Large Inverse Transient Phase Response of Titanium-nitride-based Microwave Kinetic Inductance Detectors

Following optical pulses ($\lambda=405~\text{nm}$) on titanium nitride (TiN) Microwave Kinetic Inductance Detectors (MKIDs) cooled down at temperatures $T \le T_c / 20$ ($T_c \simeq 4.6~\text{K}$), we observe a large phase-response highlighting two different modes simultaneously that are nevertheless related. The first corresponds to the well-known transition of cooper-pair breaking into quasi-particles which produces a known phase response. This is immediately followed by a large inverse response lasting several hundreds of microseconds to several milliseconds depending on the temperature. We propose to model this inverse pulse as the thermal perturbation of the superconductor and interaction with two level system (TLS) that reduces the dielectric constant which in turns modify the capacitance and therefore the resonance frequency. The ratio of the TLS responding to the illumination is on the order of that of the area of the inductor to the whole resonator