From Heat Capacity to Coherence in Ultra-Narrow-Linewidth Solid-State Optical Emitters at Sub-Kelvin Temperatures

The coherence properties of optical emitters in crystals are crucial for quantum technologies and optical frequency metrology. Cooling to sub-kelvin temperatures can markedly enhance coherence, making it important to identify the parameters governing emitter and host crystal behavior in this regime. We investigate a Czochralski-grown europium-doped yttrium orthosilicate crystal, reporting measurements of its heat capacity and optical coherence. Heat capacity not only informs thermal noise limits in metrology schemes but can also reveal two-level systems (TLS) arising from crystal imperfections via a linear-in-temperature term. Below 1 K, where phonon contributions are suppressed, TLS can drive decoherence, leading to a linear broadening of the homogeneous linewidth. From our data, we place an upper bound on the TLS contribution. This, together with constant optical linewidths between 300 mK and 2 K measured via photon-echo lifetimes, is consistent with a minimal TLS effects in our sample. A low level of TLS is particularly important for the performance of optical quantum devices based on doped crystals, since their presence could otherwise limit further improvements in coherence at sub-kelvin temperatures.