Require a source for a delocated photon pair

[Derek P]

The light source in the DCQE experiment of Kim et al is a laser which illuminates two slits which are immediately followed by an SPDC. The latter is therefore excited coherently in two narrow stripes referred to as "slits". The output has a small amplitude of down-converted entangled pairs. The authors state "A pair of entangled photons, photon 1 and photon 2, is then emitted from either atom A or atom B by atomic cascade decay."

Consider just the "erased" cases. Photon 2 is entangled with photon 1. So when, for example, an |A>+|B> detection occurs, photon 1 is assigned to the |A>+|B> "interference pattern". That's not the problem here.

But according to what I just quoted, the pair is emitted by a single atom, a single slit. To simplify things a bit, It is either |A>|A> or |B>|B>. However, later in the paper, in (2) it has become a superposition.

I would put this down to careless language by Kim et al, but it seems to me this does not get rid of the problem. |A>|A> + |B>|B> at the detectors can only have evolved from |A>|A> + |B>|B> at the SPDC. Which can only have evolved from |α>+|β> where |α> and |β> are the excited states of atom A and atom B respectively. The photon pair is therefore emitted by two, widely separated atoms acting together.

Personally I have no difficulty with this picture, because I would expect the possible different emission times to result in a superposition of |α> → |A>|A> and |β> → |B>|B>. However apparently this is not a standard description. I would dearly love to know what is the standard description given that the alleged emission from a single atom in a single slit gives rise to a state that refers to both slits.

 

[DrChinese]

But according to what I just quoted, the pair is emitted by a single atom, a single slit. To simplify things a bit, It is either |A>|A> or |B>|B>. However, later in the paper, in (2) it has become a superposition... |A>|A> + |B>|B> at the detectors can only have evolved from |A>|A> + |B>|B> at the SPDC. Which can only have evolved from |α>+|β> where |α> and |β> are the excited states of atom A and atom B respectively. The photon pair is therefore emitted by two, widely separated atoms acting together. ...
I would dearly love to know what is the standard description given that the alleged emission from a single atom in a single slit gives rise to a state that refers to both slits.

This apparently nonsensical setup is actually more common than might initially appear. Type I PDC entanglement uses a very similar technique, where there are 2 PDC crystals overlapped but perpendicular. The entangled pair originates from one or the other of the crystals, just as in your cited setup. Many Bell tests use Type I entanglement.

The answer is that the source cannot be distinguished. It could be either one. In this case (A or B), the superposition arises from the possibility it could be either. Any superposition (say spin) is a combination of states that are mutually incompatible (such as up or down). This is no different. Obviously this does not follow the classical idea that it came from one or the other, and they are fully independent.

 

[Derek P]

In this case (A or B), the superposition arises from the possibility it could be either. Any superposition (say spin) is a combination of states that are mutually incompatible (such as up or down). This is no different. Obviously this does not follow the classical idea that it came from one or the other, and they are fully independent.

Okay, well I admit I was little miffed to be slapped down hard for describing a similar situation as the photon coming from both sources so I was wondering how it "should" be described. A superposition is not too hard to accept if it started as a single emission event but then is split by a BS or a double slit etc. It becomes crazy if the emission mechanism occurs in a single atom and yet results in a superposition over two crystals.
That's why I suggest decomposing it into a large number of low amplitude components corresponding to emission from each atom. It all makes sense then.