Preliminary measurements of laser short-term frequency fluctuations

Abstract

Preliminary but relatively detailed measurements have been made of the short-term frequency or phase fluctuations of two short stable single-frequency 6328 Å He-Re lasers (Spectra-Physics Model 119). Both lasers were essentially free-running in a quiet stable environment, with no frequency-stabilization or temperature-control loops except for a slow AFC loop (one-half-second response time) which kept one laser frequency at a nominal 30-MHz spacing from the other by piezoelectric tuning. The random frequency fluctuations of the 30-MHz beat note between the lasers were measured in three ways: a) The power spectral density of the 30-MHz beat note (measured by slowly scanning an RF spectrum analyzer) was found to be accurately Gaussian, with a standard deviation <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sigma_{f} \approx 8.1</tex> kHz. b) The mean-square accumulated phase jitter during an interval of length τ seconds (measured by a sampling technique) was found to vary as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Delta\Phi^{2}(\tau) \approx 0.96 \times 10^{10} \tau^{2} rad^{2}</tex> over the range <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">100 \leq \tau \leq 1200</tex> us. Less accurate measurements extending up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\tau = 30\mu</tex> s indicated a slightly slower increase ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sim \tau^{4/3}</tex> ) for longer times. c) The spectral density of the instantaneous beat frequency variations (measured by scanning the video output from a 30-MHz frequency discriminator with an audio wave analyzer) was found to vary as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G_{\phi}(f) \approx 6.6 \times 10^{8}/f^{2} rad^{2}</tex> .s down to at least 50 Hz and probably lower. These results, which are all qualitatively compatible, and quantitatively in agreement to within better than a factor of two, indicate random Gaussian perturbation of the laser's instantaneous frequency by internal or environmental disturbances (plasma noise, acoustic noise, etc.) that have not yet been clearly identified. By improving these characteristics somewhat, and operating one laser at a very much lower power level in order to enhance its quantum phase fluctuations, it appears feasible to measure the ultimate quantum frequency fluctuations caused by random walk of the oscillator phase under the influence of spontaneous emission.