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Theory of Laser Cooling and Spectroscopy of Harmonically Trapped Single Atoms.

Ann Laurie Wells

Published Dec 1, 1987• 0 citations
OpenAlex

Abstract

Abstract : The problem of laser cooling of a single ion or atom in a harmonic trap was considered. A simple theory of sideband cooling has been developed. In the limit that the particle's secular motion can be treated semiclassically, the theory allows the calculation of a logarithmic cooling rate either numerically or, for two special cases, analytically. The theory could be used to optimize the parameters of a cooling experiment. The spectroscopy of a single atom in the ladder configuration has been treated theoretically. A dressed atom approach was used to provide qualitative information about the system.

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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.

Physical Review A•Apr 1, 1994•125 citations
Abstract : The problem of laser cooling of a single ion or atom in a harmonic trap was considered. A simple theory of sideband cooling has been developed. In the limit that the particle's secular motion can be treated semiclassically, the theory allows the calculation of a logarithmic cooling rate either numerically or, for two special cases, analytically. The theory could be used to optimize the parameters of a cooling experiment. The spectroscopy of a single atom in the ladder configuration has been treated theoretically. A dressed atom approach was used to provide qualitative information about the system.
Laser (light-pressure) cooling of two-level ions stored in a Penning trap is treated theoretically, in the limit that the frequencies of motion of the ions are much smaller than the natural linewidth of the optical transition. Rate equations for the mean-squared amplitudes of motion are derived from a semiclassical analysis, which is confirmed by quantum-mechanical perturbation theory. Simultaneous cooling of all three modes of motion is shown to require a spatially nonuniform laser-beam profile, unlike the case of the harmonic trap. Comparison is made with recent experiments. Also, the three-dimensional harmonic trap is treated by two simple methods. One is based on the energy rate equations and the other on Langevin-type equations. Identical results are obtained by the two methods for the steady-state energies. These results are compared with the works of others.
We propose a cooling scheme for realizing single-photon sideband cooling on particles trapped in a statedependent optical potential.We develop a master rate equation from an ab initio model and find that in experimentally feasible conditions it is possible to reduce the average occupation number of the vibrational levels in one dimension by more than 90% by applying a frequency sweep on the cooling laser that sequentially cools all the motional states.Notably, this cooling scheme works also when a particle experiences a deeper trap in its internal ground state than in its excited state, a condition for which conventional single-photon sideband cooling does not work.In our analysis, we consider two cases: a two-level particle confined in an optical tweezer, and Li atoms confined in an optical lattice, and we find conditions for efficient cooling in both cases.The results from the model are confirmed by a full quantum Monte Carlo simulation of the system Hamiltonian.Our findings provide an alternative cooling scheme that can be applied in principle to any particle, e.g., atoms, molecules, or ions, confined in a state-dependent optical potential.
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.
The limitations to the achievement of low kinetic energies for laser cooling of single ions confined in electromagnetic traps are discussed. Sideband cooling of an ion in an rf (Paul) trap is reexamined including the effects of finite laser bandwidth and the energy of the rf micromotion. The micromotion is the oscillatory motion of the ion at the same frequency as the rf voltage applied to the trap electrodes. Sideband cooling of ions in a Penning trap is examined for the first time. In both cases, cooling to the zero-point energy of the ion in the trap should be possible and a method for verifying this condition is suggested. The implications for high-resolution, high-accuracy spectroscopy are investigated. Under certain conditions, the uncertainty in the second-order Doppler shift may be significantly less than 1 part in 1018{10}^{18}1018. .AE
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.