Maximal Subvacuum Effects: A Single Mode Example

We discuss an example of a subvacuum effect, where a quantum expectation value is below the vacuum level, and is hence negative. The example is the time average of the mean squared electric field in a non-classical state where one mode is excited. We give some specific examples of such states, and discuss the lower bound on the squared field or its time average. We show when a lower bound can be obtained by diagonalization of the squared electric field operator, and calculate this bound. We also discuss the case of an instant time mean squared electric field, when the operator cannot be diagonalized. In this case, a lower bound still exists but is attained only by the limit of a sequence of quantum states. In general, the optimum lower bound on the mean squared electric field is minus one-half of the mean squared electric field in a one photon state. This provides a convenient estimate of the subvacuum effect, and may be useful for attempts to experimentally measure this effect.