Imperial College London

1. Imperial College London Robust Cooling of trapped particles J. Cerrillo-Moreno, A. Retzker and M.B. Plenio (Imperial College) Olomouc Feynman Festival June 2009

2. Cold ion crystals Oxford, England: 40Ca+ Innsbruck, Austria: 40Ca+ Boulder, USA: Hg+ (mercury) Aarhus, Denmark: 40Ca+ (Blue) and 24Mg+ (Red)

3. Laser – Ion Interactions Hamiltonian: mode frequencies Rabi frequency Laser frequency

4. Carrier resonance: Red sideband: Blue sideband: Cooling: Heating: Laser – Ion Interactions Lamb-Dicke parameter Detuning of laser with respect to atomic transition relates size of ground state to wave length of light In ion trap experiments, usually

5. Doppler cooling Einstein‘s relation:

6. Aspect etal, PRL, 1988 Dark state coolingVSCPT (Velocity-Selective Coherent Population Trapping) The recoil limit: Idea: Cool to the ground state, a stationary state that is decoupled from laser light The staedy state: Delocalized state

7. EIT Cooling Broad resonance: Narrow resonance: Morigi,Eschner and Keitel PRL,85 (2004) Morigi, PRA,67 (2003)

8. Motivation EIT and Side Band Using two cooling schemes which have the same common internal dark state we could possibly cool to zero temperature

9. Ωc, η Ω Ω Stark Shift Cooling Stark Shift gate ν

10. Ωc, η Ωc, ηc Ω Ω, -η Ω Ω, η Robust Cooling - concept

11. Ω, -η Ω, η Ωc, ηc Steady state solution: Robust Cooling – steady state EIT and SS:

12. Hint=HEIT+HSS=0+a HEIT HEIT HEIT HEIT HSS≠a HEIT=0 Robust cooling – Intuition

13. Robust cooling – Intuition EIT

14. Parameter conditions The steady state is a motional dark state

15. Unitary correction Dispersive coupling Start Shift cycle

16. Robust cooling - Highlights Unitary correction

17. Robustness

18. Conclusions The steady state is a pure state Null population in leading order High cooling rate Robust to experimental fluctuations Thanks