Matthias Freyberger

Various measures of quantum phase uncertainty: a comparative study

We compare and contrast five measures of phase uncertainty of a quantum state corresponding to a single mode of the electromagnetic field. The basis of this study are the states which minimize a particular measure for a fixed number of Fock states and normalization. We find these optimal states and study their characteristic properties. These optimal states allow us to establish an ordering of the different definitions for phase uncertainty.

Wave Packets Can Factorize Numbers

We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new, promising and effective method to factorize numbers.

CHIRPED PULSES, GAUSS SUMS AND THE FACTORIZATION OF NUMBERS

We present two physical systems which make Gauss sums experimentally accessible. The probability amplitude for a two-photon transition in an appropriate ladder system driven by a chirped laser pulse is determined by a Gauss sum. The autocorrelation function of a quantum rotor is also of the form of a Gauss sum. These examples suggest rules for determining prime factor components on the basis of the properties of Gauss.