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

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

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

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

Doppler cooling Einstein‘s relation:

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

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

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

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

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

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

Robust cooling – Intuition H EIT H int = H EIT + H SS = 0 + aH EIT = 0 H EIT H SS ≠ a

Robust cooling – Intuition EIT

Parameter conditions The steady state is a motional dark state

Unitary correction Dispersive coupling Start Shift cycle

Robust cooling - Highlights Unitary correction

Robustness

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