# Quantum Uncertainties for Coherent and Squeezed States

Once all images are downloaded, press reload to put them in synch.## a

## b

## c

## d

Uncertainty regions for various types of quantum states are shown in the left column, together with the time dependences of*x*(

*t*) (or

*p*(

*t*)) (blue-grey curves) and their uncertainties (light blue shaded area), in the right column.

**(a)** The uncertainty region for the **vacuum state** is
a circle centered at the origin.

**(b)** The **coherent state** exhibits a circular uncertainty
region centered about the rotating phasor. Points (*x*, *p*)
in the uncertainty circle trace out an electric field with an uncertainty
that is independent of time.

**(c)** The **squeezed-vacuum state** has an elliptical
uncertainty region.

**(d)** The **quadrature-squeezed coherent state** has an elliptical
uncertainty region centered about the phasor. As with the squeezed-vacuum
state (b), the electric field shows *a periodic reduction and enhancement
of its uncertainty*. If the minor axis of the ellipse were oriented
along the phasor, the state would also be **number squeezed**.

Modified/Expanded from Figure 2 on page 28
of M.C. Teich and B.E.A. Saleh,
"Squeezed and Antibunched Light", *Physics Today*, June, 1990.