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Optical setup for the experiment on the thorium nuclear clock.

Single-ion optical frequency standards with 171Yb+

Optical frequency standards are based on excitation of an atomic reference transition in the optical spectral range (100 – 1000 THz). The reference is a "forbidden" transition with small natural linewidth, excited by a laser with high frequency stability. The high working frequency makes it possible to achieve a stability and accuracy that is several orders of magnitude better than that of the best caesium fountain clocks. To suppress frequency shifts due to the linear Doppler effect, it is generally necessary to localise the employed atoms or ions in a storage potential and to reduce their motion to an amplitude that is smaller than the wavelength of the excitation light.

Ions can be stored over practically unlimited times in electric or magnetic traps. Single-ion optical frequency standards typically make use of traps whose confining field is an alternating electric field in a quadrupole configuration. Such a field can be produced by simple electrode arragements (Fig. 1). To load the trap, neutral atoms are evaporated and ionised in the storage region by laser excitation or electron impact.

Fig. 1: Setup of the ion traps employed in our experiments. Left: trap
with ring and cap electrodes (ring diameter 1.3 mm). Right: trap with
"endcap" configuration, formed by a pair of concentric electrodes.

Laser cooling localises trapped ions in the minimum of the storage potential (Fig. 2). For a single trapped ion, frequency shifts of the reference transition due to interaction with the storage field can be made extraordinarily small because the field strength goes through zero at the center of the trap.

Fig. 2: Fluorescence emission (370 nm) of
5 laser cooled Yb+ ions. Blue/green/red:
high/medium/low intensity. The larger residual motion of the ions located outside the trap center makes them appear somewhat darker and more blurred than the central ion.

Our Working Group develops optical frequency standards based on a single 171Yb+ ion (Fig. 3). At variance with other presently investigated ions, 171Yb+ offers two suitable reference transitions. The properties of these transitions that are relevant for optical frequency standards are quite different: one transition is allowed for electric quadrupole interaction (E2) and has a natural linewidth of 3.1 Hz. The other transition is an electric-octupole transition (E3) with negligibly small natural linewidth. Here the width of the atomic resonance signal is determined only by the stability of the excitation laser and by the length of the excitation pulse (Fig. 4).

Fig. 3: Section of the energy level system of 171Yb+, showing the investigated reference transitions ("clock") and the cooling and repumping transitions that are driven during the cooling periods.

Fig. 4: Experimentally observed resonance signal (gray bars) and calculated line shape (red) arising from excitation of the 2S1/2(F=0) – 2F7/2(F=3) transition of a trapped 171Yb+ ion. For each setting of the laser frequency, the excitation probability was determined by averaging over 20 cooling and excitation cycles. Length of the excitation pulses: 335 ms, power: 50 µW in 40 µm beam diameter.