Quantum Zeno tomography

We show that the resolution ''per absorbed particle'' of standard absorption tomography can be outper- formed by a simple interferometric setup, provided that the different levels of ''gray'' in the sample are not uniformly distributed. The technique hinges upon the quantum Zeno effect and has been tested in numerical simulations. The scheme we propose could be implemented in experiments with uv light, neutrons, or x rays. Absorption tomography is an important experimental technique revealing the internal structure of material bodies. By measuring the attenuation of a beam of particles passing through a sample one infers the absorption coefficient ~den- sity! of the sample in the beam section. The possibility of distinguishing two slightly different densities of the material is often of vital importance. Under otherwise ideal conditions the shot noise associated with the discrete character of the illuminating beam sets an upper limit to the resolution of absorption tomography: for instance, the shadow cast by a brain tumor might become totally lost in the noisy data. One possibility to overcome the fluctuations is to increase the intensity of the beam. However, in many situations, as in medicine for example, the intensity of the illuminating beam cannot be made arbitrarily high due to the damage provoked by the absorbed radiation. A significant step toward an ''absorption-free tomogra- phy'' came from quantum theory. It was demonstrated, both theoretically @1,2# and experimentally @3#, that totally trans- mitting and absorbing bodies can be distinguished without absorbing any particles, by using an interferometric setup. This idea is in fact a clever implementation of the quantum Zeno effect @4# and hinges upon the notion of ''interaction- free'' measurement @5#. A classical measuring apparatus ~here the black sample! , placed in one arm of the interferom- eter, projects the illuminating particle into the other arm, destroying interference, freezing the evolution, and forcing the particle to exit through a different channel from that it would have chosen had both arms been transparent ~white sample! In practical applications, however, samples are normally neither black nor white: they are gray. In this paper we en- deavor to understand whether application of the quantum Zeno effect, which turns out to be ideal for discriminating black and white, might be advantageous also for the more practical task of discriminating two gray bodies with differ- ent transmission coefficients. More specifically, we ask: Is it possible by quantum Zeno effect to reduce the number of absorbed particles while preserving the resolution? We show that this is indeed possible. Closely related questions have recently been investigated by other authors @6,7#. Our con- clusions are somewhat optimistic: we show that standard ab- sorption tomography can be outperformed by a Zeno setup, provided that the frequency of occurrences of the different levels of ''gray'' in the sample is not uniform. In addition, the Zeno setup, unlike the standard one, is endowed with two detection channels: as we shall see, this feature, if properly exploited, leads to even better performances in the Zeno case.