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Using an ultrastable continuous-wave laser at 580 nm we performed spectralhole burning of Eu$^{3+}$:Y$_{2}$SiO$_{5}$ at very high spectral resolution.Essential parameters determining the usefulness as a "macroscopic" frequencyreference: linewidth, temperature sensitivity, long-term stability werecharacterized, using a H-maser stabilized frequency comb. Spectral holes withlinewidth as low as 6 kHz were observed and the upper limit of the drift of thehole frequency was determined to be on the order of 5$\pm$3 mHz/s. We discussnecessary requirements for achieving ultra-high-stability in laser frequencystabilization to these spectral holes.

Spectrally narrow, long-term stable optical frequency reference based on a Eu$^{3+}$:Y$_{2}$SiO$_{5}$ crystal at cryogenic temperature