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I would like to know which type of quantum states of a bosonic field, that have an explicit analytical expression as vectors/density matrices in a symmetric Fock space, can be prepared in an experimental setting, and then manipulated (e.g. an interaction can be turned on and they are evolved by the resulting dynamics).

I think that coherent states can be prepared via lasers (even if I know there is some debate on that), and I have been told (do you know any reference?) that states with a fixed number $n$ of photons (Fock sates) have also been recently realized. But what about more general, or simply different, states (e.g. twin Fock states, statistical mixtures, eigenvectors of operators (with discrete spectrum)...)?

I am interested in established results, and precise references would be greatly appreciated.

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    $\begingroup$ This is an awfully broad question, you might like to refine your requirements a bit. For example, thermal states of bosonic fields (black-body radiation field, acoustic phonons in crystals) are ubiquitous. Fock states of photons were first unambiguously detected in the 1970s and are now routinely prepared by single-photon sources. Quantum state preparation of electromagnetic field cavity modes won Serge Haroche the Nobel Prize, etc... $\endgroup$ – Mark Mitchison Apr 27 '15 at 8:29
  • $\begingroup$ @MarkMitchison I narrowed it a bit. I am interested in states that have an explicit analytical form and can be prepared as "initial states" of an experiment and not just only observed. Thanks for the references anyways ;-) $\endgroup$ – yuggib Apr 27 '15 at 8:53
  • $\begingroup$ Squeezed states are among them, and they are used in high precision interferometry $\endgroup$ – Slereah Aug 18 '15 at 10:33
  • $\begingroup$ I answered this at physicsoverflow.org/30992 $\endgroup$ – Arnold Neumaier Apr 3 '16 at 13:38

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