Hi,

As far as I understand it, there is no interference between beams of different wavelength, and - at least in the case of the cardboard cat - also no phaseshift introduced by the sample (the cat is a simple cardboard cutout, it cannot shift the phase).

Here's how I understood it (confirmation or disproval by others very much welcome):

Without the nonlinear crystals and the infrared beampath this is simply a Michelson interferometer. Since path g and h (fig.1) lead to constructive / destructive interference, respectively, the phase shift between path c and e, meeting at BS2, must be introduced by one or both of the beamsplitters. So in this configuration, the detection probability for path h (Ph) would be zero (destructive interference), and Pg would be at max (constructive interference).

Even with the addition of the infrared beampath, nothing changes as long as there is no object. The paper states that "...if no object is placed in the setup, Ph = 0.", meaning that destructive interference at path h leads to zero detection probability.

Even after insertion of the object (the cat), it is still the same for the empty, cat-shaped center. Interference makes this shape bright in g, and dark in h, just as the whole image would be without an object.

The weird stuff happens where the cardboard blocks the infrared beampath d: Here, the signal photons do not interfere anymore. _That_ is actually the spatial information the camera detects: interference inside the cat, no interference outside. Both detectors (or halves of the camera chip) show uniform intensity in the outside region.

Why can there be no interference if path d is blocked? Because the infrared beam provides a means to discriminate which beampath a signal photon has taken. There are two possibilities:

1) If, at any signal photon detection event at g/h, there is a coincident detection of an IR photon at a (hypothetical) detector at the end of the IR beampath, this means that the signal photon took path e. 
Quote: "if T = 0 , an idler detected after D3, coincident with a signal count at g or h, would imply the signal source was NL2."

2) If it occurs without a coincident IR detection, it would necessarily have taken path c (leading to a blocking of the IR (idler) photon). 
Quote: "Detection of a signal photon without a coincident idler would imply the signal source wasNL1".

The IR beampath serves as a means to discriminate the signal beampaths c and e if IR-beam d is blocked, but preventing discrimination if IR-beam d is not blocked. However, once paths c and e are clearly distinguishable, a signal photon cannot interfere anymore. As long as there is no information as to which path it took, it has a 50% chance to go via [a -> c], and a 50% chance to go via [b -> e]. It actually takes neither one path nor the other, but both (similar as Schroedinger's cat being alive and dead at the same time). It interferes with itself. Once a measurement takes place (Schroedinger looking into the box / the presence or non-presence of a coincident IR photon revealing which beampath the signal photon took), the ambiguity ends and interference cannot happen.

What actually boggles the mind, however, is the fact that there is actually no detector for the IR photon. It is not even necessary to do the measurement. It is enough that the possibility exists (Quote: "The above arguments are valid even though the idler photons are not detected, for it is only the possibility of obtaining which-source information that matters in this experiment.")

I hope I have actually understood it correctly. I just puzzled this together for myself and I would appreciate what others think about it. 
Also, I am wondering if this or something like it would be applicable to fluorescence imaging in any way. My gut tells me no, but I cannot quite put my finger on it.

Best,
Tobias


-----Original Message-----
From: Confocal Microscopy List [mailto:[log in to unmask]] On Behalf Of Zdenek Svindrych
Sent: Friday, August 29, 2014 11:48 AM
To: [log in to unmask]
Subject: Re: A quantum microscope?

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Hi folks,
this is pretty tricky experiment, won't be easy to replicate!

It sounds almost unbelievable that two beams from different sources (two nonlinear crystals) with different wavelength (I don't know how much they can match it by heating the crystals, but I expect a kHz-MHz beating fre quency at least) can interfere...

The path lengths are matched to some 0.2 mm, which is doable. Much worse, you can't see the IR beams, an even if you could, you would be overwhelmed by the green light everywhere... That's the biggest problem: the green light is strong (150 mW) and the detected IR weak (some 10^9 photons/sec according to my quick calculations), so the detected intensity is some 10^9 times weaker than the laser. So you need to be extremely cautious about filters, any reflections, and any inconceivable nonlinear effects to be sure that your image comes from entangled photons.

Btw, I've only built a Michelson interferometer, once, long time ago. So I would never go for something like this... Great job! (well, to tease the authors a bit, Andor Luca has 8 micron pixel pitch, not 16 :-).

best, zdenek svindrych






---------- Původní zpráva ----------
Od: Reto Fiolka <[log in to unmask]>
Komu: [log in to unmask]
Datum: 29. 8. 2014 6:10:08
Předmět: Re: A quantum microscope?

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Hi John and dear listers,

Here is the link to the nature letter by Lemos et al:

http://www.nature.com/nature/journal/v512/n7515/full/nature13586.html

It is pretty mindboggling. The phase imaging is kind of neat, where the phase object introduces a 2pi shift for the light that is actually going through it, but ~pi for the entangled light that is being imaged (but never went through it), thus producing good contrast.

I immediately went through the lab to see if I could rebuild the setup, just out of sheer curiosity and disbelief!

But it appears that it needs quite precise alignment, all beams have to be in the exact same spatial mode and the path length has to be matched too, so that one can not distinguish from which nonlinear crystal the photons are coming.

It really makes you wonder what kind of revolutions lie ahead of us in the imaging field.

Best,
Reto"