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arXiv:1009.2441 · New Journal of Physics

Enhancement of laser cooling by the use of magnetic gradients

A Albrecht, Alex Retzker, C. Wunderlich, Martin Bodo Plenio

Published Mar 8, 2011• 15 citations
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Abstract

We present a laser cooling scheme for trapped ions and atoms using a combination of laser couplings and a magnetic gradient field. In a Schrieffer–Wolff transformed picture, this setup cancels the carrier and blue sideband terms completely (up to first order in the Lamb–Dicke parameter), resulting in an improved cooling behaviour compared to standard cooling schemes in the Lamb–Dicke regime (e.g. sideband cooling) and allowing cooling to the vibrational ground state. A condition for optimal cooling rates is presented and the cooling behaviour for different Lamb–Dicke parameters and spontaneous decay rates is discussed. Cooling rates of one order of magnitude less than the trapping frequency are achieved using the new cooling method. Furthermore, the scheme exhibits fast rates and low final populations, even for significant deviations from the optimal parameters, and provides good cooling rates also in the multi-particle case.

DOI
10.1088/1367-2630/13/3/033009

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We present a laser cooling scheme for trapped ions and atoms using a combination of laser couplings and a magnetic gradient field. In a Schrieffer–Wolff transformed picture, this setup cancels the carrier and blue sideband terms completely (up to first order in the Lamb–Dicke parameter), resulting in an improved cooling behaviour compared to standard cooling schemes in the Lamb–Dicke regime (e.g. sideband cooling) and allowing cooling to the vibrational ground state. A condition for optimal cooling rates is presented and the cooling behaviour for different Lamb–Dicke parameters and spontaneous decay rates is discussed. Cooling rates of one order of magnitude less than the trapping frequency are achieved using the new cooling method. Furthermore, the scheme exhibits fast rates and low final populations, even for significant deviations from the optimal parameters, and provides good cooling rates also in the multi-particle case.
We present a laser cooling scheme for trapped ions and atoms using a combination of laser couplings and a magnetic gradient field. In a Schrieffer–Wolff transformed picture, this setup cancels the carrier and blue sideband terms completely (up to first order in the Lamb–Dicke parameter), resulting in an improved cooling behaviour compared to standard cooling schemes in the Lamb–Dicke regime (e.g. sideband cooling) and allowing cooling to the vibrational ground state. A condition for optimal cooling rates is presented and the cooling behaviour for different Lamb–Dicke parameters and spontaneous decay rates is discussed. Cooling rates of one order of magnitude less than the trapping frequency are achieved using the new cooling method. Furthermore, the scheme exhibits fast rates and low final populations, even for significant deviations from the optimal parameters, and provides good cooling rates also in the multi-particle case.
Summary form only given. The preparation of quantum systems in pure states is a prerequisite for coherent control. In this context laser cooling of trapped particles to the ground state of the confining potential is a powerful tool for preparing e.g. ions for quantum logic. In particular sideband cooling has been demonstrated to be the most efficient technique, allowing to achieve more than 99% of occupation of the ground state of the trap. This cooling technique relies on two conditions: the Lamb-Dicke regime, and the strong confinement regime. This latter condition, which allows the spectral resolution of individual sidebands of the motion, is however a limitation on the cooling time. We propose a model for cooling single ions inside a trap as an alternative to sideband cooling. The scheme uses electromagnetically induced transparency (EIT) in a /spl Lambda/-level scheme, where one of the transitions is dressed by a strong laser field. For detuning of the dressing laser, the absorption spectrum for the transition shows EIT when the cooling (probe) laser has detuning. Then, by tuning the cooling laser on the dark resonance (or EIT), for a suitable set of parameters and in the Lamb-Dicke regime the atoms are cooled to the ground state by the sideband transitions which are resonantly excited. The scheme achieves efficient ground state cooling and fast cooling rates using a continuous driving, instead of a pulsed one as in Raman sideband cooling schemes. An example is illustrated, where the average vibrational number is plotted as a function of the cooling time, and the final probability of occupation is plotted as a function of the vibrational state. This method may also be applied to reduce phase errors in coherent manipulations of trapped ions for quantum logic.
We discuss a laser cooling scheme for trapped atoms or ions which is based on double electromagnetically induced transparency (EIT) and makes use of a four-level atom in tripod configuration. The additional fourth atomic state is coupled by a strong coupling laser field to the usual three-level setup of single-EIT cooling. This effectively allows to create two EIT structures in the absorption spectrum of the system to be cooled, which may be controlled by the coupling laser field parameters to cancel both the carrier- and the blue-sideband excitations. In leading order of the Lamb-Dicke expansion, this suppresses all heating processes. As a consequence, the double-EIT scheme can be used to lower the cooling limit by almost two powers of the Lamb-Dicke parameter as compared to single-EIT cooling.
We study laser cooling of two ions that are trapped in a harmonic potential and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is shown to work analogously to sideband cooling of a single ion. Outside the Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes result in a quasicontinuous energy spectrum that significantly alters the cooling dynamics. The cooling time decreases nonlinearly with the linewidth of the cooling transition, and the effect of dark states which may slow down the cooling is considerably reduced. We show that cooling to the ground state is also possible outside the Lamb-Dicke regime. We develop the model and use quantum Monte Carlo calculations for specific examples. We show that a rate equation treatment is a good approximation in all cases.
We discuss a laser cooling scheme for trapped atoms or ions which is based on double electromagnetically induced transparency (EIT) and makes use of a four-level atom in tripod configuration. The additional fourth atomic state is coupled by a strong-coupling laser field to the upper state of the usual three-level setup of single-EIT cooling. This effectively allows to create two EIT structures in the absorption spectrum of the system to be cooled, which may be controlled by the coupling laser field parameters to cancel both the carrier- and the blue-sideband excitations. In leading order of the Lamb-Dicke expansion, this suppresses all heating processes. As a consequence, the double-EIT scheme can be used to lower the cooling limit by a factor of order of the Lamb-Dicke parameter squared as compared to single-EIT cooling.