Mass spectrometry is one of the most important, essential and basic techniques in modern science. This is because the mass of a fundamental particle is a fundamental property of the particle itself, or, in a composite quantum mechanical system such as an atom, the mass is the sum of the masses of all its building blocks minus the binding energy between those constituents. The binding energy reflects all physical forces acting in such a quantum system.The most-advanced instrument for high-accuracy mass determinations is the Penning trap using the fundamental techniques of cooling and storing. The most highly developed Penning trap presently at hand needs still a drastic improvement and ground-breaking ideas in order to achieve the two scientific goals of the present grant application: (i), determination of the Q-value of the decay 187Re to 187Os with an accuracy of delta_m/m = 10^(-11) as required for the MARE I campaign aiming at a determination of the mass of the electron antineutrino via a very careful determination and analysis of the beta spectrum; (ii), measurement of the masses of superheavy nuclei (Z less or equal to 118) produced by hot fusion process enabling a clear assignment of the proton number to the different isotopes (and by this also the naming of the elements discovered by hot fusion) and making possible tests of state-of-the-art nuclear theories.A novel method, called quantum sensor, is proposed to measure the mass of a single ion with ultimate accuracy and unprecedented sensitivity while it is stored and cooled in a trap. The new device consists of a single calcium ion as sensor, which is laser-cooled to mK temperatures and stored in a trap connected to the trap for the ion under study by a common endcap. The motion of the ion under investigation is coupled to the sensor ion by the image current induced in the common endcap and observed through its fluorescence light. In this way the detection of phonons is upgraded to a detection of photons.