1.5 $μ$m lasers with sub 10 mHz linewidth (1702.04669v4)

Abstract: We report on two ultrastable lasers each stabilized to independent silicon Fabry-P\'erot cavities operated at 124 K. The fractional frequency instability of each laser is completely determined by the fundamental thermal Brownian noise of the mirror coatings with a flicker noise floor of $4 \times 10^{-17}$ for integration times between 0.8 s and a few tens of seconds. We rigorously treat the notorious divergencies encountered with the associated flicker frequency noise and derive methods to relate this noise to observable and practically relevant linewidths and coherence times. The individual laser linewidth obtained from the phase noise spectrum or the direct beat note between the two lasers can be as small as 5 mHz at 194 THz. From the measured phase evolution between the two laser fields we derive usable phase coherence times for different applications of 11 s and 60 s.

• The paper demonstrates a breakthrough by achieving 5 mHz linewidths at 1.5 μm using cavity-stabilized silicon resonators operated at 124 K.
• It employs high-finesse dielectric mirror cavities and sophisticated phase noise mitigation to suppress thermal Brownian noise and extend phase coherence up to 55 s.
• The research integrates fiber-based optical frequency combs for precise frequency comparisons, paving the way for advancements in atomic clocks and quantum sensors.

Analysis of Ultra-Stable 1.5 $\mu$m Lasers with Sub-10 mHz Linewidth

This paper reports on a significant advancement in the field of laser stabilization, presenting two ultrastable lasers each achieving a linewidth as narrow as 5 mHz at 1.5 $\mu$m. The research focuses on cavity-stabilized systems incorporating temperature-controlled silicon Fabry-Perot resonators operated at 124 K, demonstrating remarkable coherence properties critical for high-precision applications.

Technical Accomplishments

1. Thermal Noise Limitation: The lasers' frequency stability is fundamentally limited by the thermal Brownian noise of the cavity mirror coatings. With a flicker noise floor of 4 × 10^{-17}, these systems achieve fractional frequency instability constrained by the mirror's environmental and inherent thermal factors.
2. Phase Noise Mitigation: Advanced techniques are employed to address the notorious issues associated with flicker frequency noise. The authors propose methods to practically relate these noise characteristics to measurable linewidths and coherence times, yielding usable phase coherence times between 11 s and 55 s.
3. Experimental Configuration: The lasers utilize high-reflectivity $\mathrm{Ta_2O_5/SiO_2}$ dielectric mirrors, with each cavity achieving a finesse of approximately 500,000. Their design effectively insulates them against seismic and acoustic vibrations, thereby preserving the length stability crucial for minimizing frequency deviations.
4. Frequency Measurement Techniques: Employing a fiber-based optical frequency comb, the research bridges significant frequency gaps and suppresses additional noise sources to achieve accurate frequency comparisons. This system allows the thorough evaluation of the laser's pure thermal noise characteristics across various time scales.

Implications and Future Prospects

The implications of achieving such a narrow linewidth are manifold, impacting fields such as optical atomic clocks, radar systems, and potentially facilitating advancements in atom interferometry for gravitational wave detection. This paper suggests that with further reduction in temperature or adopting advanced mirror coatings, it might be possible to lower the thermal noise limit towards the 10^{-18} range, thereby opening avenues for even finer temporal coherence and stability.

Theoretical and Practical Considerations

Practical applications will notably benefit from the improved coherence times, especially in scenarios demanding high phase coherence such as VLBI or quantum sensor calibration. The theoretical implications extend to the paper of atomic interactions and shifts attributable to the interrogation laser's stability. Furthermore, the integration of quantum enhancement technologies like spin squeezing with such stable oscillators could augment measurement precision beyond classical limits.

In conclusion, the paper provides comprehensive insights into controlling and reducing laser linewidth through meticulous experimental design and advanced noise analysis. It outlines potential trajectories for future research aimed at transcending current precision limits, which is crucial for both theoretical and practical advancements in metrology and quantum measurement science.