covers other s ituations such as squeezed states, where you deamplify one phase (and corre spondingly amplify the other so that the uncertainty product is constant). The 'squeezed vacuum' interferes with a coherent state to produce e.g. ampl itude squeezing, where the resulting photocurrent has less than full shot n oise.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs  
Principal Consultant  
 Click to see the full signature
Reply to
pcdhobbs

Yeah I was thinking of that model, and it doesn't really help. There's really extra noise... it doesn't seem to me you can say the noise comes in at the detector. And though I haven't read about it, from the abstracts I think LIGO somehow sees this noise.... (As a force on the beam splitter maybe???)

If you read the beginning of the Caltech paper (link in my second post), it looks to be a much more complicated system than I first thought. George H.

Reply to
George Herold

My understanding of squeezed states is at the Sunday supplement level. (Hand wavy and probably mostly wrong.)

George H.

Reply to
George Herold

If a beam of light hits a photodiode, you can measure its power and its shot noise. If that beam had sometime passed through a splitter (maybe not to your knowledge) would it measure any different?

--
John Larkin         Highland Technology, Inc 

lunatic fringe electronics
 Click to see the full signature
Reply to
John Larkin

Normally we'd notice no difference. Noise is sqrt(N) and you get N from the power measurement. But if the light was in one of the squeezed states.

formatting link
(about which I know nothing) Then the beam splitter would reduce the squeeziness and we'd notice it.

Apparently squeezed light is part of what makes the second generation LIGO better. Those LIGO guys know a lot about noise!

George H.

Reply to
George Herold

Ah sorry, that Caltech link rolled off the page. Could you repost?

I don't see any 'extra' noise. Each detector shows shot noise, no less. If a detector after a splitter would show sqrt(N)/2 noise, I would be mightily surprised.

I'm *not* addressing these 'squeezed light' states. Those invariably involve multiple detectors with some statistical trickery to combine the results. If you would look at each detector in isolation, you'd simply get the expected shot noise again.

Jeroen Belleman

Reply to
Jeroen Belleman

Right. That is the 'extra' noise. to start there is sqrt(N) and after BS there is sqrt(N/2) + sqrt(N/2) = sqrt(2) * sqrt(N)

Here,

formatting link

This is not a good reference...

If you go here,

formatting link
'look inside' and search for 'beamsplitter noise' you will be directed to pages 382 to 384, which was my first encounter.

George H.

Reply to
George Herold

You could certainly generate light with a different photon time distribution than thermal radiation, so see more than classic shot noise. But would a beam splitter do that?

--
John Larkin         Highland Technology, Inc 

lunatic fringe electronics
 Click to see the full signature
Reply to
John Larkin

Would the non-zero temperature of a splitter or a mirror add noise to light?

--
John Larkin         Highland Technology, Inc 

lunatic fringe electronics
 Click to see the full signature
Reply to
John Larkin

I haven't worked with amplitude-squeezed laser diodes, but if you amplitude-squeeze a coherent state, its phase becomes more uncertain. That is, you have redistributed some of the "vacuum fluctuations" on the amplitude expectation value onto the phase expectation value.

Quantum optics is fun.

? David

Reply to
David Nadlinger

Yes ? but in most cases, the effect is small enough to be ignored in typical quantum-optics experiments.

At room temperature, the black-body spectrum has little power in the visible region, so usually doesn't directly matter for quantum optics experiments.

In the case of mirrors, the fact that the atoms making up the coatings vibrate thermally can matter though when building very stable cavities, though. People have started going to cryogenically cooled silicon single-crystal cavities for the most demanding experiments, see e.g. the

2017 PRL by the PTB/JILA crews (Matei et al., PRL 118 (2017) [1]).

rather remarkable feat. The fact that silicon isn't transparent in the visible is a bit annoying, but thanks to frequency combs, this ultimately isn't a big limitation. For a taste what people are up to these days, have a look at the pre-print they recently put out (arXiv:1902.02741 [2]), where they compared two clocks to 6e?19 precision in a single hour.

? David

[1]
formatting link
[2]
formatting link
Reply to
David Nadlinger

That's what I was thinking about, atomic-scale thermally induced vibrations. Maybe that could induce angular noise too.

Macroscopic modulation of a light beam could modulate the amplitude at relatively low frequencies. That would change the apparent spectrum of the shot noise.

--
John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  
 Click to see the full signature
Reply to
John Larkin

My understanding of photon statistics is still evolving. (Meaning I had misconceptions in the past, and I maybe still. :^)

You can get photon anti-bunching in some special cases.. resonant florescence of a single atom.

formatting link

But it's hard.

Thermal radiation has super-Poissonian statistics... photon bunching.

Again hard to see.

I would think a beam splitter would make either type of light less so.. so move the statistics to be more Poissonian... more random.

This is a good (Sohpmore level) paper on photon statistics

formatting link

I can send you (and any others) a copy by email, but it's from a colleague and I don't wnat to get people in trouble by putting it in drop box.

George H.

Reply to
George Herold

Hi,

formatting link

That image could be thought of as a beam splitter which frequency doubles the reflected light via second harmonic generation. This is just a special case low entropy version of what the thread title refers to.

cheers, Jamie

Reply to
Jamie M

Thanks! Zeilinger was the guy with the 'imaging with undetected photons' article a few years back. A quantum mystic, in my opinion.

I'll stroll over to the library to have a look at that book. For some reason, it takes forever to get a peek from Amazon.

Jeroen Belleman

Reply to
Jeroen Belleman

OK, There's not much more in the Atomic physics book... It's at home but if I remember I'll scan the few pages and post 'em.

George H.

Reply to
George Herold

ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.