TABLE II.

Operating parameters and calculated collisional frequency shifts for ²⁷Al⁺, ⁴⁰Ca⁺, ⁸⁸Sr⁺, and ¹⁷¹Yb⁺ clocks. For ²⁷Al⁺, we use the parameters of and calculate the BGC shift and uncertainty specifically for the clock described in Ref. [19]. For the ⁴⁰Ca⁺, ⁸⁸Sr⁺, and ¹⁷¹Yb⁺ clocks, we use parameters similar to experimental implementations at WIPM [28,29], NRC [9,30], and PTB [8], but we do not perform a rigorous analysis of the uncertainty of the BGC shift. For all clocks, we simulate Rabi interrogation. Current ¹⁷¹Yb⁺ clocks based on the 467 nm electric-octupole (E3) transition use hyper-Ramsey [8] or autobalanced Ramsey [31] interrogation, so this calculated collision shift for ¹⁷¹Yb⁺ should be taken as a rough estimate.

	27Al+	40Ca+	88Sr+	171Yb+ E3
Trap drive frequency [MHz]	40.7	24.7	14.4	15
Secular frequencies [MHz], x direction	2.85,3.31	1.01	1.13	0.7
y direction	3.54, 3.95	1.07	1.15	0.7
z direction (axial)	1.47, 2.55	2.31	2.25	1.4
Interrogation time [ms]	150	80	100	150
Clock laser direction, $\widehat{k}$	(1/2, 1/2, $\sqrt{2}$)	(1,0, 1)/$\sqrt{2}$	(1, 1,0)/$\sqrt{2}$	(1, 1,0)/$\sqrt{2}$
BG temperature [K]	294.15 ± 2.70	300	300	300
BG pressure [nPa]	38 ± 19	30	16	6
Fractional frequency shift, Time dilation [10−19]	${-0.6}_{-0.3}^{+0.6}$	−0.9	−0.2	0.0
Phase shift [10−19]	±2.3	±13.3	±11.9	±2.5
Total [10−19]	−0.6 ± 2.4	−0.9 ± 13.3	−0.2 ± 11.9	0.0 ± 2.5