Fast and RobustLaser Cooling of

Trapped SystemsJavier Cerrillo-Moreno, Alex Retzker, Martin B.

Plenio

Obergurgl, 7th June 2010

2

Motivation

Quantum Information ProcessingQuantum SimulationQuantum OpticsLocalized quantum objectPrecision measurementsSpectroscopy

R. Blatt

3

Overview

Cooling schemes for trapped systems

Building BlocksEIT coolingStark-shift cooling

ProposalConceptMechanismFeatures

4

One-phonon processesCarrier transitionBlue side-band transitionRed side-band transition

1

2

g

e 1

0

2

0

neng

1 neng

1 neng

g

e

g

e

g

e

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1

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0€

2

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3

€

4

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5

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⊗

5

Side-band cooling

1

2

g

e 1

0

2

0g

e

g

e

Carrier TransitionBlue side-band transitionRed side-band transition

6

Dark-state cooling

1

2

g

e 1

0

2

0g

e

g

e

Carrier TransitionBlue side-band transitionRed side-band transition

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Dark-state cooling

1

2

g

e 1

0

2

0g

e

g

e

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Double Dark-state cooling ?

1

2

g

e 1

0

2

0g

e

g

e

9

Overview

Cooling schemes for trapped systems

Building BlocksEIT coolingStark-shift cooling

ProposalConceptMechanismFeatures

10

Electromagnetically-Induced Transparency EIT cooling

22

e

}

Ω, -ηΩ, η

Morigi, Eschner and Keitel PRL, 85 (2004)

11

Stark Shift cooling

2

c

e

}

ΩΩ

Ωc, η

1 nn

1n n 1n

ν

Stark Shift gate

A. Retzker, M. Plenio, New J. of Phys. 9 (2007) 279

€

− =↑ −↓

+ =↑ + ↓

Cooling schemes for trapped systems

Building BlocksEIT coolingStark-shift cooling

ProposalConceptMechanismFeatures

12

Overview

J. Cerrillo, A. Retzker, M. Plenio, Phys. Rev. Lett. 104,

043003 (2010)

13

Robust cooling – Concept

e

}

ΩaΩa

Ωb, ηb

e

}

Ωa, -ηaΩa, ηa

Ωb, ηb

J. Cerrillo, A. Retzker, M. Plenio, Phys. Rev. Lett. 104, 043003 (2010)

14

Robust cooling – Steady state

Stark Shift OREIT cooling

Stark Shift ANDEIT cooling €

ρss = ↓ −↑ ↓ −↑ ⊗ an

n

∑ n n ⎛

⎝ ⎜

⎞

⎠ ⎟+ o(η 2)

€

Ψss

= ↓ −↑ 0 + o(η ) )(00 2ρ oss

€

Ψss

= ↓ −↑ 0 − iη ↓ +↑ 1 + o(η 2)

η b

η a

=ν + 2Ωb

Ωb

e

}

Ωa, -ηaΩa, ηa

Ωb, ηb

J. Cerrillo, A. Retzker, M. Plenio, Phys. Rev. Lett. 104, 043003 (2010)

€

∂∂t

ρ = Lρ = −i H,ρ[ ] +Γ

2˜ L ρ = 0

15

Robust cooling – Mechanism

e

e

e

e

e

1 2 3 40

HEIT

Hint = HEIT + HSS = 0 + a

ssΨ

ssΨ

ssΨ

ssΨHEIT

= 0ss

Ψ

HEIT

HEITHEIT

HSS ≠ a

ssΨ

ssΨ

J. Cerrillo, A. Retzker, M. Plenio, Phys. Rev. Lett. 104, 043003 (2010)

16

Robust cooling – Features

)(0 2on

2

2

W

e

}

Ωa, -ηaΩa, ηa

Ωb, ηb

J. Cerrillo, A. Retzker, M. Plenio, Phys. Rev. Lett. 104, 043003 (2010)

Final Temperature

Cooling rate

€

b

η a

=ν + 2Ωb

ΩbImplementation

Robust cooling - Implementation

17

e

}

Ωa, -ηaΩa, ηa

Ωb, ηb

€

b

η a

=ν + 2Ωb

Ωb

=2η p

η 'A cosθ=

2

cosθ

J. Cerrillo, A. Retzker, M. Plenio, Phys. Rev. Lett. 104, 043003 (2010)

18

Robust cooling – Features

)(0 2on

€

n ∝ ΔΩb( )4

ΔΩa( )4

2

2

W

e

}

Ωa, -ηaΩa, ηa

Ωb, ηb

J. Cerrillo, A. Retzker, M. Plenio, Phys. Rev. Lett. 104, 043003 (2010)

Final Temperature

Cooling rate

Robustness

€

b

η a

=ν + 2Ωb

ΩbImplementation

19

Robust cooling – Robustness

e

}

Ωa, -ηaΩa, ηa

Ωb, ηb

J. Cerrillo, A. Retzker, M. Plenio, Phys. Rev. Lett. 104, 043003 (2010)

20

Summary

Interference of 2 cooling schemes

Steady state is a pure state

Best final T and cooling rate

Easy implementation

Experimentally robust

€

Ψss

= − 0 − iη + 1 + o(η 2)

)(0 2on

e

e

10

2

2

W

e

}

Ωa, -ηaΩa, ηa

Ωb, ηb

J. Cerrillo, A. Retzker, M. Plenio, Phys. Rev. Lett. 104, 043003 (2010)