squeezing was first studied in photonic systems. The photons in a laser beam are in the so-called "coherent state" (or Glauber's coherent state). In these states the quantum fluctuations in the two quadratures of the electric field have equal magnitude, with the product of the two satisfying the minimum condition of the Heisenberg principle. The noise in each of the quadratures is called the standard quantum limit. "Squeezing" refers to manipulations (for example, by introducing inter-photon interactions) in which the noise in one of the quadratures is squeezed below the SQL, while Heisenber principle dictates that noise in the other quadrature would have to increase. If squeezing can be realized periodically, one cna focus on one of the quadratures with the same period and realize smaller quantum noise by coinciding any measurement with periods of suppressed noise.
During my PhD study at University of Michigan, with Professor Franco Nori, we studied how squeezing of quantum noise might be achieved in condensed matter systems. We were motivated by the fact that several metrological standards were based on phenomena in solid state (quantum Hall effect, Josephson tunneling, etc.), where squeezing of noises could potential further improve these standards, while drawing out new interesting physics. We studied mainly two systems: phonons and Josephson junctions. With phonon squeezing, we suggested mechanisms such as polaritons, phonon parametric down conversion, and second order Raman scattering. for Josephson junctions, we were mostly focused on the nonlinearity of the junctions and its implications.
For more details of my studies in this area, check out my thesis: Table of Contents and Chapter 1, Chapter 2 and Chapter 3 on squeezed phonons, Chapter 4 and Chapter 5 on squeezing in Josephson junctions, and Chapter 6 and references.