High-Precision Frequency Comparisons and Searches for New Physics with Yb+ Optical Clocks

State-of-the-art optical atomic clocks are based on laser-cooled trapped atoms or
ions featuring forbidden transitions. A laser with sub-Hertz linewidth is frequency
stabilized to such a transition, which permits frequency measurements with relative
systematic uncertainties in the low 10-18 range. The performance of optical atomic
clocks is continuously improved by more efficient detection and suppression of external perturbations that cause shifts of the atomic transition frequency, and by
enhancing the coherent interaction between atom and laser oscillator.
In this thesis, advances of the 171Yb+ single-ion optical clocks at the national
metrology institute of Germany (PTB) are reported, realizing the frequencies of both
an electric quadrupole (E2) and an electric octupole (E3) transition. Two Yb+(E3)
clocks are compared and an agreement within their combined fractional uncertainty
of 4.2×10−18 is found. An analysis of the data for potential frequency oscillations improves the limits on Lorentz violating parameters for electrons by about two orders of
magnitude. A long-term comparison of the E3/E2 transition frequency ratio tightens
the limit on potential temporal variations of the fine structure constant α by about
a factor of 20 to (1/α)(dα/ dt) = 1.0(1.1) × 10−18/yr. Comparisons of an Yb+(E3)
clock and two caesium fountain clocks yields νE3 = 642 121 496 772 645.10(8) Hz, the
most accurate determination of an optical transition frequency to date.
Relevant atomic parameters of the E3 transition are investigated in more detail:
From the transition strength and laser intensity, the excited state natural lifetime
is determined as 1.58(7) years. For a characterization of the light shift of the E3
transition, the zero-crossing point of the scalar differential polarizability is measured
at 681.2(5) nm, which is called a magic wavelength. Precision measurements of the
electric quadrupole moments of the excited states of both the E2 and E3 transition,
Θ(2D3/2) = 1.95(1)ea20
and Θ(2F7/2) = −0.0297(5)ea20, with e the elementary
charge and a0 the Bohr radius, indicate the different electronic structure of the
excited states and the different sensitivities of the two transitions to shifts induced
by electric field gradients.
The characterization of an advanced single-ion Yb+ trap system employing goldcoated endcap electrodes is presented. A reduction of the ion motional heating rate
by a factor of 25 compared to previous trap versions is obtained, facilitating longer
interaction times between ion and laser. First frequency comparisons to the other
Yb+ clocks at PTB yield agreements at the low 10−17 level, presumably limited by
photoelectric stray fields.
Novel interrogation methods for the control or suppression of specific frequency
shifts are discussed: A coherent suppression scheme for tensorial frequency shifts is
introduced, relying on a rotation of the magnetic field vector during the dark time of a
Ramsey sequence, and a suppression of the electric quadrupole shift by a factor of 260
is demonstrated. Autobalanced Ramsey spectroscopy is presented that provides universal immunity to frequency shifts related to aberrations of the pulses in a Ramsey
sequence. Finally, excitation of an E3 transition using twisted light, i. e. with the ion
placed in the dark center of a Laguerre-Gaussian beam featuring orbital angular momentum, is demonstrated for the first time, permitting a reduction of the light shift.