Frequency to power conversion by an electron turnstile

Direct frequency to power conversion (FPC), to be presented here, links both quantities through a known energy, like single-electron transport relates an operation frequency $f$ to the emitted current $I$ through the electron charge $e$ as $I=ef$. FPC is a natural candidate for a power standard resorting to the most basic definition of the watt -- energy, which is traceable to Planck's constant $h$, emitted per unit of time. This time is in turn traceable to the unperturbed ground state hyperfine transition frequency of the caesium 133 atom $\Delta\nu_\mathrm{Cs}$; hence, FPC comprises a simple and elegant way to realize the watt. In this spirit, single-photon emission and detection at known rates have been proposed and experimented as radiometric standard. However, nowadays power standards are only traceable to electrical units, i.e., volt and ohm. In this letter, we demonstrate the feasibility of an alternative proposal based on solid-state direct FPC using a SINIS (S = superconductor, N = normal metal, I = insulator) single-electron transistor (SET) accurately injecting $N$ (integer) quasiparticles (qps) per cycle to both leads with discrete energies close to their superconducting gap $\Delta$, even at zero drain-source voltage. Furthermore, the bias voltage plays an important role in the distribution of the power among the two leads, allowing for an almost equal injection $N\Delta f$ to the two. We estimate that under appropriate conditions errors can be well below $1\%$.