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### Fock and Thermal States

When is zero, these two states are similar. The principle difference between them is in their photon number variables. The reason for this similarity is that their density matrices have no off--diagonal elements. This implies that their position and momentum are zero on average. The variance of these two quantities will also be equal under these conditions. Verify each of these statements with FieldApp.

Plot both p, and q, versus time for the Fock and Thermal state. Notice that the plots are similar. Figure shows a Thermal state's plot.

Figure: q, vs t and p, vs t for a thermal state with temperature of one

One is equally likely to find either p or q in a rectangular region about zero. This result is not wavelike. The amplitude information in these states is completely certain; however, the phase information is maximally uncertain. This plot may lead the student to believe that measurements of the electric and magnetic fields would be homogeneously distributed inside the cavity. This result is not the case. As Figure shows, the sine and cosine functions by which p and q must be multiplied generate nodes. No matter how uncertain the fields are, the nodes are always well--defined.

Figure: 2048 E and B measurements at t=0

Andy Antonelli
Wed May 17 14:34:24 EDT 1995