Extension of the Ion Optical Clock to Multi-Ion Systems

The optical clock is a fundamental applications of the coherence of ultracold atoms. Most of the implementations with trapped ions are based on the single-ion optical clock by Dehmelt [1], and some of them have successfully achieved inaccuracies in the 10
^-18
level [2]. The idea has been extended to systems consisting of many neutral atoms by Katori with proper engineering on light shift associated with the optical lattice [3]. The enhanced stability is the great advantage obtained by multiple atoms. Extension of the single-ion system to multi-ion systems requires considerations on the inhomogeneous electric quadrupole shift originating from non-uniform electric field gradient at the location of each ion. A straightforward approach is to use ion species with null quadrupole moment such as In
⁺
, Al
⁺
[4]. We present another approach using ions with non-zero quadrupole moment. In the approach we use a planar surface trap to arrange the ions in an equally-spaced manner to vanish the inhomogeneous shift. We show that a clock with multiple Ca
⁺
ions can be operated even without a reference cavity for the clock laser, and that superradiant clock is expected when the ions are coupled to a cavity.