Quantum Nondemolition Measurements of a Particle in Electric and Gravitational Fields

Abstract

In this work we obtain a nondemolition variable for the case in which a charged particle moves in the electric and gravitational fields of a spherical body. Afterwards we consider the continuous monitoring of this nondemolition parameter, and calculate, along the ideas of the so called restricted path integral formalism, the corresponding propagator. Using these results the probabilities associated with the possible measurement outputs are evaluated. The limit of our results, as the resolution of the measuring device goes to zero, is analyzed, and the dependence of the corresponding propagator upon the strength of the electric and gravitational fields is commented. The role that mass plays in the corresponding results, and its possible connection with the equivalence principle at quantum level, are studied. *

Continuous Quantum Nondemolition Measurements of a Particle in Electromagnetic and Gravitational Fields

“…( 12) and (13). This obviously differs from the onedimensional case when only considering the electric and gravitational fields, [8] where what we obtain is only one QND variable.…”

“…Looking at expression (18), the mass m of the particle appears in the relation mh, which is consistent with the result of QND measurement in electric and gravitational fields. [8] It differs from the result of Colella, Werner, and Overhauser experiment, [11] and differs from the case of a quantum demolition measurement, [12] which has the combination m/h.…”

“…( 4), it can be easily seen that the particle in our model is a harmonic oscillator subjected to force F . Compare our model with that of a particle moving in electric and gravitational fields [8] in which the condition for ω 2 > 0 is qQ > GM m/k, and the charge are only of the same sign, or, if the charges are of opposite sign (qQ < 0), the harmonic oscillator is then provided with a complex frequency (ω 2 < 0). We find that in our model the effect of magnetic field on the particle are represented by 2n 2 q 2 Q 2 /mR and 5n 2 q 2 Q 2 /m 2 R 2 in Eqs.…”

“…Camacho discussed QND measurement of a particle in electric and gravitational fields. [8,9] In his model he ignored the magnetic fields. In this work we shall find a set of QND variables for the case of a particle moving in an electromagnetic and gravitational fields of a spherical body, for instance, in the Earth's electromagnetic and gravitational fields.…”