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❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡ ◆✉❝❧❡❛r ▼♦♠❡♥ts ●r♦✉♣✱ ■❑❙✱ ❑❯ ▲❡✉✈❡♥ ▼❛② ✼✱ ✷✵✶✹✱ ❇❘■❳ ♠❡❡t✐♥❣

✵ ✕ ❖✉t❧✐♥❡ ✶✴✶✷ ✶ ❘❡s❡❛r❝❤ ❝♦♥t❡①t✿ ❝♦♣♣❡r ✷ ❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✸ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✹ ❙✉♠♠❛r② ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✶ ✕ ❖✉t❧✐♥❡ ✶ ❘❡s❡❛r❝❤ ❝♦♥t❡①t✿ ❝♦♣♣❡r ✷ ❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✸ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✹ ❙✉♠♠❛r② ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✶ ✕ ❘❡s❡❛r❝❤ ❝♦♥t❡①t✿ ❝♦♣♣❡r ✷✴✶✷ ❘❡s❡❛r❝❤ ❝♦♥t❡①t✿ ❈✉✿ Z = 28 + 1 = ⇒ t❡st✐♥❣ ❣r♦✉♥❞ ❢♦r t❤❡ Z = 28 s❤❡❧❧ ❝❧♦s✉r❡ 79 ❈✉✿ N = 50 = ⇒ ❞♦✉❜❧❡ s❤❡❧❧ ❝❧♦s✉r❡✦ ◆✉❝❧❡❛r ▼♦♠❡♥ts✿ ✜♥❣❡r♣r✐♥ts ❢♦r ♥✉❝❧❡❛r str✉❝t✉r❡ ❈❛♥ ❜❡ ❞❡r✐✈❡❞ ❢r♦♠ ❤②♣❡r✜♥❡ str✉❝t✉r❡ s♣❡❝tr❛ ✭❤❢s✮ ❚❡❝❤♥✐q✉❡✿ ❈❘■❙ ❂ ❈♦❧❧✐♥❡❛r ❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr♦s❝♦♣② = ⇒ ♥❡❡❞ ❛ ❣♦♦❞ ✐♦♥✐③❛t✐♦♥ s❝❤❡♠❡ ✭❡✣❝✐❡♥t ✰ ❧❛r❣❡ ❤❢s✮ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✶ ✕ ❘❡s❡❛r❝❤ ❝♦♥t❡①t✿ ❝♦♣♣❡r ✸✴✶✷ ■♦♥✐③❛t✐♦♥ s❝❤❡♠❡s✿ ✷✹✹ ♥♠✿ 2 S 1 / 2 → 4 P 1 / 2 ✿ 4 D 3/ 2 oddCu 7.726eV 5000 63 441.6nm Cu F = 2 4 P ◦ 4000 1/ 2 F = 1 3000 A B C D 244.164nm 2000 1000 2 F = 2 S 1/ 2 -15 -10 -5 0 5 10 15 20 F = 1 Frequency [GHz] ▲❛r❣❡ ❙♣❧✐tt✐♥❣ ✭✷✹✸✷✭✽✮ ▼❍③✮ � ◆♦ ❛❝❝❡s t♦ ◗ � ✷✹✾ ♥♠✿ 2 S 1 / 2 → 4 P 3 / 2 ✿ ❆❝❝❡s t♦ ◗ ▲❛r❣❡ ❙♣❧✐tt✐♥❣❄ ✭✷✶✹✵✳✵✭✷✸✮ ▼❍③❬❇◆❲✻✼❪✳ ✳ ✳ ✮ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✷ ✕ ❖✉t❧✐♥❡ ✶ ❘❡s❡❛r❝❤ ❝♦♥t❡①t✿ ❝♦♣♣❡r ✷ ❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✸ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✹ ❙✉♠♠❛r② ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✷ ✕ ❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✹✴✶✷ ❆t♦♠✐❝ ❧❡✈❡❧ s❝❤❡♠❡ ❢♦r ♦❞❞ ❈✉✿ ❊①❛♠♣❧❡ s♣❡❝tr✉♠✿ odd Cu 3d 9 4s( 3 D)5s 2 D 3/2 Experiment IP 4000 63 Cu F = 3 398 nm Fit F = 2 F=1 GS 3000 3d 9 4s4p 4 P 3/2 F = 1 F=2 GS Ion Rate F = 0 249 nm 2000 F = 2 3d 10 4s 2 S 1/2 F = 1 1000 = ⇒ s✐① ♣❡❛❦s ❡①♣❡❝t❡❞ 0 -5 5 -10 0 10 Detuning (GHz) ❖✈❡r❧❛♣♣✐♥❣ ♣❡❛❦s✿ ❞✐✣❝✉❧t t♦ ❛♥❛❧②s❡ ❈♦rr❡❧❛t❡❞ ♣❡❛❦ ✐♥t❡♥s✐t✐❡s✱ ✇✐❞t❤ ❈♦rr❡❧❛t❡❞ ❤②♣❡r✜♥❡ ♣❛r❛♠❡t❡rs ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✷ ✕ ❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✺✴✶✷ Fitted A 2 Fitted A 1 ✻✸ A 1 σ st❛t s s❝❛t A 2 σ st❛t s s❝❛t ✶❉ ✻✵✵✵ ✹✽ ✸✶✵ ✷✹✺✷ ✹✼ ✸✾✻ ▲✐t ✺✽✻✻✳✾✵✽✼✵✻✭✷✵✮ ✷✶✹✵✳✵✵✭✷✸✮ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❖✉t❧✐♥❡ ✶ ❘❡s❡❛r❝❤ ❝♦♥t❡①t✿ ❝♦♣♣❡r ✷ ❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✸ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✹ ❙✉♠♠❛r② ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✻✴✶✷ Cu 3d 9 4s( 3 D)5s 2 D 3/2 IP 785 nm F = 2 3d 9 6s 2 S 1/2 F = 1 398 nm 785 nm F = 3 F = 2 3d 9 4s4p 4 P 3/2 F = 1 F = 0 249 nm 249 nm F = 2 3d 10 4s 2 S 1/2 F = 1 ❉♦✉❜❧❡✲r❡s♦♥❛♥❝❡ ❛♣♣r♦❛❝❤ ❬❇◆❲✾✾✱ ❍❛❦✶✸❪✿ ❚❤r❡❡✲st❡♣ ✐♦♥✐③❛t✐♦♥✱ t✇♦ r❡s♦♥❛♥t st❡♣s s❝❛♥ ❜♦t❤ r❡s♦♥❛♥t st❡♣s = ⇒ s♣❡❝tr❛ ✐♥ ✷❉ ❢r❡q✉❡♥❝② s♣❛❝❡ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✼✴✶✷ ω 2 ω 1 ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✼✴✶✷ ω 2 ω 1 ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✼✴✶✷ ω 2 ω 1 ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✽✴✶✷ ← 1 8 ← 6 10 1 Detuning second step (GHz) 4 10 2 ← 2 10 3 ion rate 0 10 4 -2 10 5 ← -4 10 6 Experiment -6 63 Cu Fit 10 7 F=1 GS F=2 GS -10 -5 0 5 10 Ion Rate 2000 Detuning first step (GHz) 1000 0 -10 -5 0 5 10 Detuning (GHz) ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✾✴✶✷ 1→0→1 2→1→1,2 1→1→1,2 1→2→1,2 2→2→1,2 2→3 →2 -10 -5 0 5 Experiment 4000 Detuning first step (GHz) 63 Cu Fit F=1 GS 3000 F=2 GS Ion Rate 2000 1000 0 -10 -5 0 5 10 Detuning (GHz) ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✶✵✴✶✷ Fitted A 2 Fitted A 2 Fitted A 1 Fitted A 1 ✻✸ A 1 σ st❛t s s❝❛t A 2 σ st❛t s s❝❛t ✶❉ ✻✵✵✵ ✹✽ ✸✶✵ ✷✹✺✷ ✹✼ ✸✾✻ ✷❉ ✺✾✵✻ ✺ ✶✶✽ ✷✶✷✽ ✶ ✸✷ ▲✐t ✺✽✻✻✳✾✵✽✼✵✻✭✷✵✮ ✷✶✹✵✳✵✵✭✷✸✮ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✹ ✕ ❖✉t❧✐♥❡ ✶ ❘❡s❡❛r❝❤ ❝♦♥t❡①t✿ ❝♦♣♣❡r ✷ ❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✸ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛ ✹ ❙✉♠♠❛r② ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡