Direct frequency comb spectroscopy and high-resolution coherent control

We present the first experiments demonstrating absolute frequency measurements of one- and two-photon transitions using direct frequency comb spectroscopy (DFCS). In particular we phase stabilized the inter-pulse period and optical phases of the pulses emitted from a mode-locked Ti:Sapphire laser, creating a broad-bandwidth optical frequency comb. By referencing the optical comb directly to the cesium microwave frequency standard, we were able to measure absolute transition frequencies over greater than a 50 nm bandwidth, utilizing the phase coherence between wavelengths spanning from 741 nm to 795 nm. As an initial demonstration of DFCS we studied transitions from the 5S to 5P, 5D, and 7S states in Rb. To reduce Doppler broadening the atoms were laser cooled in a magneto-optical trap. We present an overview of several systematic error sources that perturb the natural transition frequencies, magnitudes, and linewidths. These include radiation pressure from the probe beam, AC-Stark shifts, Zeeman shifts, power-broadening, and incoherent optical pumping. After careful study and suppression of these systematic error sources, we measured transition linewidths as narrow as 1.1 MHz FWHM and 10 kHz linecenter uncertainties. Our measurements of the 5S to 7S two-photon transition frequency demonstrated the ability to determine the comb mode order numbers when the initial transition frequency is not known to better than the comb mode frequency spacing. By modifying the spectral phase of the pulses we demonstrated high-resolution coherent control. Our first coherent control experiment utilized a grating based pulse stretcher/compressor to apply a large chirp to the pulses. We measured the two-photon transition rate as a function of linear frequency chirp. The results illustrate the differences between similar classic coherent experiments done with a single femtosecond pulse and ours conducted with multiple pulses. Furthermore, we show that it is possible to reduce the two-photon transition rate by tuning the comb such that the two-photon amplitudes from all comb mode pairs destructively interfere. One of the unique features of DFCS is the large bandwidth over which atomic coherence may be established. We tuned the comb frequencies to not only be two-photon resonant, but also resonant with two different intermediate states separated by 7 THz. In this experiment we demonstrate the phase sensitive excitation of a closed-loop four-level system in a diamond configuration. Using a spatial light modulator based pulse shaper, we adjusted the relative phase of the two different two-photon transition pathways. We measured a sinusoidally varying two-photon transition rate as a function of the pulse shaper phase, with a fringe visibility of up to 69%. As a final example of high-resolution coherent control, we adjusted the spectral phase of the pulses to force constructive interference between the two-photon amplitudes that arise from the many thousands of mode pairs detuned from an intermediate state. This resulted in an increase of the two-photon transition rate by approximately 250%.