You have not specified the purpose, but High Harmonic Generation fulfills your requirement [ https://en.wikipedia.org/wiki/High_harmonic_generation ].

The time delay here is of course extremely short, but well defined.

If the reemmision is through fluorescence, on the other hand, the reemitted light is generally no longer coherent.

Dear Xiaolei Zhu,

Thanks for the reference, I will read it.

About the purpose, I can't afford describing it publicly before I make sure that the process of delayed and coherent re-emission exists. However, please be kind and read the message I sent you, you'll see there what I want to prove. If the proof is possible, I think that it would provide a step further in the issue of measurement in quantum mechanics.

With kind regards and thanks again,

Sofia

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Dear William,

Thanks a lot for the rich bibliography, but what I need is different. I don't want to measure the two wave-packets, not even once. I want them to pass through the medium, be absorged, and re-emitted, without distubing the coherence etween the wave-packets.

For instance if the initial wave-function is of the form |a> + i|b>, after passing through the material, being absorbed and re-emitted, the wave-packets should become |a'>, respectively |b'>, and I expect the wave-function to remain a coherent superposition, |a'> + i|b'>. That means, if we bring |a'> and |b'> to cross one another, and repeat the experiment many times, I expect that an interference pattern appears.

I would be glad if you'd be able to indicate a material that absorbs and re-emits the wave-packets in this way. Measurement, to the contrary, produces decoherence, and I don't want it.

With thanks in advance,

Sofia

The point is, that given the problem of the decoherence via the QZE, you will get a result that reflects exactly how you eventually look at the data, regardless. The Xiao-Peres Delayed Choice Quantum Swapping experiment already demonstrated this. A third observer (Victor), receiving entangled photons chooses a detection method, as a result, the entangled photons that Alice and Bob received in the past yield the same result, regardless of already having been detected (but not yet observed). You cannot get around the entanglement problem in this.

If you do the experiment in 5 different ways, and send entangled photons to friends around the planet, but tell them not to look at the results until you say so, whatever results you get, when they open their results, they will also observe the same answer.

This is even more bizarre than the Delayed Choice Quantum Eraser, but explains the phenomenon of a detector in the past yielding an observed result in the future.

In short, your coherent superposition will not yield a result that suggests a linear time-line.

Dear William,

You are very kind. Now let me tell you something: as long as I don't find an implementation of my experiment as I describe it, it's meaningless to explain why I need this experiment. On the other hand, if I could explain the purpose, you would understand that the experiment should be done exactly as I say: no entanglements, no measurements before the wave-packets are re-emitted, and the re-emission should preserve the coherence of the wave-function.

If, and when, I find an implementation of my experiment, I will explain its theoretical signification, which in my opinion is very interesting.

With kindest regards,

Sofia