Table 1 Parameters used for the calculation.

From: The polarization and the fundamental sensitivity of 39K (133Cs)-85Rb-4He hybrid optical pumping spin exchange relaxation free atomic magnetometers

parameter

value

Boltzmann’s constant kB

1.38 × 10−23 J/K

Atomic mass unit m

1.660539040(20) × 10−27  kg

π

3.14

Electron spin g factor

2 × 1.001159657

Planck’s constant ħ

1.054589 × 10−34 Js

Bohr magneton μ B

9.27408 × 10−24 J/T

D 0 (K − He)41

0.35 cm 2/s

D 0 (Rb − He)42

0.5 cm 2/s

D 0 (Cs − He)43

0.291 cm 2/s

D 0 (K − N2)44

0.2 cm 2/s

D 0 (Rb − N2)42

0.19 cm 2/s

D 0 (Cs − N2)43

0.098 cm 2/s

\({\sigma }_{SE}^{K}\) 31

1.8 × 10−14  cm 2

\({\sigma }_{SE}^{Rb}\) 27

1.9 × 10−14  cm 2

\({\sigma }_{SE}^{Cs}\) 27

2.1 × 10−14  cm 2

\({\sigma }_{SD}^{K}\) 32

1 × 10−18  cm 2

\({\sigma }_{SD}^{Rb}\) 33

1.6 × 10−17  cm 2

\({\sigma }_{SD}^{Cs}\) 34

2 × 10−16  cm 2

\({\sigma }_{SE}^{K-Rb}\)

\({\sigma }_{SE}^{K}\frac{{n}_{K}}{{n}_{K}+{n}_{Rb}}+{\sigma }_{SE}^{Rb}\frac{{n}_{Rb}}{{n}_{K}+{n}_{Rb}}\)

\({\sigma }_{SE}^{Rb-K}\)

\({\sigma }_{SE}^{Rb}\frac{{n}_{Rb}}{{n}_{K}+{n}_{Rb}}+{\sigma }_{SE}^{K}\frac{{n}_{K}}{{n}_{K}+{n}_{Rb}}\)

\({\sigma }_{SE}^{Cs-Rb}\)

\({\sigma }_{SE}^{Cs}\frac{{n}_{Cs}}{{n}_{Cs}+{n}_{Rb}}+{\sigma }_{SE}^{Rb}\frac{{n}_{Rb}}{{n}_{Cs}+{n}_{Rb}}\)

\({\sigma }_{SE}^{Rb-Cs}\)

\({\sigma }_{SE}^{Rb}\frac{{n}_{Rb}}{{n}_{Cs}+{n}_{Rb}}+{\sigma }_{SE}^{Cs}\frac{{n}_{Cs}}{{n}_{Cs}+{n}_{Rb}}\)

\({\sigma }_{SE}^{{}^{87}Rb-{}^{133}Cs}\) 26

(2.3 ± 0.2) × 10−14  cm 2

\({\sigma }_{SD}^{K-Rb}\)

\({\sigma }_{SD}^{K}\frac{{n}_{K}}{{n}_{K}+{n}_{Rb}}+{\sigma }_{SD}^{Rb}\frac{{n}_{Rb}}{{n}_{K}+{n}_{Rb}}\)

\({\sigma }_{SD}^{Rb-K}\)

\({\sigma }_{SD}^{Rb}\frac{{n}_{Rb}}{{n}_{K}+{n}_{Rb}}+{\sigma }_{SD}^{K}\frac{{n}_{K}}{{n}_{K}+{n}_{Rb}}\)

\({\sigma }_{SD}^{Cs-Rb}\)

\({\sigma }_{SD}^{Cs}\frac{{n}_{Cs}}{{n}_{Cs}+{n}_{Rb}}+{\sigma }_{SD}^{Rb}\frac{{n}_{Rb}}{{n}_{Cs}+{n}_{Rb}}\)

\({\sigma }_{SD}^{Rb-Cs}\)

\({\sigma }_{SD}^{Rb}\frac{{n}_{Rb}}{{n}_{Cs}+{n}_{Rb}}+{\sigma }_{SD}^{Cs}\frac{{n}_{Cs}}{{n}_{Cs}+{n}_{Rb}}\)

\({\sigma }_{SD}^{K-He}\) 11

8 × 10−25  cm 2

\({\sigma }_{SD}^{Rb-He}\) 11

9 × 10−24  cm 2

\({\sigma }_{SD}^{Cs-He}\) 11

2.8 × 10−23  cm 2

\({\sigma }_{SD}^{K-{N}_{2}}\) 5, 35

7.9 × 10−23  cm 2

\({\sigma }_{SD}^{Rb-{N}_{2}}\) 5, 11

1 × 10−22  cm 2

\({\sigma }_{SD}^{Cs-{N}_{2}}\) 5, 11

5.5 × 10−22  cm 2

Nuclear Spin of 39K I K

1.5

Nuclear Spin of 85Rb I Rb

2.5

Nuclear Spin of 133Cs I Cs

3.5

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