First-order thermal insensitivity of the frequency of a narrow spectral hole in a crystal

The possibility of generating a narrow spectral hole in a rare-earth doped crystal opens the gateway to a variety of applications, one of which is the realization of an ultrastable laser. As this is achieved by locking in a prestabilized laser to the narrow hole, a prerequisite is the elimination of frequency fluctuations of the spectral hole. One potential source of such fluctuations can arise from temperature instabilities. However, when the crystal is surrounded by a buffer gas subject to the same temperature as the crystal, the effect of temperature-induced pressure changes may be used to counterbalance the direct effect of temperature fluctuations. For a particular pressure, it is indeed possible to identify a temperature for which the spectral hole resonant frequency is independent of the first-order thermal fluctuations. Here, we measure frequency shifts as a function of temperature for different values of the pressure of the surrounding buffer gas, and identify the “magic” environment within which the spectral hole is largely insensitive to temperature.

Figure 1

The thermal sensitivity of the spectral hole (crystal site 1) in a vacuum chamber. The crystal is attached to a cold copper plate using silver lacquer. The data points represent the measured frequency shift of the spectral hole at steady state when the temperature is changed and stabilized, with a starting temperature at 3.15 K. The statistical error bars (for both temperature and frequency) are of the size of the data markers, and thus appear invisible. The dashed line is the fitting of the data with a quadratic model.

Figure 2

Typical temperature fluctuations (Allan deviation) as a function of averaging (integration) time. The circles show the free running temperature, and the triangles show the stabilized temperature (as measured by the sensor used in the servo loop, since we do not currently have the necessary extra sensors for an independent out-of-loop measurement). The temperature fluctuations are on the order of hundreds of microkelvin or below for an averaging time of 1 s or longer once the servo loop is turned on.

Figure 3

The internal vacuum chamber for achieving the temperature and pressure coupled environment. A photo of the IVC which consists of a cylindrical cell, with a diameter of 52 mm, is shown in (a), in which a tube allows the injection of helium gas, forming an isotropic pressure on the crystal as illustrated in (b).

Figure 4

When temperature is varied, the spectral holes shift in frequency. Data are shown for three different initial pressures corresponding to a starting temperature of 3.4 K for crystal site 1. When the temperature is increased, the pressure (not shown) is also led to evolve (increase, in fact). Each data set is fitted using a quadratic model (dashed lines). In the middle curve, indicated by circle-shaped markers, a magic point at 3.7 K is identified, for which a first-order cancellation of temperature and pressure effects is observed. The statistical error bars (for temperature and frequency) are also included here. Since they are of the size of the data markers, they appear to be invisible.

Figure 5

The normalized FWHM of the spectral holes (with respect to the initial spectral hole) as a function of temperature. The values correspond to the measurements presented in Fig. 4.