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Quantum Uncertainties for Coherent and Squeezed States

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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.

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