Spin-motion coupling in atoms
description
Transcript of Spin-motion coupling in atoms
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
|
|
/2 = 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
/2 = 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
/2 = 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
/2 = 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
1nn
PPblueex
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
1nn
PPblueex
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