Laser-Frequency Stabilization Based on Steady-State Spectral-Hole Burning in ${\mathrm{Eu}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$

We present and analyze a method of laser-frequency stabilization via steady-state patterns of spectral holes in ${\mathrm{Eu}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$. Three regions of spectral holes are created, spaced in frequency by the ground-state hyperfine splittings of ${{}^{151}\mathrm{Eu}}^{3+}$. The absorption pattern is shown not to degrade after days of laser-frequency stabilization. An optical frequency comparison of a laser locked to such a steady-state spectral-hole pattern with an independent cavity-stabilized laser and a Yb optical lattice clock demonstrates a spectral-hole fractional frequency instability of $1.0\times {10}^{-15}{\tau }^{-1/2}$ that averages to $8.5_{-1.8}^{+4.8}\times {10}^{-17}$ at $\tau =73\mathrm{s}$. Residual amplitude modulation at the frequency of the rf drive applied to the fiber-coupled electro-optic modulator is reduced to less than $1\times {10}^{-6}$ fractional amplitude modulation at $\tau >1\mathrm{s}$ by an active servo. The contribution of residual amplitude modulation to the laser-frequency instability is further reduced by digital division of the transmission and incident photodetector signals to less than $1\times {10}^{-16}$ at $\tau >1\mathrm{s}$.

Figure 1

Absorption of a steady-state spectral-hole pattern with three regions of spectral holes. The left-hand inset shows a level diagram of ${{}^{151}\mathrm{Eu}}^{3+}$ positioned at crystallographic site 1. The right-hand inset shows the absorption (blue) and corresponding PDH error signal (red) of a subset of the center region.

Figure 2

Schematic diagram of the spectral-hole burning experiment. Solid yellow lines denote 580 nm laser propagation, and dashed red lines denote 1160 nm laser propagation. AOM, acousto-optic modulator; FEOM, fiber-coupled electro-optic modulator; DET, detector; ECDL, external cavity diode laser.

Figure 3

Pulse sequence of the interleaved probe scheme for 100% duty cycle laser-frequency stabilization. Frequency feedback from the previous probe pulse on each crystal is applied to the prestabilization cavity AOM at the times indicated by vertical arrows.

Figure 4

Frequency feedback and residual amplitude modulation servo schematic diagram. Black arrows denote electronic signal propagation, and the dashed box denotes calculations performed digitally on a field-programmable gate array (FPGA). LP, low-pass filter; HP, high-pass filter; LO, local oscillator; NF, notch filter.

Figure 5

Time evolution of a spectral hole in the absence of degradation due to probing. The top plot shows a decrease in the absorption depth (red circles, left axis) and an increase in the FWHM (blue triangles, right axis) with a fit of the width to a function $A+B(1-e^{-t/\tau })$. The bottom plot shows the area of the spectral hole normalized to the initial area. The data are fit to a three-part exponential decay.

Figure 6

Absorption (blue line) and corresponding PDH error signal (red line) of two out of a total of 603 spectral holes in a single-region spectral-hole pattern.

Figure 7

Comparison of a single-region pattern (blue squares) versus a three-region steady-state spectral-hole pattern (red circles). The top plot shows the error signal slope averaged over all of the holes in the pattern, and the bottom is the 1 s crystal versus crystal Allan deviation with linear frequency drift removed. Both are plotted with respect to the run time of the laser-frequency stabilization.

Figure 8

Fractional frequency instability of a laser locked to a steady-state pattern of spectral holes in ${\mathrm{Eu}}^{3+}:{\mathrm{Y}}_2{\mathrm{SiO}}_5$. Absolute laser-frequency instability from a three-cornered hat measurement is shown (blue squares), as well as the differential instability of a crystal versus crystal frequency comparison (triangles) where much of the technical noise is common mode. The instability of the crystal versus crystal measurement is worse at small averaging times because the duty cycle is 50%, while the absolute spectral-hole stability measurement uses feedback from both crystals to achieve 100% duty cycle. The expected frequency noise due to temperature fluctuations (dashed gray line), Doppler shifts due to motion of the pillbox (solid gray line), as well as RAM and detection noise (open red circles) are also shown.