Spin-motion coupling in atoms

Cooling to motional ground statesand

Quantum logic spectroscopy

Ingredients

a)ˆcos(0 txkEE

k

t

a)ˆcos(0 txkEE

k

kmotionmotion ,, kmotionmotion ,,

a)ˆcos(0 txkEE

k

)ˆcos(ˆˆ 0 txkEE

)ˆcos()ˆˆ(2 txk

Rotating frame titi AA ee 2 )ˆcos( txk txkitxki ee ˆˆ titi AA ee

tixiktixik AA eeee ˆˆ Rotating wave approximation

kmotionmotion ,, kmotionmotion ,,

a

xikxik ee ˆˆ

a)ˆcos(0 txkEE

k

t

kHz '10 srecoil

MHz 1-kHz 100t

A nn ,,

)ˆcos(0 txkEE

k

tA

a

1,, nn

1,, nn

t

)ˆcos(0 txkEE

k

tA

a

1,, nn

1,, nn

a)ˆcos(0 txkEE

k

t

11ˆ† nnna

1ˆ nnna

aaxx ˆˆˆ †0

tmx

20

tixiktixik AA eeeeH ˆˆint

xike xik ˆ1ˆ Another rotating frame titi tt eaeaikx ˆˆ1 †0

tititi

tititi

Att

Att

eeaeai

eeaeaiH

ˆˆ1

ˆˆ1

†

†

int

1 ,0 kx

tititi

tititi

tAtAA

tAtAA

eaieaie

eaieaieH

ˆˆ

ˆˆ

†

†

int

tixiktixik AA eeeeH ˆˆint

xike xik ˆ1ˆ Another rotating frame titi tt eaeaikx ˆˆ1 †0

1 ,0 kx

A

intH Carrier interaction

tititi

tititi

Att

Att

eeaeai

eeaeaiH

ˆˆ1

ˆˆ1

†

†

int

tititi

tititi

tAtAA

tAtAA

eaieaie

eaieaieH

ˆˆ

ˆˆ

†

†

int

tixiktixik AA eeeeH ˆˆint

xike xik ˆ1ˆ Another rotating frame titi tt eaeaikx ˆˆ1 †0

tititi

tititi

Att

Att

eeaeai

eeaeaiH

ˆˆ1

ˆˆ1

†

†

int

1 ,0 kx

tA

†int ˆˆ aaiH Red sideband interaction

1,,,1,int nnnnnniH 1,,,1,int nnnnniH Interaction strengthgiven by n

tititi

tititi

tAtAA

tAtAA

eaieaie

eaieaieH

ˆˆ

ˆˆ

†

†

int

tixiktixik AA eeeeH ˆˆint

xike xik ˆ1ˆ Another rotating frame titi tt eaeaikx ˆˆ1 †0

tititi

tititi

Att

Att

eeaeai

eeaeaiH

ˆˆ1

ˆˆ1

†

†

int

1 ,0 kx

tA

aaiH ˆˆ†int Blue sideband interaction

1,,,1,int nnnnnniH 1,,,1,1int nnnnniH Interaction strengthgiven by 1n

Resolved sideband coolingStep 1: Doppler cool

2Dopp

E

tDopp

t

E

2

MHz 52/

MHz 202/

Ion cooled to ground state: PRL 75, 4011 (1995)

Neutral atom cooled to ground state: PRX 2, 041014(2012)

Resolved sideband coolingStep 1: Doppler cool

Step 2: Pump to

2S1/2

2P1/2

370 nm

|

|

/2g p = 20 MHz

F=1

F=0

F=1

F=0

Ion cooled to ground state: PRL 75, 4011 (1995)

Neutral atom cooled to ground state: PRX 2, 041014(2012)

GHz 6.12A

Resolved sideband coolingStep 1: Doppler cool

Step 2: Pump to 2P1/2

/2g p = 20 MHzF=1

F=0

Ion cooled to ground state: PRL 75, 4011 (1995)

Neutral atom cooled to ground state: PRX 2, 041014(2012)

Step 3: Apply red sideband

tA

kk

1,, nn

Resolved sideband coolingStep 1: Doppler cool

Step 2: Pump to 2P1/2

/2g p = 20 MHzF=1

F=0

Ion cooled to ground state: PRL 75, 4011 (1995)

Neutral atom cooled to ground state: PRX 2, 041014(2012)

Step 3: Apply red sideband

tA

Step 4: Pump to

1,1,, nnn

Resolved sideband coolingStep 1: Doppler cool

Step 2: Pump to 2P1/2

/2g p = 20 MHzF=1

F=0

Ion cooled to ground state: PRL 75, 4011 (1995)

Neutral atom cooled to ground state: PRX 2, 041014(2012)

Step 3: Apply red sideband

tA

Step 4: Pump to

etc

Finish in !0, n

… How to check?

Measuring phonon number

Red sideband interaction strength given by n

Blue sideband interaction strength given by 1n

Ion cooled to ground state: PRL 75, 4011 (1995)

Neutral atom cooled to ground state: PRX 2, 041014(2012)

Assume thermal state with mean phonon number n

Probe red, blue sidebands for same duration

1n

n

P

Pblueex

redex

and spin state

Measuring phonon number

Ion cooled to ground state: PRL 75, 4011 (1995)

Neutral atom cooled to ground state: PRX 2, 041014(2012)

Assume thermal state with mean phonon number n

1n

n

P

Pblueex

redex

and spin state

Before:

5.0nasymmetry 1/3

After: 014.0nasymmetry 1/67

Quantum logic spectroscopyMotivation: Probe a “clock” transition when you don’t have a cycling transition

Spectroscopy ionLogic ion

Science 309, 749 (2005)

Quantum logic spectroscopyMotivation: Probe a “clock” transition when you don’t have a cycling transition

Spectroscopy ionLogic ion

Science 309, 749 (2005)

Quantum logic spectroscopy

Science 309, 749 (2005)

Step 1: Initialization n=1n=0

n=1n=0

Be+Al+

mAlBe0

Quantum logic spectroscopy

Science 309, 749 (2005)

Step 1: Initialization

mAlAlBemAlBe

00

n=1n=0

n=1n=0

Be+Al+

Step 2: Interrogate clock transition

mAlBe0

Quantum logic spectroscopy

Science 309, 749 (2005)

Step 1: Initialization

mAlAlBemAlBe

00

n=1n=0

n=1n=0

Be+Al+

Step 2: Interrogate clock transition

mAlBe0

Step 3: Drive red sideband on Al

mmAlBemAlAlBe

100

Quantum logic spectroscopy

Science 309, 749 (2005)

Step 1: Initialization

mAlAlBemAlBe

00

n=1n=0

n=1n=0

Be+Al+

Step 2: Interrogate clock transition

mAlBe0

Step 3: Drive red sideband on Al

mmAlBemAlAlBe

100

Step 4: Drive red sideband on Be

mAlBeBemmAlBe

010

Step 5: Read out Be

Quantum logic spectroscopy

Science 309, 749 (2005)

n=1n=0

n=1n=0

Be+Al+

Quantum logic spectroscopy: Initialization sequence

n=1n=0

mF = 1/2

mF = 1/2

mF = 3/2

mF = 3/2

Al+

mF =5/2

mF = 5/2

…

- Carrier transition with 0 Fm

Quantum logic spectroscopy: Initialization sequence

n=1n=0

mF = 1/2

mF = 1/2

mF = 3/2

mF = 3/2

Al+

mF =5/2

mF = 5/2

…

- Carrier transition with 0 Fm

- Red sideband transition with 1 Fm

Quantum logic spectroscopy: Initialization sequence

n=1n=0

mF = 1/2

mF = 1/2

mF = 3/2

mF = 3/2

Al+

mF =5/2

mF = 5/2

…

- Carrier transition with 0 Fm

- Red sideband transition with 1 Fm

- Laser cool the motional mode (with Be)

Quantum logic spectroscopy: Initialization sequence

n=1n=0

mF = 1/2

mF = 1/2

mF = 3/2

mF = 3/2

Al+

mF =5/2

mF = 5/2

…

- Carrier transition with 0 Fm

- Red sideband transition with 1 Fm

- Laser cool the motional mode (with Be)

Other uses for spin-motion coupling

• Cooling oscillators to their ground state– Trapped ions, neutral atoms– Mesoscopic oscillators

• Making ions talk to each other– Entanglement– Spectroscopy for atomic clocks

• Quantum simulations– Magnetism in ions– Synthetic gauge fields in neutral atoms