Probing interacting two-level systems with rare-earth ions.

Two-level systems (TLS) in amorphous materials currently limit coherence times of a number of solid-state quantum devices. Interactions between TLS become prominent below 100 mK, but the coupling mechanism and statistical properties are still unclear. Here we determine the homogeneous linewidth of ytterbium ions (Yb$ ^{3+} $) in silica glass at 10$ - $80 mK by using photon echo techniques as a probe of TLS. First, the homogeneous linewidth can be reduced by applying a magnetic field of 0.3 T. This effect is due to reduced magnetic interactions between adjacent Yb$ ^{3+} $ and between Yb$ ^{3+} $ and nuclear spins of $ ^{29} $Si. Secondly, we observe saturation of the linewidth below 50 mK to a level of $ \sim $30 kHz, which is much larger than the lifetime-limited value of 0.2 kHz, in contradiction to the model for independent TLS. We explain this effect by a model of coherently coupled TLS pairs.