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state. 

The experimental set-up is shown in Fig. 2. We ex- cite the cascaded two-photon transitions using a mode- locked Ti:Sapphire laser that generates a broad optical frequency comb. The portion of the output spectrum that was used extended from 650 nm to 1000 nm, cov- ering all of the excitation transitions of interest in Fig. 1. The laser is described in detail in Ref. [24] and here we only briefly mention the information relevant for the experiment. The Kerr-lens mode-locked Ti:Sapphire ring laser produces an output spectrum consisting of discrete equally spaced coherent optical modes. The frequency of each optical mode, ν$_{n}$ , can be related to two mi- crowave frequencies, the laser repetition rate, f$_{rep}$ , and the carrier-envelope offset frequency, f$_{0}$ , by 

where n is an integer mode number ∼ 4 × 10 $^{5}$. The carrier-envelope-offset frequency is stabilized by use of an f -to-2 f interferometer, thus “self-referencing” all modes of the comb [7]. For the measurements described here f$_{0}$ was stabilized to 45 MHz. The repetition rate of the laser is ≈ 1 GHz. The repetition rate was phase-locked to a signal generator that was referenced to a hydrogen maser. With the comb stabilized in this way, the frac- tional instability of every optical frequency of the comb is ≈ 2 × 10 − 13 τ − 1 2 , where τ is the averaging period in 

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sec o nds. 

The laser beam was split by use of a 50-50 nonpolar- izin g beam-splitting cube (BS 2). The two output laser beams were linearly polarized along the same axis. The beams were filtered by use of either narrow-band inter- ference filters or a combination of long-pass and short- pass filters to select specific transition pathways. The counter-propagating beams were then focused by lenses of 25 cm focal length to a spot size of ∼ 100 µ m inside the vapor cell. Focusing the beams to a smaller waist size increases the two-photon excitation rate, but also leads to broadening of the resonances due to the finite transit- time of the atoms through the beams. The transit-time broadening for a waist of this size is about 2 MHz for room-temperature Cs atoms. The average optical inten- sities in the vapor cell were tens of W / cm 2 spread over ≈ 10 nm bandwidth, corresponding to ≈ 4000 optical frequencies. 

An evacuated Pyrex Cs vapor cell was used in the ex- periment. The cell has a diameter of 2.5 cm and is a wedged shape with an optical path length ranging from 0.5 cm - 1 cm. Windows were fused directly to the cell at an angle. The cell was carefully cleaned and filled on an oil-free vacuum system and was evacuated to a base pres- sure of ∼ 10 − 5 Pa. A small amount of Cs was introduced into the cell prior to removing it from the vacuum system. The cell temperature was varied by resistive heater wires wound around the cell. We note that we observed shifts in the transition frequencies as large as 0.5 MHz in a Cs vapor cell that was not cleaned and vacuum processed as carefully as the cell used in these measurements. 

Most of the measurements in this experiment were taken with the Cs cell temperature at 297 K, with fluctu- ations less than 1 K. Data were taken at higher temper- atures to evaluate systematic shifts arising from pressure shifts as described in Section IV B. 

A set of six coils was used to zero out the earth’s mag- 

