  Counterintuitively, experiments show that an electromagnetically levitated
particle escapes from its trap when the ambient pressure is reduced below a
certain level even if the particle's motion is cooled by a resonator-based or
feedback-based mechanism. Here, we theoretically show that the ambient pressure
must be kept well above a critical value arising from gradient force
fluctuations (viz., fluctuations in part of the EM force whose Hamiltonian is
quadratic in the position of the particle). Also, we consider other force
fluctuations, and determine whether different realizations of feedback cooling
are able to reach the ground state. In some realizations, the cooling rate must
be kept well below a critical value arising from feedback-induced gradient
force fluctuations.
