Absolute Frequency Measurements of theHg+and Ca Optical Clock Transitions with a Femtosecond Laser

Abstract

The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg + and Ca optical standards with respect to the SI second as realized at NIST. We find the transition frequencies to be fHg = 1 064 721 609 899 143(10) Hz and fCa = 455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg + and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of |(∂fCa/∂t)/fCa| ≤ 8 × 10 −14 yr −1 , and |(∂fHg/∂t)/fHg| ≤ 30 × 10 −14 yr −1 .Optical standards based on a single ion or a collection of laser-cooled atoms are emerging as the most stable and accurate frequency sources of any sort [1,2,3,4,5]. However, because of their high frequencies (∼ 500 THz), it has proven difficult to count cycles as required for building an optical clock and comparing to the cesium microwave standard. Only recently, a reliable and convenient optical clockwork fast enough to count optical oscillations has been realized [6,7,8]. Here, we report an optical clockwork based on a single femtosecond laser that phase coherently divides down the visible radiation of the Hg + and Ca optical frequency standards to a countable radio frequency. By this means we determine the absolute frequencies of these optical transitions with unparalleled precision in terms of the SI second as realized at NIST [9]. Indeed, for the Hg + standard, the statistical uncertainty in the measurement is essentially limited by our knowledge of the SI second at ∼ 2 × 10 −15 . The high precision and high demonstrated stability of the standards [1,4] combined with the straightforward femtosecond-laser-based clockwork suggest Hg + and Ca as excellent references for future all-optical clocks. Additionally, the comparison of atomic frequencies over time provides constraints on the possible time variation of fundamental constants. When combined with previous measurements, the current level of precision allows us to place the tightest constraint yet on the possible variation of optical frequencies with respect to the cesium standard.The Hg + and Ca systems have recently been described elsewhere [1,4,10,11], so we summarize only the basic features. The heart of the mercury optical frequency standard is a single, laser-cooled 199 Hg + ion that is stored in a cryogenic, radio frequency spherical Paul trap. The 2 S 1/2 (F = 0, M F = 0) ↔ 2 D 5/2 (F = 2, M F = 0) electric-quadrupole transition at 282 nm [ Fig. 1(a)] provides the reference for the optical standard [1]. We lock the frequency-doubled output of a well-stabilized 563 nm dye laser to the center of the quadrupole resonance by irradiating the Hg + ion alternately at two frequencies near the maximum slope of the resonance signal and on opposite sides of its center. Transitions to the metastable 2 D 5/2 state are detected with near unit ...

Optical frequency standards based on mercury and aluminum ions

“…In fact there is a large shift of the g factor of the 3 P 0 state compared to that of the 1 S 0 state that has recently been measured. 37 It was found that g( 3 P 0 ) = -0.001 976 86(21) and g( 1 S 0 ) = -0.000 792 48 (14), where the g factors are defined in terms of the Bohr magneton, and the numbers in parentheses are the uncertainties in units of the least significant digits. The shift of g( 3 P 0 ) relative to g( 1 S 0 ) is due to the hyperfine interaction mixing the 3 P 0 with other other J states, mainly 3s3p 3 P 1 .…”

Making optical atomic clocks more stable with 10−16-level laser stabilization

“…In neutral atom systems, the Dick limit is usually well above fundamental limits such as quantum projection noise [6] and often corresponds closely with experimentally observed clock instability (e.g. [1,7,8]). Improving LO stability directly reduces the Dick effect both by reducing the frequency noise that is aliased and by enabling longer atomic probing, which reduces the fractional 'dead' time between consecutive probe cycles.…”

“…This makes them strong candidates for reaching measurement instability ≤ 10 −17 in 1 s. However, this stability remains far from realized. In a seminal research effort in 2001, two optical atomic clocks at NIST were directly compared with a frequency comb [1]. The instability of these clocks was shown to be at record levels, ∼ 4 × 10 −15 / √ τ (for measurement time τ ).…”

Ultrashort Laser Pulses Applications

“…In some specially designed resonators it is nowadays possible to generate octave-spanning spectra that support pulses shorter than 5 fs (Ell et al, 2001), and these ultra-broadband pulses are used to synthesize optical combs (Holzwarth et al, 2000;Ye & Cundiff, 2005). These optical combs are frequency synthesizers with uncertainties bellow 10 -15 that are being used as time standards replacing atomic clocks (Takamoto et al, 2005), and to absolutely measure optical frequencies (Reichert et al, 1999;Udem et al, 2001). These combs are also used to stabilize the phase between the pulse carrier frequency and its envelope to a few milirads, corresponding to tens of attoseconds (Telle et al, 1999).…”