# Uncertainty Regions for the Vacuum, Coherent, and Squeezed States

Schematic diagram of the uncertainty areas in the generalized coordinate
and momentum (*X*, *P*) phase space of a photon **squeezed state**
(ellipse) and a **coherent state** (circle). In quantum optics, *X*
and* P *are the two quadratures of the electric field. Notice that
the coherent state has the same uncertainty area as the vacuum state (circle
at the origin), and that its area is circular, while the squeezed state
has an elliptical uncertainty area. Therefore, in the direction parallel
to the q/2 line, the squeezed state has a smaller
noise than the coherent state.

Image Source: X. Hu, *Quantum Fluctuations In Condensed Matter Systems*,
UM Ph.D. Thesis 1997, Page 5.

Information on squeezed states in quantum optics can be found in:

D. Walls, *Nature 306*, 141, 1983.

M.C. Teich and B.E.A. Saleh, 1988 in *Progress
in Optics 26*, 1, ed. E. Wolf.