Shaping optical pulses with linear optics? Where's Von Neumann?

[al onestone]

I'm trying to get to the bottom of things concerning the shaping of an optical pulse(change of state) with linear optics. Using linear optical apparatus we can shape the pulse of a photon in such methods as cavity dumping. You feed an optical cavity with near monochromatic(short bandwidth) input and allow no output. The light builds up and then you release all the light at once by opening up the cavity, and in the end you have an output with pulse length equal to the inner loop length of the cavity, even if the cavity loop is shorter than the coherence length of the input. So you can shorten the coherence length of the output which consequently widens the bandwidth. This is a change of state.

In QM all changes of state can be modeled by a physically real coupling, aka the Von Neumann measurement scheme. My question is, what physically real coupling is taking place when the photon output has its change of state?

You can create a mathematical model of the unitary operator which would act on the initial state description to produce the final output state, but what is the physically real meaning of the operation? Is there an answer?

 

[eljose79]

Thank you for your interest in the shaping of optical pulses using linear optics. I am always eager to engage in discussions about the physical mechanisms behind such phenomena.

Firstly, I would like to clarify that the change of state you are referring to is the transformation of an input pulse with a certain coherence length and bandwidth into an output pulse with a different coherence length and bandwidth. This is indeed a commonly observed phenomenon in linear optics, and it is often achieved through the use of techniques such as cavity dumping, as you have described.

Now, to address your question about the physically real coupling that takes place during this change of state. As you have mentioned, in quantum mechanics, all changes of state can be modeled by a physically real coupling, also known as the Von Neumann measurement scheme. This refers to the interaction between the quantum system (in this case, the photon) and the measuring apparatus (in this case, the linear optical setup).

In the context of shaping optical pulses, the physically real coupling that occurs is the interaction between the photon and the elements of the linear optical apparatus, such as the mirrors and lenses. This interaction causes the photon to undergo a transformation, resulting in a change of state.

To further understand the physically real meaning of this operation, we can look at it from a classical optics perspective. In classical optics, the input pulse is described as a superposition of different frequency components, each with a certain amplitude and phase. When this pulse interacts with the linear optical elements, the different frequency components experience different phase shifts and attenuation, resulting in a change in the overall shape of the pulse.

In terms of the unitary operator that acts on the initial state description to produce the final output state, this can be thought of as the mathematical representation of the physical interactions between the photon and the linear optical apparatus. It describes how the different frequency components of the input pulse are transformed into the output pulse.

In summary, the physically real coupling that takes place during the shaping of an optical pulse with linear optics is the interaction between the photon and the linear optical elements. The resulting change of state can be mathematically represented by a unitary operator, but its physical meaning lies in the transformation of the different frequency components of the input pulse. I hope this helps answer your question. Keep exploring and asking questions about the fascinating world of optics!