Magnetic gradients

The laser cooling scheme using magnetic gradients is an extended sideband cooling concept for trapped ions and atoms in the Lamb-Dicke regime. Relying on interference in a three level atomic system, an elimination of heating contributions (carrier and blue sideband transitions) in lowest order in the Lamb-Dicke expansion is achieved. The significant new idea consists of the use of a magnetic gradient field beside standard laser beam interference. Magnetic gradients are already used in ion trap experiments in the context of realizing microwave couplings with significant coupling strength to the vibrational dynamics and replacing Raman transitions.

A proper choice of the magnetic gradient strength together with the phase relation between the coupling lasers allows for the lowest order heating contributions cancellation independent of the magnitude of the coupling Rabi frequencies. Moreover, fulfilling the resonance condition for the cooling transition, fast rates of the order of one magnitude less than the trapping frequency can be obtained as well as the vibrational ground state is reached in lowest order in the expansion parameter (Lamb-Dicke parameter). This outperforms the cooling behaviour of similar sideband cooling schemes working in the Lamb-Dicke regime.

The magnetic gradient cooling scheme can be extended straightforwardly to the cooling of multiple modes, i.e. to the case of several trapped particles. Albeit losing some of its efficiency for higher vibrational modes, it can be shown that the scheme is always faster than sideband cooling concepts in the Lamb-Dicke regime, which do not provide any blue sideband cancellation.

Enhancement of laser cooling by the use of magnetic gradients