Singly ionized lutetium is a unique atomic clock candidate in that it supports three clock transitions:

  • 1S0-to-3D1 : a highly forbidden magnetic dipole (M1) transition at 848 nm with a lifetime of approximately one week
  • 1S0-to-3D2 : a spin-forbidden electric quadrupole (E2) transition at 804 nm with a lifetime of approximately 18 seconds
  • 1S0-to-1D2 : an E2 transition at 577 nm with a lifetime of approximately 180 ms
  • The basic level structure of 176Lu+ is shown above with the clock transitions shown in brown. As the v level is so long-lived, it is used effectively as a ground state with detection and cooling carried out via scattering on the 3D1-to-3P0 transition at 646 nm (red). To facilitate preparation into the 3D1 level, optical pumping lasers at 350, 622, and 895 (blue) are used during clock operation. All the lasers needed are based on inexpensive diode lasers.

    Hyperfine Averaging

    Each of the upper clock states has an electronic angular momentum, J, which nominally results in a significant sensitivity to electromagnetic fields. To mitigate this problem our group introduced the concept of hyperfine averaging in which the laser is stabilized to the average frequency of transitions to all possible hyperfine states of a fixed mF, specifically |F , mF=0> for all possible F. This averaging technique takes full advantage of the insensitivity of mF=0 states to magnetic fields, and eliminates most of the frequency shifts from electromagnetic fields by realizing an effective J=0 level. For each upper D level, the result is a reference frequency with very low sensitivity to electromagnetic fields.

    Clock properties

    Several effects limit the performance of an optical clock and must be considered. Lu+ has several favourable atomic properties, such that all of these shift can be made extremely small. The table below gives an estimate of the systematic shifts and associated uncertanties we expect are achievable for each of the three clock transitions in Lu+.


    Both 3D2 and 1D2 transitions have Δα0(0)<0 and so micromotion shifts can be eliminated at the magic rf frequnecy, near 33 MHz and 15 MHz respectively. For the 3D1 transition, micromotion shifts will depend on the level of compensation. It is noted compensation at the level of 10-20 has been demonstrated on the similarly heavy Yb+ ion.

    Blackbody Radiation

    The 3D1 transition has the lowest BBR shift of all estabilished optical clocks. The 3D2 transition has the lowest BBR shift of clock candidates with the property Δα0(0)<0.

    Second-Order Doppler

    The 2.5 MHz linewidth of the cooling transition facilitates both effective Doopler cooling and state detection. At the Doppler temperature (TD), second order Doppler shifts are <10-19.

    Zeeman (DC)

    Hyperfine averaging eliminates most magnetic field sensitivity. Residual quadradric dependence arises from hyperfine mixing of the fine structure states.

    Zeeman (AC)

    An oscillating magnetic field at the trap RF frequnecy and transverse to the DC magnetic field results in shifts that do not cancel with hyperfine averaging. Values in the table are given for an rms transverse field of 0.65 μT, as measured for our current ion trap using Ba+.

    Probe AC-stark

    Only significant for the 3D1 transition which has ~1 week lifetime. Effective control of the probe ac-Stark shift at the <10-18 level has already been demonstrated using hyper-Ramsey and auto-balancing methods on the E3 transtion in Yb+, for which the Stark shifts are much larger than Lu+(3D1). The value in the above table is evaluated for hyper-Ramsey with a 10 ms π/2 pulse time, 100 ms free evolution time, and a 10% clock laser intensity instability.