MEASURING QUANTUM STATES - EXPERIMENTAL SETUP FOR MEASURING THE SPATIAL DENSITY-MATRIX

To quantify the effect of decoherence in quantum measurements, it is d esirable to measure not merely the square modulus of the spatial wave function, but the entire density matrix, whose phases carry informatio n about momentum and how pure the state is; An experimental setup is p resented that can measure the density matrix (or equivalently, the Wig ner function) of a beam of identically prepared charged particles to a n arbitrary accuracy, limited only by count statistics and detector re solution. The particles enter into an electric field, causing simple h armonic oscillation in the transverse direction. This corresponds to r otating the Wigner function in phase space. With a slidable detector, the marginal distribution of the Wigner function can be measured from all angles. Thus the phase-space tomography formalism can be used to r ecover the Wigner function by the standard inversion of the radon tran sform. By applying this technique to, for instance, double-slit experi ments with various degrees of environment-induced decoherence, it shou ld be possible to make our understanding of decoherence and apparent w ave-function collapse less qualitative and more quantitative.