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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✿ ✷✹✹ ♥♠✿ 2S1/2 →4 P1/2✿

2S1/ 2 4P ◦ 1/ 2

244.164nm D C B A 7.726eV

4D 3/ 2

441.6nm F = F = F = F =

• ddCu

1 2 1 2

1000 2000 3000 4000 5000 Cu

63

Frequency [GHz]

• 15
• 10
• 5

5 10 15 20

▲❛r❣❡ ❙♣❧✐tt✐♥❣ ✭✷✹✸✷✭✽✮ ▼❍③✮ ◆♦ ❛❝❝❡s t♦ ◗

✷✹✾ ♥♠✿ 2S1/2 →4 P3/2✿

❆❝❝❡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 ♦❞❞ ❈✉✿

F = 0 F = 1 F = 2 F = 3 F = 1 F = 2

3d104s 2S1/2 3d94s4p 4P3/2 249 nm 398 nm 3d94s(3D)5s 2D3/2 IP

• dd Cu

= ⇒ s✐① ♣❡❛❦s ❡①♣❡❝t❡❞ ❊①❛♠♣❧❡ s♣❡❝tr✉♠✿

Detuning (GHz)

5 10

• 5
• 10

Experiment Fit F=1 GS F=2 GS

63Cu

1000 2000 3000 4000

Ion Rate

❖✈❡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 A1 Fitted A2

✻✸ A1 σst❛t ss❝❛t A2 σst❛t ss❝❛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❛

✻✴✶✷

F = 1 F = 2 F = 0 F = 1 F = 2 F = 3 F = 1 F = 2

249 nm 785 nm

3d104s 2S1/2 3d94s4p 4P3/2 3d96s 2S1/2

785 nm 249 nm 398 nm

3d94s(3D)5s 2D3/2 IP

Cu

❉♦✉❜❧❡✲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❛

✼✴✶✷

ω1 ω2

❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛

✼✴✶✷

ω1 ω2

❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛

✼✴✶✷

ω1 ω2

❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛

✽✴✶✷

Detuning first step (GHz) Detuning second step (GHz)

5 10

• 5
• 10

2 4 6 8

• 2
• 4
• 6

← ← ← ←

ion rate

1 103 106 101 102 104 105 107

5 10

• 5
• 10

Experiment Fit F=1 GS F=2 GS 63Cu

1000 2000

❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛

✾✴✶✷

Detuning first step (GHz)

5

• 5
• 10

2→3 →2 1→2→1,2 2→2→1,2 1→1→1,2 2→1→1,2 1→0→1

5 10

• 5
• 10

Experiment Fit F=1 GS F=2 GS 63Cu

1000 2000 3000 4000

❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✸ ✕ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ❙♣❡❝tr❛

✶✵✴✶✷

Fitted A1 Fitted A2 Fitted A1 Fitted A2

✻✸ A1 σst❛t ss❝❛t A2 σst❛t ss❝❛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❡

✹ ✕ ❙✉♠♠❛r②

✶✶✴✶✷ ❖✤✐♥❡ ✐♦♥✐③❛t✐♦♥ s❝❤❡♠❡ ❞❡✈❡❧♦♣♠❡♥t ✐♥s♣✐r❡❞ ❞♦✉❜❧❡✲r❡s♦♥❛♥❝❡ ♠❛♣♣✐♥❣ ❇❡♥❡✜ts✿ ❉✐s❡♥t❛♥❣❧✐♥❣ ♦✈❡r❧❛♣♣✐♥❣ ❤❢s ♣❡❛❦s ❘❡❞✉❝✐♥❣ ♦❢ ✜t ♣❛r❛♠❡t❡r ❝♦rr❡❧❛t✐♦♥s ❛♥❞ ❡rr♦rs ❊♥❤❛♥❝✐♥❣ ♦❢ s❡❧❡❝t✐✈✐t② ▼❛❥♦r ❞✐s❛❞✈❛♥t❛❣❡✿ t✐♠❡ ❋✉❧❧ ✷❉ ♠❛♣✿ q✉❛❞r❛t✐❝ t✐♠❡ r❡q✉✐r❡❞ ❇❡tt❡r ✐❞❡❛✿ ♠❛❦❡ s❧✐❝❡s ❜❛s❡❞ ♦♥ s✐♥❣❧❡✲r❡s♦♥❛♥❝❡ ✐♥❢♦r♠❛t✐♦♥ = ⇒ ❵▼❡r❡❧②✬ ❛ ♠✉❧t✐♣❧✐❝❛t✐✈❡ ❢❛❝t♦r t✐♠❡ ✐♥❝r❡❛s❡ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✹ ✕ ❇✐❜❧✐♦❣r❛♣❤② ■

✶✷✴✶✷ ❍ ❇✉❝❦❛✱ ❏ ❑ ◆❡②✱ ❛♥❞ P ❲✐rt♥✐❦✳ ❍②♣❡r❢❡✐♥str✉❦t✉r❛♥♦♠❛❧✐❡ ✉♥❞ ❑❡r♥q✉❛❞r✉♣♦❧✇❡❝❤s❡❧✇✐r❦✉♥❣s❦♦♥st❛♥t❡♥ ❞❡s ❛♥❣❡r❡❣t❡♥ ✸❞✾ ✹s ✹♣✲❚❡r♠s ✐♥ ❈✉ ■✲❙♣❡❦tr✉♠ ✈♦♥ ❈✉ ✻✸ ✉♥❞ ❈✉✳ ❩❡✐ts❝❤r✐❢t ❢ür P❤②s✐❦✱ ✷✵✷✿✷✷✕✸✶✱ ✶✾✻✼✳ ❇ ❆ ❇✉s❤❛✇✱ ❲ ◆♦rt❡rs❤❛✉s❡r✱ ❛♥❞ ❑ ❲❡♥❞t✳ ▲✐♥❡s❤❛♣❡s ❛♥❞ ♦♣t✐❝❛❧ s❡❧❡❝t✐✈✐t② ✐♥ ❤✐❣❤✲r❡s♦❧✉t✐♦♥ ❞♦✉❜❧❡✲r❡s♦♥❛♥❝❡ ✐♦♥✐③❛t✐♦♥ ♠❛ss s♣❡❝tr♦♠❡tr②✳ ❙♣❡❝tr♦❝❤✐♠✐❝❛ ❆❝t❛ P❛rt ❇✱ ✺✹✿✸✷✶✕✸✸✷✱ ✶✾✾✾✳ ❆♠✐♥ ❍❛❦✐♠✐✳ ❉✐♦❞❡♥❧❛s❡r❜❛s✐❡rt❡ ③✉r ❙♣❡❦tr♦s❦♦♣✐❡ ✉♥❞ ❯❧tr❛s♣✉r❡♥❛♥❛❧②s❡ ❛♥ ❯r❛♥✐s♦t♦♣❡♥✳ P❤❉ t❤❡s✐s✱ ✷✵✶✸✳ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✹ ✕ ❇❛❝❦✉♣ ❙❧✐❞❡s

✶✴✸

Detuning first step (GHz)

5 10

• 5

Iopn rate (arb. units)

• 10

❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✹ ✕ ❇❛❝❦✉♣ ❙❧✐❞❡s

✷✴✸

Detuning first step (GHz) Detuning second step (GHz)

5 10

• 5
• 10

2 4 6 8

• 2
• 4
• 6

Detuning first step (GHz)

5 10

• 5

Iopn rate (arb. units)

• 10

Multimode structure

❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡

✹ ✕ ❇❛❝❦✉♣ ❙❧✐❞❡s

✸✴✸ σ2

st❛t =

1 N

i=1 1/σ2 i

. ✭✶✮ s2

s❝ =

1 1 − N

i=1 1/σ4 i,♥♦r♠ N

• i=1

(xi − µ)2/σ2

i,♥♦r♠,

✭✷✮ σs❝ = ss❝ √ N . ✭✸✮ ❉♦✉❜❧❡✲❘❡s♦♥❛♥❝❡ ■♦♥✐③❛t✐♦♥ ▼❛♣♣✐♥❣ ✕ ❘✉❜❡♥ P✳ ❞❡ ●r♦♦t❡