# Femtosecond frequency comb measurement of absolute frequencies and hyperfine coupling constants in cesium vapor 

Jason E. Stalnaker $^{∗}$, 1, 2 Vela Mbele $^{†}$, 2, 3 Vladislav Gerginov $^{‡}$, 2 Tara M. Fortier, 2 Scott A. Diddams, 2 Leo Hollberg $^{§}$, 2 and Carol E. Tanner 4 

$^{1}$Department of Physics and Astronomy, Oberlin College, 110 N. Professor St., Oberlin, OH 44074 

$^{2}$Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway MS 847, Boulder CO 80305 

$^{3}$School of Physics, University of Witwatersrand, Private Bag 3, WITS, 2050, RSA 

$^{4}$Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556-5670 

(Dated: November 5, 2018) 

We report measurements of absolute transition frequencies and hyperfine coupling constants for the 8S 1 / 2 , 9S 1 / 2 , 7D 3 / 2 , and 7D 5 / 2 states in $^{133}$Cs vapor. The stepwise excitation through either the 6P 1 / 2 or 6P 3 / 2 intermediate state is performed directly with broadband laser light from a stabilized femtosecond laser optical-frequency comb. The laser beam is split, counter-propagated and focused into a room-temperature Cs vapor cell. The repetition rate of the frequency comb is scanned and we detect the fluorescence on the 7P 1 / 2 , 3 / 2 → 6S 1 / 2 branches of the decay of the excited states. The excitations to the different states are isolated by the introduction of narrow-bandwidth interference filters in the laser beam paths. Using a nonlinear least-squares method we find measurements of transition frequencies and hyperfine coupling constants that are in agreement with other recent measurements for the 8S state and provide improvement by two orders of magnitude over previously published results for the 9S and 7D states. 

The basic ideas of using repetitive pulses and mode- locked lasers for high-resolution precision spectroscopy were originally developed in the 1970’s, with particular focus on Doppler-free two-photon transitions [1–6]. The advent of fully stabilized optical frequency combs [7, 8] in 2000 renewed interest in many spectroscopic applications of mode-locked lasers (for a review see Ref. [9]). In many instances the use of direct frequency-comb spectroscopy (DFCS) offers many advantages over spectroscopy done with cw lasers. In particular, the spectral versatility pro- vided by modern frequency combs allows the simultane- ous study of multiple atomic transitions with a single experimental setup. Additionally, DFCS allows for a rel- atively simple determination of the absolute frequency by providing a direct link to the S.I. second. In this work we exploit this versatility to study multiple transitions in cesium (Cs). 

Precision spectroscopy of Cs plays an important role in atomic and fundamental physics, including measure- ments of atomic parity violation [10–12], searches for the permanent electric dipole moment of an electron [13, 14], photon recoil measurements that help determine the fine structure constant [15, 16], measurements of the distri- 

PACS numbers: 42.62.Fi, 42.62.Eh, 32.30.-r, 32.10.Fn 

## I. INTRODUCTION 

bution of nuclear charge and magnetization [17], and nu- merous applications in laser cooling, Bose-Einstein con- densation [18], atomic clocks [19], and magnetometers [20]. 

The present work focuses on measuring multiple tran- sition frequencies and the hyperfine structure of select low-lying states in cesium via two-photon excitation. The relatively simple experimental setup uses a room- temperature Cs vapor cell and a self-referenced optical frequency comb to excite Doppler-free two photon tran- sitions from the Cs ground state to the 8S$_{1}$$_{/}$$_{2}$ , 9S$_{1}$$_{/}$$_{2}$ , 7D$_{3}$$_{/}$$_{2}$ , and 7D$_{5}$$_{/}$$_{2}$ states. Our results are consistent with previous measurements for the well-studied 8S$_{1}$$_{/}$$_{2}$ state [21, 22] and provide significantly reduced uncertainties for the 9S$_{1}$$_{/}$$_{2}$ , 7D$_{3}$$_{/}$$_{2}$ , and 7D$_{5}$$_{/}$$_{2}$ states [23]. 

This paper is structured as follows: Section II contains a description of our experimental system and measure- ments. In Section III we examine the features of the flu- orescence spectra and discuss the theoretical model used to describe the results. Section IV describes the analy- sis of the two-photon transitions and the recipe used in extracting the transition energies. This section also in- cludes our results and the details of the systematic effects. We conclude our work in Section V. 

The relevant Cs energy levels are shown in Fig. 1. The excitation pathways to the four states 8S$_{1}$$_{/}$$_{2}$ , 9S$_{1}$$_{/}$$_{2}$ , 7D$_{3}$$_{/}$$_{2}$ , or 7D$_{5}$$_{/}$$_{2}$ proceed through a stepwise excitation through either the 6P$_{1}$$_{/}$$_{2}$ or 6P$_{3}$$_{/}$$_{2}$ states. We detect the two-photon excitation as blue fluorescence emission as the atoms decay from the 7P$_{1}$$_{/}$$_{2}$$_{,}$$_{3}$$_{/}$$_{2}$ states to the ground 

## II. EXPERIMENTAL SETUP 

