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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Population inversion for a single trapped two-level ion

Gagik Yu. Kryuchkyan, B. Kneer

Published Dec 28, 1999• 0 citations
Publisher

Abstract

We investigate the conquest of sideband laser cooling and heating due to weak broad-band noise for a harmonically trapped two-level ion. The two opposite processes from an equilibrium distribution in the ion's quantum state of motion, i.e., the ground state of motion is depopulated. As another consequence we find population inversion between different manifolds of the ion's combined quantum states of internal electronic structure and external motion. This effect only results from the quantized treatment of the ion's motion.

DOI
10.1117/12.375302

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We investigate the conquest of sideband laser cooling and heating due to weak broad-band noise for a harmonically trapped two-level ion. The two opposite processes from an equilibrium distribution in the ion's quantum state of motion, i.e., the ground state of motion is depopulated. As another consequence we find population inversion between different manifolds of the ion's combined quantum states of internal electronic structure and external motion. This effect only results from the quantized treatment of the ion's motion.
We present the results of simulations of optical sideband cooling of atomic ions in a trap with a shallow potential well. In such traps, an ion cannot be Doppler cooled near to the Lamb-Dicke regime $\mathrm{[}{\ensuremath{\eta}}^{2}(2\ensuremath{\langle}n\ensuremath{\rangle}+1)\ensuremath{\ll}1]$. Outside the Lamb-Dicke regime, the sideband cooling dynamics are altered by the existence of various Fock states with weak coupling where the cooling becomes very slow. A 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ion trapped in our Penning trap realizes such a situation; hence single stage cooling is inefficient to prepare the ion in the motional ground state. For these systems, it is necessary to study the cooling dynamics in detail and we show that it is possible to implement an optimized cooling sequence to achieve efficient ground-state cooling. We also present the simulated cooling dynamics of two ions trapped in a Penning trap, where the presence of an additional motional mode requires a complicated cooling sequence in order to cool both axial modes to the ground state simultaneously. Additionally, we demonstrate the dissipative preparation of Fock states outside the Lamb-Dicke regime by sideband heating a single ion in a Penning trap.
We have cooled a two-ion crystal to the ground-state of its collective modes of motion. Laser cooling, more specifically resolved sideband cooling, is performed sympathetically by illuminating only one of the two 40 Ca + ions in the crystal. The heating rates of the motional modes of the crystal in our linear trap have been measured, and we found them considerably smaller than those previously reported by Turchette et al (2000 Phys.Rev. A 61 063418) in the case of trapped 9 Be + ions. After the ground state is prepared, coherent quantum state manipulation of the atomic population can be performed. Up to 12 Rabi oscillations are observed, showing that many coherent manipulations can be achieved. Coherent excitation of each ion individually and ground state cooling are important tools for the realization of quantum information processing in ion traps.
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.
A single ion trapped in a harmonic potential and laser cooled at the node of a standing wave can be described in terms of the Jaynes-Cummings Hamiltonian known in quantum optics. Similar to nonclassical states of light we propose to prepare nonclassical states of the ion motion in a harmonic trap. In particular, several schemes for the preparation of Fock states are presented, and techniques for the preparation of squeezed states and coherent states of the ion motion are indicated. For an observation of these nonclassical states we propose to measure quantum collapse and revival in the population inversion of a single trapped ion.