Measurement-induced interference in an inhomogeneous gravitational field

A very interesting quantum mechanical effect is the emergence of gravity-induced interference, which has already been detected. This effect also shows us that gravity is at the quantum level not a purely geometric effect, the mass of the employed particles appears explicitly in the interference expression. In this work we will generalize some previous results. It will be shown that the introduction of a second order approximation in the propagator of a particle, immersed in the Earth's gravitational field, and whose coordinates are being continuously monitored, allows us to include, in the corresponding complex oscillator, a frequency which now depends on the geometry of the source of the gravitational field, a fact that is absent in the case of a homogeneous field. Using this propagator we will analyze the interference pattern of two particle beams whose coordinates are being continuously monitored. We will compare our results againt the case of a homogeneous field, and also against the measurement ouputs of the Colella, Overhauser, and Werner experiment, and find that the difference in the dependence upon the geometry of the source of the gravitational field could render detectable differences in their respective measurement outputs.Comment: 15 pages, accepted in Physics Letters

Quantum nondemolition measurements in a Paul trap

In this work a family of quantum nondemolition variables for the case of a particle caught in a Paul trap is obtained. Afterwards, in the context of the so called restricted path integral formalism, a continuous measuring process for this family of parameters is considered, and then the corresponding propagators are calculated. In other words, the time evolution of a particle in a Paul trap, when the corresponding quantum nondemolition parameter is being continuously monitored, is deduced. The probabilities associated with the possible measurement outputs are also obtained, and in this way new theoretical results emerge, which could allow us to confront the predictions of this restricted path integral formalism with the readouts of some future experiments.Comment: 10 pages, accepted in Physics Letters

Quantum nondemolition measurements of a particle in an inhomogeneous gravitational field

In this work we obtain a family of quantum nondemolition variables for the case of a particle moving in an inhomogeneous gravitational field. Afterwards, we calculate the corresponding propagator, and deduce the probabilitites associated with the possible measurements outputs. The comparison, with the case in which the position is being monitored, will allow us to find the differences with respect to the case of a quantum demolition measuring process.Comment: Contribution in honour of Heinz Dehnen's 65 birthday. 3 new references, minor changes. Accepted in General Relativity and Gravitatio