  We report the experimental evidence of the ac Josephson effect in a
transition edge sensor (TES) operating in a frequency domain multiplexer and
biased by ac voltage at MHz frequencies. The effect is observed by measuring
the non-linear impedance of the sensor. The TES is treated as a weakly linked
superconducting system and within the resistively shunted junction model
framework. We provide a full theoretical explanation of the results by finding
the analytic solution of the non-inertial Langevian equation of the system and
calculating the non-linear response of the detector to a large ac bias current
in the presence of noise.
