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Physical Review A

Sideband cooling of atoms with the help of an auxiliary transition

Zhen Yi, Wen-ju Gu, Gao‐xiang Li

Published Nov 19, 2012• 13 citations
Publisher

Abstract

We propose a cooling scheme for the V-type three-level atom tightly confined in a harmonic trap. Two excited levels are coupled to the ground state by a quadrupole transition with a small dissipation rate and a dipole transition with a large dissipation rate, respectively. The quadrupole transition is strongly driven by a running-wave laser 1, which acts as the cooling channel in the Lamb-Dicke regime. The dipole one is weakly driven by another running-wave laser 2 as the auxiliary transition. Ground-state cooling with a large rate can be achieved through the appropriate choice of Rabi frequency for laser 1 and the detuning of the auxiliary transition.

DOI
10.1103/physreva.86.055401

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We propose a cooling scheme for the V-type three-level atom tightly confined in a harmonic trap. Two excited levels are coupled to the ground state by a quadrupole transition with a small dissipation rate and a dipole transition with a large dissipation rate, respectively. The quadrupole transition is strongly driven by a running-wave laser 1, which acts as the cooling channel in the Lamb-Dicke regime. The dipole one is weakly driven by another running-wave laser 2 as the auxiliary transition. Ground-state cooling with a large rate can be achieved through the appropriate choice of Rabi frequency for laser 1 and the detuning of the auxiliary transition.
Laser cooling of three-level ions of the cascade, vee, and lambda configuration is considered with simultaneous excitation on a weak and strong transition. Choosing appropriate parameters for the Rabi frequencies and the respective detunings allows one to eliminate adiabatically one of the levels. The thus designed two-level ion can acquire decay rates \ensuremath{\Gamma}' smaller than the trap frequency \ensuremath{\nu} such that sideband cooling becomes possible and accordingly allows cooling of the ion to its lowest oscillator state 〈n〉=0 in the trap. Explicit expressions for the detunings and the Rabi frequencies for sideband cooling of the effective two-level system are derived.
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.
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 study the mechanical effects of light on an atom trapped in a harmonic potential when an atomic dipole transition is driven by a laser and it is strongly coupled to a mode of an optical resonator. We investigate the cooling dynamics in the bad cavity limit, focussing on the case in which the effective transition linewidth is smaller than the trap frequency, hence when sideband cooling could be implemented. We show that quantum correlations between the mechanical actions of laser and cavity field can lead to an enhancement of the cooling efficiency with respect to sideband cooling. Such interference effects are found when the resonator losses prevail over spontaneous decay and over the rates of the coherent processes characterizing the dynamics.
We propose a ground-state cavity-mediated cooling scheme for a trapped atom, which is in the $\ensuremath{\Lambda}$ configuration and confined inside a high-finesse optical cavity, using a standing-wave cooling laser. The carrier transition can be prohibited by placing the atom at the node of the cavity field, and the blue-sideband transition can be simultaneously eliminated by exploiting quantum interference via tuning the frequency of the cooling laser. As a consequence, the ground-state cooling for the trapped atom can be achieved. Moreover, we numerically demonstrate the superiority by placing the atom at the antinode of the standing-wave cooling laser as compared with the running-wave cooling laser, and the robustness of the scheme using the standing-wave laser. Meanwhile, the cooling rate can reach the same order of magnitude as that obtained in the cavity--electromagnetically-induced-transparency cooling scheme, and the explicit expression for the final phonon number in higher order is also presented.
We study the mechanical effects of light on an atom trapped in a harmonic potential when an atomic dipole transition is driven by a laser and it is strongly coupled to a mode of an optical resonator. We investigate the cooling dynamics in the bad cavity limit, focusing on the case in which the effective transition linewidth is smaller than the trap frequency, hence when sideband cooling could be implemented. We show that quantum correlations between the mechanical actions of laser and cavity field can lead to an enhancement of the cooling efficiency with respect to sideband cooling. Such interference effects are found when the resonator losses prevail over spontaneous decay and over the rates of the coherent processes characterizing the dynamics.