Production of Fock mixtures in trapped ions for motional metrology

We present a protocol to produce a class of non-thermal Fock state mixtures in trapped ions. This class of states features a clear metrological advantage with respect to the ground state, thus overcoming the standard quantum limit without the need for full sideband cooling and Fock-state preparation on a narrow electronic transition. The protocol consists in the cyclic repetition of red-sideband (RSB), measurement and preparation laser pulses. By means of the Kraus map representation of the protocol, it is possible to relate the length of the RSB pulses to the specific class of states that can be generated. With the help of numerical simulations, we analyse the parametric regime where these states can be reliably reproduced.