The stability of optical atomic clocks is limited by thermomechanical noise in laser-local-oscillators (LLOs). Spectral hole burning using Eu3+:Y2SiO5 has recently been identified as a means of improving LLO performance through laser frequency stabilization. A stumbling block has been the strong temperature dependence of the spectral hole frequency, which varies as temperature to the fourth power (i.e. Df ~ T4). In a recent report , the spectral hole burning crystal was immersed in helium gas at modest gauge pressure (270 Pa). The shift in frequency with temperature is positive, while the shift in frequency with pressure is negative. Thus, by enclosing the sample in a pressurized chamber, a temperature increase leads to a pressure increase, which can compensate the temperature-induced change in frequency. This clever self-compensating method significantly improves the frequency stabilization. Fig. 1 illustrates the frequency shift at numerous temperature setpoints (panel a) while panel b illustrates the frequency shift for two crystals. Without the compensation afforded by this modest pressure of 270 Pa, a 0.1 k change in temperature would result in a frequency shift of 1500 Hz. Thus, Fig. 1(b) shows that this method results in a 95% reduction in temperature-induced changes in frequency. These experiments benefited from the low-vibration environment and excellent temperature stability (see Fig. 1(c)) afforded by the Montana Instruments Cryostation.
Fig. 1. (a) Temperature set point (right abscissa and solid line) and frequency shift (left abscissa and data points) for two crystals versus time in 270 Pa of helium gas. (b) Frequency shifts for two crystals, note the quadratic temperature dependence. (c) Temperature stability of the sample chamber versus time.
 M. J. Thorpe, D. R. Leibrandt, and T. Rosenband, New Journal of Physics 15 (2013) 033006.