We have developed a frequency stabilized laser system to supply light to measure atomic-scale displacements of a stage moved in real time. Each laser in the array provides enough power (~1 mW) for four Michelson interferometers whose accuracy requires a frequency stability of 20 kHz. In addition, each laser must be stable on both short and long time scales due to the real time control requirements.
The iodine-stabilized laser is the standard method of realizing the international definition of the meter in the visible and has an absolute accuracy of ~3x10-11 (12 kHz). Unfortunately, this laser is not suitable for fast measurements because its frequency is modulated by 6 MHz p-p at 8.3 kHz in order to lock to an iodine transition. In addition, it is very susceptible to optical feedback and only supplies ~100 microwatts of power.
We combine the long-term stability of the iodine-stabilized laser with the short-term stability and relative high power of sealed-cavity HeNe laser tubes by frequency-locking the sealed-cavity tubes to the iodine-stabilized laser using a digital feedback control loop. After we outfitted the sealed-cavity tubes with heaters to control their frequency by thermal expansion, we built-in two layers of thermal isolation to reduce environmental effects.
Cyclic averaging is used to remove the 6 MHz modulation by averaging an integral number (approximately 200) of complete cycles of the 8.3 kHz signal from the iodine-stabilized laser. Even after cyclic averaging, the iodine-stabilized laser must be further averaged to attain the cited accuracy of 3x10-11.
In order to determine the amount of averaging necessary, frequency deviations of the iodine-stabilized laser were measured by setting up a disequilibrated Mach-Zender interferometer in vacuum and recording the phase fluctuations. This data was time-averaged with increasing integration times and we determined that 24 ms of averaging is needed to reduce the error in the iodine-stabilized laser to between 20-30 kHz rms (Fig. 1).
To measure the quality of the frequency lock, two identical sealed-cavity lasers were independently frequency-locked to the iodine-stabilized laser. The beat frequency (offset to zero) between the iodine-stabilized laser and one sealed-cavity tube (Fig. 2a) as well as the beat between the two sealed-cavity tubes is recorded (Fig. 2b). As expected from the 24 ms integration time, the standard deviation between the iodine-stabilized laser and the sealed-cavity tube is 33 kHz while that between the two sealed-cavity tubes is 10 kHz.
The modular nature of our setup allows additional lasers to be added with minimal effort creating an array of lasers with sufficient power (1 mW) and accuracy (10 kHz) to perform atomic scale displacement measurements. These lasers have resolution better than the iodine-stabilized laser at short time scales and perform as well as the iodine-stabilized laser over longer times.
(b) Beat between two sealed-cavity tubes (sigma=10 kHz)