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Minimum Uncertainty States

The Fock and thermal states have the same uncertainties in momentum and position; their product is . As the average number of photons in the field increases, this product will also increase. Therefore, as more and more photons can exist in the system, the system becomes more and more unpredictable.

The final two field states that shall be discussed in this text have a constant uncertainty product for momentum and position, . This class of states is called minimum uncertainty because by the uncertainty principle this product must be greater than or equal to . The squeezed coherent and coherent states are therefore very unique. The difference between them is that in a coherent state the uncertainty in position and momentum are both constant at ; however, in a squeezed state, one of these uncertainties can be made arbitrarily small while the other becomes arbitrarily large in order to keep the product constant. The coherent state is a special case of the squeezed state, but it was the first of these minimum uncertainty states to be fully analyzed.

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