A Mesoscopic Spectrometer Based on the Josephson Effect**

A key element of mesoscopic topological systems, such as hybrid semiconductor-superconductor circuits, are Andreev Bound States, single quasiparticles localized at superconducting weak links. The characteristic transition energy of these states is twice the superconducting gap (90 GHz in Al). Conventional microwave techniques allow probing these states but only in a limited bandwidth. We implement a new broadband spectrometer operating at frequencies up to 180 GHz, with a 2 MHz linewidth and a minimal theoretical sensitivity of 5 kHz, based on the Josephson effect which converts a DC voltage to microwave oscillations at a frequency proportional to this voltage. Conveniently the absorption of the emitted photons is measured in the spectrometer DC current-voltage characteristic. Using a symmetrical SQUID biased at half a flux quantum allows decoupling the spectrometer from parasitic environmental modes. We demonstrate this spectroscopy technique by detecting the plasma frequency, near 100 GHz, of an RF-SQUID, fabricated both on- and off-chip, inductively coupled to the spectrometer.