Improving Laser Coherence

The convenient approximation of a real laser field by a Coherent State is again a relevant topic of interest, as laser spectroscopy scenarios are being developed in which remarkably long atomic lifetimes and extended interaction times (~100 s) can be enjoyed. Years ago, appropriate locking techniques were shown to allow precise locking of a laser field to a cavity, even in the milliHz domain, but lab vibrations modulated the cavity length and so the obtained optical frequency. Methods such as mechanical isolation (on a heroic scale) or active anti-vibration approaches are sufficiently productive such that, by now several groups have developed visible optical sources with ~Hz linewidths. Still, linewidths in the 100 milliHz domain have seemed very challenging -- all the margins have been used up. We discuss mounting systems for an optical reference cavity, particularly an improved one based on implementing vertical symmetry, which provides dramatic reduction in the vibration sensitivity and can yield sub-Hz linewidths on an ordinary optical table in an ordinary lab. Interesting and commanding new issues -- such as temporally-dependent spatial structure of the EO-modulated probe beam, and thermally-generated mechanical position noise -- are found to dominate the laser phase errors in the sub-Hz linewidth domain. The theoretical scaling -- and the spectral character -- of this thermal noise motion of the cavity mirror surfaces have been studied and confirmed experimentally, showing an ~1 × 10^-16 m/√(Hz) thermal noise amplitude at 1 Hz, with a 1/√f amplitude spectral density, with f being the Fourier frequency of this noise process. For effective temperature stabilization, multi-point thermal control and dual thermal shells provide stable operation near the ULE thermally-stationary point. Spectral filtering in the optical and vacuum paths is critically important to prevent ambient thermal radiation from entering the inner shell. The observed frequency drift-rate of ~0.05 Hz/s is not yet ideally stable, but it appears possible to compensate drift accurately enough to allow 1 radian coherence times to approach ~100 s -- if other problems such as the thermal noise can be adequately suppressed. Recent JILA spectra of lattice-trapped cold Sr atoms show an excellent prospect for ultrahigh resolution spectroscopy and highly stable optical atomic clocks and make us anxious to perfect improved phase-stable laser sources for the ¹S₀ - ³P₀ doubly-forbidden transition at 698 nm. These laser developments are aided by optical comb techniques, allowing useful phase comparison of several prototype stable laser sources, despite their various different wavelengths.