Table 1 Measured harmonic motional frequencies ωqi for the two atomic ions q = AB along direction i and their commensurability with the photonic excitation rate τ−1 = 165.35 kHz (τ = 6048 ns)

From: High-fidelity remote entanglement of trapped atoms mediated by time-bin photons

q (ion)

i (mode)

\(\frac{{\omega }_{qi}}{2\pi }\) (kHz)

\(\frac{{\omega }_{qi}\tau }{2\pi }\)

ηqi

ζqi

A

Axial

991.5

5.996

0.055

0

A

Radial 1

1157.5

7.000

0.086

0.051

A

Radial 2

1488.0

8.999

0.013

0.045

B

Axial

330.3

1.997

0.095

0

B

Radial 1

826.7

4.999

0.066

0.0067

B

Radial 2

992.0

5.999

0.073

0.077

  1. The six mode frequencies are set to be nearly integer multiples of the excitation rate, suppressing errors from residual entanglement with motion. Also shown are the Lamb-Dicke parameters ηqi and ζqi with respect to the excitation/emission wavevector difference and the wavevector of emission, respectively.