  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.

General Relativity and Quantum Cosmology;High Energy Physics - Theory