Proton-electron mass ratio from laser spectroscopy of HD+ at the part-per-trillion level.

Recent mass measurements of light atomic nuclei in Penning traps have indicated possible inconsistencies in closely related physical constants such as the proton-electron and deuteron-proton mass ratios. These quantities also influence the predicted vibrational spectrum of the deuterated molecular hydrogen ion (HD+) in its electronic ground state. We used Doppler-free two-photon laser spectroscopy to measure the frequency of the v = 0→9 overtone transition (v, vibrational quantum number) of this spectrum with an uncertainty of 2.9 parts per trillion. By leveraging high-precision ab initio calculations, we converted our measurement to tight constraints on the proton-electron and deuteron-proton mass ratios, consistent with the most recent Penning trap determinations of these quantities. This results in a precision of 21 parts per trillion for the value of the proton-electron mass ratio.

Measurement of optical to electrical and electrical to optical delays with ps-level uncertainty.

We present a new measurement principle to determine the absolute time delay of a waveform from an optical reference plane to an electrical reference plane and vice versa. We demonstrate a method based on this principle with 2 ps uncertainty. This method can be used to perform accurate time delay determinations of optical transceivers used in fiber-optic time-dissemination equipment. As a result the time scales in optical and electrical domain can be related to each other with the same uncertainty. We expect this method will be a new breakthrough in high-accuracy time transfer and absolute calibration of time-transfer equipment.

Theoretical Hyperfine Structure of the Molecular Hydrogen Ion at the 1 ppm Level.

We revisit the mα^{6}(m/M) order corrections to the hyperfine splitting in the H_{2}^{+} ion and find a hitherto unrecognized second-order relativistic contribution associated with the vibrational motion of the nuclei. Inclusion of this correction term produces theoretical predictions which are in excellent agreement with experimental data [K. B. Jefferts, Phys. Rev. Lett. 23, 1476 (1969)], thereby concluding a nearly 50-year-long theoretical quest to explain the experimental results within their 1-ppm error. The agreement between the theory and experiment corroborates the proton structural properties as derived from the hyperfine structure of atomic hydrogen. Our work furthermore indicates that, for future improvements, a full three-body evaluation of the mα^{6}(m/M) correction term will be mandatory.

Probing QED and fundamental constants through laser spectroscopy of vibrational transitions in HD(.).

The simplest molecules in nature, molecular hydrogen ions in the form of H2(+) and HD(+), provide an important benchmark system for tests of quantum electrodynamics in complex forms of matter. Here, we report on such a test based on a frequency measurement of a vibrational overtone transition in HD(+) by laser spectroscopy. We find that the theoretical and experimental frequencies are equal to within 0.6(1.1) parts per billion, which represents the most stringent test of molecular theory so far. Our measurement not only confirms the validity of high-order quantum electrodynamics in molecules, but also enables the long predicted determination of the proton-to-electron mass ratio from a molecular system, as well as improved constraints on hypothetical fifth forces and compactified higher dimensions at the molecular scale. With the perspective of comparisons between theory and experiment at the 0.01 part-per-billion level, our work demonstrates the potential of molecular hydrogen ions as a probe of fundamental physical constants and laws.

Effect of soil temperature on optical frequency transfer through unidirectional dense-wavelength-division-multiplexing fiber-optic links.

Results of optical frequency transfer over a carrier-grade dense-wavelength-division-multiplexing (DWDM) optical fiber network are presented. The relation between soil temperature changes on a buried optical fiber and frequency changes of an optical carrier through the fiber is modeled. Soil temperatures, measured at various depths by the Royal Netherlands Meteorology Institute (KNMI) are compared with observed frequency variations through this model. A comparison of a nine-day record of optical frequency measurements through the 2×298 km fiber link with soil temperature data shows qualitative agreement. A soil temperature model is used to predict the link stability over longer periods (days-months-years). We show that optical frequency dissemination is sufficiently stable to distribute and compare, e.g., rubidium frequency standards over standard DWDM optical fiber networks using unidirectional fibers.

Laser cooling of beryllium ions using a frequency-doubled 626 nm diode laser.

We demonstrate laser cooling of trapped beryllium ions at 313 nm using a frequency-doubled extended cavity diode laser operated at 626 nm, obtained by cooling a ridge waveguide diode laser chip to -31°C. Up to 32 mW of narrowband 626 nm laser radiation is obtained. After passage through an optical isolator and beam shaping optics, 14 mW of 626 nm power remains of which 70% is coupled into an external enhancement cavity containing a nonlinear crystal for second-harmonic generation. We produce up to 35 µW of 313 nm radiation, which is subsequently used to laser cool and detect 6×10(2) beryllium ions, stored in a linear Paul trap, to a temperature of about 10 mK, as evidenced by the formation of Coulomb crystals. Our setup offers a simple and affordable alternative for Doppler cooling, optical pumping, and detection to presently used laser systems.

Widely tunable laser frequency offset lock with 30 GHz range and 5 THz offset.

We demonstrate a simple and versatile method to greatly extend the tuning range of optical frequency shifting devices, such as acousto-optic modulators (AOMs). We use this method to stabilize the frequency of a tunable narrow-band continuous-wave (CW) laser to a transmission maximum of an external Fabry-Perot interferometer (FPI) with a tunable frequency offset. This is achieved through a servo loop which contains an in-loop AOM for simple radiofrequency (RF) tuning of the optical frequency over the full 30 GHz mode-hop-free tuning range of the CW laser. By stabilizing the length of the FPI to a stabilized helium-neon (HeNe) laser (at 5 THz offset from the tunable laser) we simultaneously transfer the ~ 1 MHz absolute frequency stability of the HeNe laser to the entire 30 GHz range of the tunable laser. Thus, our method allows simple, wide-range, fast and reproducible optical frequency tuning and absolute optical frequency measurements through RF electronics, which is here demonstrated by repeatedly recording a 27-GHz-wide molecular iodine spectrum at scan rates up to 500 MHz/s. General technical aspects that determine the performance of the method are discussed in detail.

Delivering 10 Gb/s optical data with picosecond timing uncertainty over 75 km distance.

We report a method to determine propagation delays of optical 10 Gb/s data traveling through a 75 km long amplified fiber link with an uncertainty of 4 ps. The one-way propagation delay is determined by two-way exchange and cross correlation of short (< 1 ms) bursts of 10 Gb/s data, with a single-shot time resolution better than 2.5 ps. We thus achieve a novel optical communications link suited for both long-haul high-capacity data transfer and time transfer with picosecond-range uncertainty. This opens up the perspective of synchronized optical telecommunication networks allowing picosecond-range time distribution and millimeter-range positioning.

Infrared dynamic polarizability of HD+ rovibrational states.

A calculation of dynamic polarizabilities of rovibrational states with vibrational quantum number v = 0-7 and rotational quantum number J = 0,1 in the 1sσ(g) ground-state potential of HD(+) is presented. Polarizability contributions by transitions involving other 1sσ(g) rovibrational states are explicitly calculated, whereas contributions by electronic transitions are treated quasi-statically and partially derived from existing data [R. E. Moss and L. Valenzano, Mol. Phys., 2002, 100, 1527]. Our model is valid for wavelengths >4 µm and is used to assess level shifts due to the blackbody radiation (BBR) electric field encountered in experimental high-resolution laser spectroscopy of trapped HD(+) ions. Polarizabilities of 1sσ(g) rovibrational states obtained here agree with available existing accurate ab initio results. It is shown that the Stark effect due to BBR is dynamic and cannot be treated quasi-statically, as is often done in the case of atomic ions. Furthermore it is pointed out that the dynamic Stark shifts have tensorial character and depend strongly on the polarization state of the electric field. Numerical results of BBR-induced Stark shifts are presented, showing that Lamb-Dicke spectroscopy of narrow vibrational optical lines (∼10 Hz natural linewidth) in HD(+) will become affected by BBR shifts only at the 10(-16) level.

Frequency comparison of two high-accuracy Al+ optical clocks.

We have constructed an optical clock with a fractional frequency inaccuracy of 8.6x10{-18}, based on quantum logic spectroscopy of an Al+ ion. A simultaneously trapped Mg+ ion serves to sympathetically laser cool the Al+ ion and detect its quantum state. The frequency of the {1}S{0}<-->{3}P{0} clock transition is compared to that of a previously constructed Al+ optical clock with a statistical measurement uncertainty of 7.0x10{-18}. The two clocks exhibit a relative stability of 2.8x10{-15}tau{-1/2}, and a fractional frequency difference of -1.8x10{-17}, consistent with the accuracy limit of the older clock.

Observation of the 1S0-->3P0 clock transition in 27Al+.

We report, for the first time, laser spectroscopy of the 1S0-->3P0 clock transition in 27Al+. A single aluminum ion and a single beryllium ion are simultaneously confined in a linear Paul trap, coupled by their mutual Coulomb repulsion. This coupling allows the beryllium ion to sympathetically cool the aluminum ion and also enables transfer of the aluminum's electronic state to the beryllium's hyperfine state, which can be measured with high fidelity. These techniques are applied to measure the clock transition frequency nu=1,121,015,393,207,851(6) Hz. They are also used to measure the lifetime of the metastable clock state tau=20.6+/-1.4 s, the ground state 1S0 g factor gS=-0.000,792,48(14), and the excited state 3P0 g factor gP=-0.001,976,86(21), in units of the Bohr magneton.