Experimental aspects of squeezing of photons and phonons

Question

I know that photons have been squeezed to 15 dB and phonons have been squeezed by 7.2 dB. Spins have been squeezed by 20 dB. Why is it so hard to squeeze the states of particles? If I wanted to squeeze a phonon to 100 dB, what sorts of problems would I encounter?

Answer 1

My answer is in part an excerpt from the the synopsis that accompanies the PRL paper of Schnabel:

Quantum squeezing can, in principle, reduce noise to arbitrarily low levels. But in practice, photon losses and detector noise limit the maximum achievable squeezing...In their new work, the researchers bested themselves by increasing this factor to 32 (15 dB of squeezing), using a light-squeezing scheme with low optical losses and minimal fluctuations in the phase of the readout scheme.

They are generated by passing coherent light through a non-linear crystal, and a good qualitative discussion can be found in the answers to this older question.

Answer 2

In broad strokes (non-technical answer coming up) squeezing requires a very well controlled system. You create a system which implements a squeezing Hamiltonian. If you could implement it perfectly well you could get arbitrary squeezing.

However, in practice, a lot of things come in to mess you up. Often squeezing is implemented using some sort of non-linearity. When the Hamiltonian you set up runs for long enough this non-linearity begins to saturate and either higher order terms come in to ruin the squeezing or the Hamiltonian simply stops being as good at squeezing.

Noise sources can also mess you up. Whatever you a squeezing must be coupled to some squeezer. If your squeezed thing is coupled to a squeezer it might also be coupled to other systems which perturb it in uncontrolled ways (noise). To be able to squeeze something very deeply you must make sure any noise that enters the system introduces a variance which is less then the variance of the squeezed quadrature. This would require a very high level of noise insensitivity for 100 dB of squeezing.

Laser phase noise is probably a common culprit but I'd have to think a little harder before making a strong claim about that. I haven't had a close look at the papers you cite but likely they comment as to what limits the depth of their squeezing.