  The best clocks to date control the atomic motion by trapping the sample in
an optical lattice and then interrogate the atomic transition by shining on
these atoms a distinct laser of controlled frequency. In order to perform both
tasks simultaneously and with the same laser field, we propose to use instead
the levitation of a Bose-Einstein condensate through multiple-wave atomic
interferences. The levitating condensate experiences a coherent localization in
momentum and a controlled diffusion in altitude. The sample levitation is bound
to resonance conditions used either for frequency or for acceleration
measurements. The chosen vertical geometry solves the limitations imposed by
the sample free fall in previous optical clocks using also atomic
interferences. This configuration yields multiple-wave interferences enabling
levitation and enhancing the measurement sensitivity. This setup, analogous to
an atomic resonator in momentum space, constitutes an attractive alternative to
existing atomic clocks and gravimeters.
