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Physical Review A

Laser cooling of trapped three-level ions: Designing two-level systems for sideband cooling

Irene Marzoli, J. I. Cirac, R. Blatt, P. Zoller

Published Apr 1, 1994• 125 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.49.2771

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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.
A detailed study of a robust and fast laser cooling scheme on a three level system is presented. A special laser configuration, applicable to trapped ions, atoms or cantilevers, designs a quantum interference that eliminates the blue sideband in addition to the carrier transition, thus excluding any heating process involving up to one-phonon processes. As a consequence cooling achieves vanishing phonon occupation up to first order in the Lamb-Dicke parameter expansion. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very stable under fluctuations of the physical parameters such as laser intensity or detuning, making it a viable candidate for experimental implementation. Furthermore, it is considerably faster than existing ground state cooling schemes, overcoming one of the limitations of current quantum information processing implementations. Its suitability as a cooling scheme for several ions in a trap or for a cloud of atoms in a dipole trap is shown.
We present a detailed analysis of a robust and fast laser cooling scheme [J. Cerrillo et al., Phys. Rev. Lett. 104, 043003 (2010)] on a three-level system. A special laser configuration, applicable to trapped ions, atoms, or cantilevers, designs a double-path quantum interference that eliminates the blue sideband in addition to the carrier transition, thus excluding any heating process involving up to one-phonon interactions. As a consequence, cooling achieves vanishing phonon occupation up to first order in the Lamb-Dicke parameter expansion. Underlying this scheme is a combined action of two cooling schemes which makes the proposal very flexible under constraints of the physical parameters such as laser intensity, detuning, or optical access, making it a viable candidate for experimental implementation. Furthermore, it is considerably faster than existing ground state cooling schemes. Its suitability as a cooling scheme for several ions in a trap and three-dimensional cooling is shown.
An experimental study of sideband laser cooling of trapped ions in miniature radio-frequency traps is presented. In+{\mathrm{In}}^{+}In+ ions are laser cooled by exciting the narrow intercombination line ${5s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5s5p{}^{3}{P}_{1}$, which shows resolved sidebands due to the vibrational motion of the ions in the trap. The influence of the micromotion at the frequency of the oscillating trapping field is investigated. Heating processes through coupling with the trapping field occur for certain regions of negative laser detuning. A method of bichromatic sideband cooling is introduced that combines efficient cooling from high temperatures with the possibility of reaching low mean vibrational quantum numbers 〈n〉<1〈n〉<1〈n〉<1 by using narrow optical transitions. This technique allows recording of high-resolution excitation spectra of the cooling transition in the Lamb-Dicke regime and thus determination of 〈n〉〈n〉〈n〉. Single ions as well as two-ion Coulomb crystals have been cooled to temperatures below $100 \ensuremath{\mu}\mathrm{K}$, and population of the ground state of motion to more than 50% over long time scales is demonstrated. These values are close to the lower limit for the detection of vibrational excitation with the present method.
We develop an expression for the final temperature achieved by laser cooling of a trapped three-level ion with the Λ configuration of states by employing an expansion in the photon momenta and degenerate perturbation theory. The special cases of low intensities or large detunings for the intermediate level are studied analytically. A cooling mechanism based on two-photon transitions with a simultaneous reorganization of the center-of-mass motion is isolated. The limit of the temperature is set either by the two-photon linewidth or by optical pumping between the long-lived states of the three-level system and may be extremely low.
An experimental and theoretical study of laser sideband cooling of a trapped ion in a radiofrequency trap is presented. The influence of the micromotion in the time-dependent potential of a Paul trap can lead to a counterintuitive situation, where sideband cooling is possible for positive values of the laser detuning, i.e., for a laser frequency that is higher than the resonance frequency of the ion at rest. The cooling rate and the capture range are calculated in a semiclassical model. Experimental results of laser sideband cooling at positive detuning are demonstrated with a single trapped In+{\mathrm{In}}^{+}In+ ion stored in a miniature Paul trap.
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.