  We theoretically show that a magnet can be stably levitated on top of a
punctured superconductor sheet in the Meissner state without applying any
external field. The trapping potential created by such induced-only
superconducting currents is characterized for magnetic spheres ranging from
tens of nanometers to tens of millimeters. Such a diamagnetically levitated
magnet is predicted to be extremely well isolated from the environment. We
therefore propose to use it as an ultrasensitive force and inertial sensor. A
magnetomechanical read-out of its displacement can be performed by using
superconducting quantum interference devices. An analysis using current
technology shows that force and acceleration sensitivities on the order of
$10^{-23}\text{N}/\sqrt{\text{Hz}}$ (for a 100 nm magnet) and
$10^{-14}g/\sqrt{\text{Hz}}$ (for a 10 mm magnet) might be within reach in a
cryogenic environment. Such unprecedented sensitivities can be used for a
variety of purposes, from designing ultra-sensitive inertial sensors for
technological applications (i.e. gravimetry, avionics, and space industry), to
scientific investigations on measuring Casimir forces of magnetic origin and
gravitational physics.
