H. A. Klein

Quantum Physics Exploring Gravity in the Outer Solar System: The SAGAS Project

We summarise the scientific and technological aspects of the Search for Anomalous Gravitation using Atomic Sensors (SAGAS) project, submitted to ESA in June 2007 in response to the Cosmic Vision 2015–2025 call for proposals. The proposed mission aims at flying highly sensitive atomic sensors (optical clock, cold atom accelerometer, optical link) on a Solar System escape trajectory in the 2020 to 2030 time-frame. SAGAS has numerous science objectives in fundamental physics and Solar System science, for example numerous tests of general relativity and the exploration of the Kuiper belt. The combination of highly sensitive atomic sensors and of the laser link well adapted for large distances will allow measurements with unprecedented accuracy and on scales never reached before. We present the proposed mission in some detail, with particular emphasis on the science goals and associated measurements and technologies.

Laser cooling of trapped Yb

Abstract172Yb+ ions in an rf trap have been laser cooled for the first time by driving the 2S1/2–2P1/2 transition at 369.5 nm. It was necessary to irradiate the ions with 2.438 μm infra-red radiation to depopulate the metastable 2D3/2 state. An upper limit on ion energies was determined by observing the size of the trapped cloud and corresponds to a temperature below 2 K. Cooled ion lineshapes were compared with simulations and coherence nulls were observed in the infra-red frequency scans.

Trapped ion optical frequency standards

Optical frequency standards based on narrow absorptions in laser-cooled single trapped ions have recently begun to demonstrate stabilities that are competitive with cold atom fountain microwave standards. This paper presents a short review of the wider state-of-the-art development of these single cold trapped ion frequency standards, coupled with a more detailed account of recent results achieved at National Physical Laboratory in respect of single ion systems based on 88Sr+, 87Sr+ and 171Yb+. Narrow linewidth data for the optical clock quadrupole and octupole transitions respectively at 674 nm in 88Sr+ and 467 nm in 171Yb+, are presented, together with a discussion of current systematics and future projections. The potential for optical clock operation is outlined.

Precision Measurement of the 2

The 4f 13 6s 2 2 F 7/2 –4f 14 5d 2 D 5/2 3•43 μm infrared transition in 172 Yb + has been driven for the first time and measured to be 87 360 087(4) MHz. The frequency was determined by probing a cloud of 172 Yb + ions held in a radiofrequency trap in the presence of helium buffer gas. The infrared radiation was generated by difference frequency mixing in LiNbO 3 . The frequency measurement is part of a programme to locate the 4f 14 6s 2 S 1/2 –4f 13 6s 2 2 F 7/2 467 nm ultra-narrow transition in laser-cooled Yb + .

Clearly resolved secular sidebands on the /sup 2/S/sub 1/2/-/sup 2/D/sub 5/2/ 674-nm clock transition in a single trapped Sr/sup +/ ion

A prestabilized 674-nm diode laser has been narrowed by locking it to a high-finesse ultra-low-expansion cavity and kilohertz error signals have been observed. Lamb-Dicke confinement of single laser cooled Sr/sup +/ ions in a miniature rf trap has been demonstrated and micromotion reduction achieved. RF trap sidebands have been observed on the Sr/sup + 2/S/sub 1/2/-/sup 2/D/sub 5/2/ 674 mm clock transition. The transition frequency has been measured to be (444779043.98/spl plusmn/0.12) MHz (2/spl sigma/).

Sub-kHz “clock” transition linewidths in a cold trapped 88Sr+ ion in low magnetic fields using 1092-nm polarisation switching

Abstract A small RF (Paul) trap has been developed, which allows Lamb–Dicke confinement of a single strontium ion. This paper describes the trap and the diagnostics used to verify Lamb–Dicke confinement. In particular, it is necessary to operate in a near zero magnetic field, so that the Zeeman splitting is minimised. In such low magnetic fields, the ion fluorescence at the 2 S 1/2 – 2 P 1/2 cooling wavelength at 422 nm normally falls to zero. This arises from optical pumping into some of the Zeeman sub-levels of the 2 D 3/2 state, which occurs because the laser which drives the 1092 nm transition ( 2 P 1/2 – 2 D 3/2 ) has a fixed polarisation state. However, if the polarisation state of this laser is rapidly switched, the fluorescence is recovered. A scan over the strontium ion 2 S 1/2 – 2 D 5/2 quadrupole transition shows only the carrier and sidebands corresponding to the radial and axial secular frequencies. Short range high resolution scans over a part of the carrier reveal Zeeman structure with ≤1 kHz-linewidth features.

Automatic laser control for a 88Sr+ optical frequency standard

Optical frequency standards, based on the 674 nm 2S1/2?2D5/2?transition in a single cold trapped 88Sr+?ion, are being characterized at the UK National Physical Laboratory. Routine operation is required for measurement campaigns over several days and there is also a long-term requirement for unattended operation in remote environments, such as on a satellite or at a spacecraft tracking ground station. Software algorithms have been developed which enable the automatic relocking of multiple extended cavity diode lasers to optical cavities following out-of-lock errors. Additional algorithms are used to monitor and control auxiliary distributed feedback diode lasers by means of a wavemeter. Using this control system, unattended operation for more than 60 h has been demonstrated. Preliminary results are presented giving a single-trap relative frequency stability of 2.5???10?16?at ? = 4000 s. This capability paves the way for a reliable Sr+?ion-trap-based optical standard capable of operating remotely for extended periods.

Analysis of thermal radiation in ion traps for optical frequency standards

In many of the high-precision optical frequency standards with trapped atoms or ions that are under development to date, the AC Stark shift induced by thermal radiation leads to a major contribution to the systematic uncertainty. We present an analysis of the inhomogeneous thermal environment experienced by ions in various types of ion traps. Finite element models which allow the determination of the temperature of the trap structure and the temperature of the radiation were developed for 5 ion trap designs, including operational traps at PTB and NPL and further optimized designs. Models were refined based on comparison with infrared camera measurement until an agreement of better than 10% of the measured temperature rise at critical test points was reached. The effective temperature rises of the radiation seen by the ion range from 0.8 K to 2.1 K at standard working conditions. The corresponding fractional frequency shift uncertainties resulting from the uncertainty in temperature are in the 10-18 range for optical clocks based on the Sr+ and Yb+ E2 transitions, and even lower for Yb+ E3, In+ and Al+. Issues critical for heating of the trap structure and its predictability were identified and design recommendations developed.

The NPL Rydberg Constant Experiment

We describe the characterization of the apparatus that has been constructed at the National Physical Laboratory for absolute optical frequency measurements of a number of two-photon 2S-nS,D transitions in the hydrogen atom. The use of a femtosecond optical frequency comb will enable many transitions to be studied under near-identical conditions, whereas the use of optical excitation for efficient production of the metastable 2S state will reduce ac Stark shifts. These improvements are expected to lead to significantly reduced uncertainty in the measured transition frequencies. Together with results from other experiments worldwide, this paper will contribute to an improved determination of the Rydberg constant

Observation of a Sub-10-Hz Linewidth

In this paper, a pair of diode lasers at 674 nm, locked to two independent ultralow-expansion high-finesse cavities, have been characterized by monitoring the beat frequency between them. The individual laser linewidth of 1.4 Hz for a 3-s averaging time broadened to 4 Hz at 30 s. The relative frequency stability of the beat at 1s is 2.5 10^-15. One of the lasers has been used to interrogate the ⁸⁸Sr⁺ ²Si_1/2-²D _5/2 transition at 674 nm, and a transition linewidth of 9 Hz has been observed