Imperial College London
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Transcript of Imperial College London
Imperial College London
Robust Cooling of trapped particles
J. Cerrillo-Moreno, A. Retzker and M.B. Plenio
(Imperial College)
OlomoucFeynman Festival
June 2009
Cold ion crystals
Boulder, USA: Hg+ (mercury)
Aarhus, Denmark: 40Ca+ (Blue) and 24Mg+ (Red)
Innsbruck, Austria: 40Ca+
Oxford, England: 40Ca+
Hamiltonian:
Laser – Ion InteractionsLaser – Ion Interactions
( ) ( ) ( )Internal External InteractionH H H H
InternalH
( ) 0
2
( ) †Externali i
iiH a a
InteractionH x tk ( ) ˆcos( )
mode frequencies
Laser frequency
Rabi frequency
Laser – Ion InteractionsLaser – Ion Interactions
i t i t i t iH i e a e a e h c
†
int exp . .2
0
Detuning of laser with respect to atomic transition
Lamb-Dicke parameter
relates size of ground stateto wave length of light
In ion trap experiments,
usually
0 2kx k
m
1
n n , ,
0 int 2i iH e e
Carrier resonance:
int 2i iH i ae a e
Red sideband:
int 2i iH i a e ae
Blue sideband:n n , , 1
Heating:
n n , , 1
Cooling:
Doppler coolingDoppler cooling
ekT
2
g
e Laser atom
e}
e 2
disspF vRE M 2D
kT
Einstein‘s relation:
Dark state coolingVSCPT (Velocity-Selective Coherent Population
Trapping)
Dark state coolingVSCPT (Velocity-Selective Coherent Population
Trapping)
R De Broglie Photon
q kE E
m m
2 2
2 2
The recoil
limit:
g g0
ee0 e
g
RkT EAspect etal, PRL,
1988
Idea: Cool to the ground state, a stationary state that is decoupled from laser light
NA g , k g , k / 2
The staedy state:
Delocalized state
k
P( p )
k
EIT CoolingEIT Cooling
g , '' 0
Morigi,Eschner and Keitel PRL,85 (2004)
Morigi, PRA,67 (2003)
Broad resonance:
g r
rg
e
r
g r , ' Narrow resonance:
g
g
r
r
0
rr r r
r
/
2
2 2 12
4
finE
2
4
W '
)(00 2 oss
)( 2 onnan
nss
MotivationMotivation
Using two cooling schemes which have the same common internal dark state we could possibly cool to zero temperature
Using two cooling schemes which have the same common internal dark state we could possibly cool to zero temperature
)(0 oss
EIT and Side BandEIT and Side Band
2
c ss
iH a a
2
01
2
e
ee
n n 1
e
}
ΩΩ
Ωc, η
1 nn
1n n 1nν
Stark Shift gate
Stark Shift CoolingStark Shift Cooling
e
}
ΩΩ
Ωc, η
e
}
Ω, -ηΩ, η
Ωc, ηc
Robust Cooling - conceptRobust Cooling - concept
L [ H , ] Lt i
1
2
)(0 oss
)(00 2 oss
c
cc
ssoi
2
)(10 2
e
}
Ω, -ηΩ, η
Ωc, ηc
[ H , ] Li
1
02
Steady state solution:
)( 2 onnan
nss
EIT and SS:
Robust Cooling – steady stateRobust Cooling – steady state
Robust cooling – Intuition
e
e
e
e
e
1 2 3 40
HEIT
Hint = HEIT + HSS =
0 + a
ss
ss
ss
ss
HEIT
= 0
ss
HEIT
HEITHEIT
HSS ≠ a
ss
ss
Robust cooling – Intuition
e
e
10
EITEIT
10 iss
13 13 † 23 23 †EIT A x A y A x A yH b b b b
12 12 †SSH B x B yH b b
int
†0
'
' ,
EIT SS
x x y yEIT e e e e
x ySS c c c
H H H
H a a
H a a H a a
10 iss
ssssaH
c
cc
2
10 iBaHss
Parameter conditionsParameter conditions
The steady state is a motional dark state
The steady state is a motional dark state
Unitary correctionUnitary correction
20 1 ( )ss
i o
20 1 ( )ss
i o
Dispersive coupling
Dispersive coupling
2int 0 ( )o
Start Shift cycleStart Shift cycle
Robust cooling - HighlightsRobust cooling - Highlights
20n o 40n o Unitary
correction
Unitary correction
2
2W
2 4
cn
RobustnessRobustness
ConclusionsConclusions
The steady state is a pure state
The steady state is a pure state
Null population in leading order
Null population in leading order
High cooling rateHigh cooling rate
Robust to experimental fluctuations
Robust to experimental fluctuations