Multiple Sequential Delayed Choice Experiment

[knightwing]

Hi all;

This goes under the heading of experimental predictions... gone awry. Let me say from the start that I think I've got something wrong, and would have no problem having it pointed out to me. I'm a newbie, and I've been boning up on basic quantum physics phenomena on Youtube, and trying to wrap my brain around it. I recently came up with a thought experiment that gives utterly weird results I don't believe.

Let's start with an extreme version of the "delayed choice experiment".

* Atop a mountain at the north pole of the moon, we have a very strong laser, shining through double slits, with a splitter crystal behind them. The splitter creates entangled photons...
- photons going though slit A are split into an entangled pair; one going to a local CCD-detector and one going just over the north pole of Mars ( I did say this was an extreme version )
- photons going though slit B are split into an entangled pair; one going to a local CCD detector and one going just over the south pole of Mars
- at each Martian pole, there is a detector that can be either retracted into the ground or extended into the beam
- in addition to the laser beam, there's a radio signal beamed to Mars for synchronization purposes, e.g. WWV.

* Identical setup at the other end. Atop a ridge at the north pole of Mars, we have a very strong laser, shining through double slits, with a splitter crystal behind them. The splitter creates entangled photons. And there are detectors at the north and south poles of the moon, pointed at the Martian laser.

* A couple of questions...

1) Does "delayed choice" need 2 detectors, or would 1 detector suffice as in the "which way" experiment?

2) Rather than have the detectors pop up and down to detect or not detect the photons from the laser, would it work to have mirrors or shutters block or not block the the photons from the laser getting to the detectors?

* Now on to the experiment(s).

1) The standard delayed choice experiment involves a laser sending out a beam. Let's say that Earth and Mars are 11 "light-minutes" apart in their orbits. A short blast is sent out from Mars at 2:49 PM EST, arriving at the earth-moon system 3:00 PM EST. Depending on whether the detectors on the moon are detecting or not, the CCD detector on Mars will get 2 lines or an interference pattern at 2:50 EST. So far, so good.

2) Now on to the "Multiple Sequential Delayed Choice Experiment". Some definitions
- both lasers are transmitting 1-second pulses, with a half-second gap between pulses
- let's call an remotely-undetected pulse (interference pattern observed locally) a "0"
- let's call an remotely-detected pulse (two lines observed locally) a "1"
- we could do binary transmission directly
- or let "0" = "space"
- "010" = "space dot space"
- "01110" = "space dash space"
- yes, we've implemented a space version of Morse Code

And now for the "really good stuff"
- The Martian laser is shining pulses at Earth around 2:49 PM EST
- A trader on Earth has a live stock market feed
- At 3:00 PM EST he transmits the stock price of a company to the lunar station
- The lunar station toggles the lunar laser detectors up/down, on/off, whatever
- Allow 1 minute for the messaging process
- Due to the weirdness of delayed choice, the Mars station receives the stock price, encoded as a series of interference-fringe and 2-line patterns, between 2:49 and 2:50 PM EST at their end of the delayed choice experiments
- Oh yeah, the lunar laser is pulsing at Mars around 2:39 PM EST
- Somebody on Mars repeats back the info by toggling their detectors up/down for a minute 2:50 to 2:51 PM EST
- By 2:40 PM EST (delayed choice again) the CCD-detector at the moon will have received the message, and relayed the 3:00 PM EST stock price to the trader.
- We could "ping-pong" info backwards in time indefinitely, but even 20 minutes is an eternity in high frequency stack market trading.

OK, people... WHAT... AM... I... DOING... WRONG... ? I may be a university dropout, but even I know this result is ridiculous.

 

[PeroK]

I'm struggling to understand what is going on here. Could you boil down your experiment to the basics? Forget Mars, the moon and all the rest. What is the essence of your experiment?

 

[PeterDonis]

The splitter creates entangled photons

That's not what a beam splitter does. A beam splitter splits a single photon's wave function. It does not create two entangled photons out of one.

There are devices such as parametric down conversion crystals that convert one photon into two entangled photons, both of lower energy. However, doing this destroys interference; if you put these in your apparatus instead of beam splitters, the CCD will never record an interference pattern.

Depending on whether the detectors on the moon are detecting or not, the CCD detector on Mars will get 2 lines or an interference pattern at 2:50 EST. So far, so good.

No, not so good.

The experiment you are describing is not the same as the standard delayed choice experiment, because the branch of the photon wave function that goes to the CCD on Mars will reach it long before the "choice" mechanism on the Moon is reached. In the standard delayed choice experiment, all the detectors are after the "choice" (or at it, if the "choice" is a choice whether or not to put a detector in the beam).

Also, since, as above, beam splitters don't create two entangled photons, they just split one photon's wave function, a detection on the Moon does not mean two lines at the CCD: it means nothing detected at the CCD at all. So what will actually be observed in your experiment is: if you just run a beam of photons, without trying to distinguish individual photons, you will get an interference pattern at the CCD, of somewhat lower intensity than the original beam (because it's only being produced by the photons that don't get detected on the Moon), and you will get a beam detected on the Moon, of somewhat lower intensity than the original beam (because it's only being produced by the photons that do get detected on the Moon). The simple causal explanation of this is that each photon's wave function has to "decide", when it reaches the CCD, whether to get detected or not. Those that do get detected form the interference pattern; those that don't get detected go on to the Moon. If you only have the detector on the Moon in the beam path some of the time, then some photons won't get detected at either place and will fly past the Moon and off into space.

If you slow down the photon source so that it is only emitting one photon at a time, then each run will have one of the following three outcomes:

(1) Detected at CCD (some of these might be runs where the detector on the Moon was in the beam path, for these the detector on the Moon detects nothing);

(2) Not detected at CCD and detected on Moon (these have to be runs where the detector on the Moon was in the beam path);

(3) Not detected at CCD and not detected on Moon (these have to be runs where the detector on the Moon was not in the beam path).

The results that have outcome #1 will build up an interference pattern on the CCD (note that each individual result is just a dot on the CCD, where that particular photon landed).

WHAT... AM... I... DOING... WRONG... ?

See above.

 

[PeroK]

In the meantime, here is a simpler experiment that highlights how the UP (uncertainty principle) works.

You have a delayed choice set up and enough photons hit the screen to register an interference pattern or not. Meanwhile, the other photons have been trapped somehow, bouncing around off mirrors, still potentially with the "which way" information.

Once we know what we see on the screen (let's say it is an interference pattern) we release the trapped photons into detectors to determine which way. And thereby try to outwit the UP!

So, what goes wrong? In this case, holding the photons introduces some uncertainty: some get absorbed by the mirrors and the longer we delay the eventual detection, the more the uncertainty builds up around the which way information we eventually gleen. Ultimately, nature conspires so that the more certain the interference pattern, the less certain the which way information that remains is.

There are a number of such experiments where the precise details of how the UP operates differ. But, in all cases, a careful analysis of any experimental set-up leads to results consistent with the UP.

 

[knightwing]

Thanks everybody. I knew I was doing something wrong, but wasn't sure where.

 

[PeterDonis]

The results that have outcome #1 will build up an interference pattern on the CCD

Actually, on thinking it over, I'm not sure this is exactly true. I think the results that have outcome #1 will build up a pattern on the CCD that is a mixture of the interference pattern and the two single-slit no interference patterns.

The reason I think that is as follows: if we look at the photon wave function before any detections are made, we have the following evolution:

Before the slits: well collimated wave function with momentum in the direction towards the slits.

After the slits, before the beam splitters: Superposition of the wave functions from each slit.

After the beam splitters (but before any detections): Superposition of four different terms:

(i) Both beam splitters send their photon towards the CCD: this is an interference pattern between the two one-slit wave functions, just as in the normal double slit experiment;

(ii) Beam splitter A sends its photon towards the CCD, beam splitter B sends its photon towards the Moon: at the CCD this is just a no interference image of slit A;

(iii) Beam splitter B sends its photon towards the CCD, beam splitter A sends its photon towards the Moon: at the CCD this is just a no interference image of slit B;

(iv) Both beam splitters send their photon towards the Moon.

At the CCD, we will get a combination of photons consisting of all of (i), half of (ii), half of (iii), and none of (iv). Each of the four alternatives is of equal probability (assuming we are using the usual 50-50 beam splitters), so the final pattern at the CCD is composed of all of (i) plus half each of (ii) and (iii), or the interference pattern at 1/4 of the original beam intensity plus an image of each slit at 1/8 of the original beam intensity.