Quantum nondemolition measurements in the relativistic Dirac oscillator

We investigate the feasibility of performing quantum nondemolition (QND) measurements in the one-dimensional Dirac oscillator, a frequently used toy model to investigate relativistic extensions of nonrelativistic quantum effects. We derive general expressions for its QND observables and find that they are in general complex combinations of the position, momentum, and spin operators, which makes them challenging to realize experimentally. However, the situation is considerably simplified in both the weakly and strongly relativistic limits, where they should be amenable to an experimental demonstration. This suggests exploiting continuous measurements of small departures from the QND character of these variables in the intermediate regime as probes of relativistic effects.