Analysis of the quantum bouncer using polymer quantization

作者：Martin Ruiz A^*; Frank A; Urrutia L F

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2015, 92(4): 045018.

DOI：10.1103/PhysRevD.92.045018

Polymer quantization (PQ) is a background independent quantization scheme that arises in loop quantum gravity. This framework leads to a new short-distance (discretized) structure characterized by a fundamental length. In this paper we use PQ to analyze the problem of a particle bouncing on a perfectly reflecting surface under the influence of Earth's gravitational field. In this scenario, deviations from the usual quantum effects are induced by the spatial discreteness, but not by a new short-range gravitational interaction. We solve the polymer Schrdinger equation in an analytical fashion, and we evaluate numerically the corresponding energy levels. We find that the polymer energy spectrum exhibits a negative shift compared to the one obtained for the quantum bouncer. The comparison of our results with those obtained in the GRANIT experiment leads to an upper bound for the fundamental length scale, namely. lambda << 0.6 angstrom. We find polymer corrections to the transition probability between levels, induced by small vibrations, together with the probability of spontaneous emission in the quadrupole approximation.

• 出版日期2015-8-17