Quantum limited velocity readout and quantum feedback cooling of a trapped ion via electromagnetically induced transparency

Abstract

We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven $\Lambda$-system based on electromagnetically induced transparency (EIT). In the ideal limit of unit collection efficiency this provides a quantum limited measurement with minimal backaction on the atomic motion. A feedback loop, which drives the atom with a force proportional to measured signal, provides a cooling mechanism for the atomic motion. We derive the master equation which describes the feedback cooling and show that in the Lamb-Dicke limit the steady state energies are close to the ground state, limited only by the photon collection efficiency. Outside of the Lamb-Dicke regime the predicted temperatures are well below the Doppler limit.

13 pages, 6 figures

References in corpus (2)

• Optimal Unravellings for Feedback Control in Linear Quantum Systems
• Quantum Feedback Control of Atomic Motion in an Optical Cavity

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• Steady state phonon occupation of EIT cooling: higher order calculations
• Fast optical cooling of a nanomechanical cantilever by a dynamical Stark-shift gate
• Shot noise limited interferometry for measuring classical force