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