Locally detecting UV cutoffs on a sphere with particle detectors

Abstract

The potential breakdown of the notion of a metric at high energy scales could imply the existence of a fundamental minimal length scale below which distances cannot be resolved. One approach to realizing this minimum length scale is construct a quantum field theory with a bandlimit on the field. We report on an investigation of the effects of imposing a bandlimit on a field on a curved and compact spacetime and how best to detect such a bandlimit if it exists. To achieve this operationally, we couple two Gaussian-smeared UDW detectors to a scalar field on a $S^2 \times R$ spherical spacetime through delta-switching. The bandlimit is implemented through a cut-off of the allowable angular momentum modes of the field. We observe that a number of features of single detector response in the spherical case are similar to those in flat spacetime, including the dependence on the geometry of the detector, and that smaller detectors couple more strongly to the field, leading to an optimal size for bandlimit detection. We find that in flat spacetime squeezed detectors are more senstive to the bandlimit provided they are larger than the optimal size; however, in spherical spacetime the bandlimit itself determines if squeezing improves the sensitivity. We also explore setups with two detectors, noting that in the spherical case, due to its compact nature, there is a lack of dissipation of any perturbation to the field, which results in locally excited signals being refocused at the poles. Quite strikingly, this feature can be exploited to significantly improve bandlimit detection via field mediated signalling. Moreover, we find that squeezing on a sphere introduces extra anisotropies that could be exploited to amplify or weaken the response of the second detector.