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Physical Review A

Damped Rabi oscillations of a cold trapped ion

C. Di Fidio, W. Vogel

Published Aug 3, 2000• 48 citations
Publisher

Abstract

We demonstrate that the recently observed damping of Rabi oscillations of a trapped ${}^{9}{\mathrm{Be}}^{+}$ ion initially cooled to its motional ground state [Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)] is caused by quantum jumps to an auxiliary electronic state. This mechanism also predicts an asymmetric decay of the electronic-state population that is found to be in good agreement with the measured data.

DOI
10.1103/physreva.62.031802

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We demonstrate that the recently observed damping of Rabi oscillations of a trapped 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ ion initially cooled to its motional ground state [Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)] is caused by quantum jumps to an auxiliary electronic state. This mechanism also predicts an asymmetric decay of the electronic-state population that is found to be in good agreement with the measured data.
We investigate the mechanism of damping and heating of trapped ions associated with the polarization of the residual background gas induced by the oscillating ions themselves. Reasoning by analogy with the physics of surface electrons in liquid helium, we demonstrate that the decay of Rabi oscillations observed in experiments on 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ can be attributed to the polarization phenomena investigated here. The measured sensitivity of the damping of Rabi oscillations with respect to the vibrational quantum number of a trapped ion is also predicted in our polarization model.
We present a nonlinear decoherence model which models decoherence effects caused by various decohering sources in a quantum system through a nonlinear coupling between the system and its environment, and apply it to investigating decoherence in nonclassical motional states of a single trapped ion. We obtain an exactly analytic solution of the model and find very good agreement with experimental results for the population decay rate of a single trapped ion observed in the NIST experiments by Meekhof and co-workers [D. M. Meekhof et al., Phys. Rev. Lett. 76, 1796 (1996)].
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 demonstrate ground-state cooling of a trapped ion using radio-frequency (rf) radiation. This is a powerful tool for the implementation of quantum operations, where rf or microwave radiation instead of lasers is used for motional quantum state engineering. We measure a mean phonon number of n[over ¯]=0.13(4) after sideband cooling, corresponding to a ground-state occupation probability of 88(7)%. After preparing in the vibrational ground state, we demonstrate motional state engineering by driving Rabi oscillations between the |n=0⟩ and |n=1⟩ Fock states. We also use the ability to ground-state cool to accurately measure the motional heating rate and report a reduction by almost 2 orders of magnitude compared with our previously measured result, which we attribute to carefully eliminating sources of electrical noise in the system.
We develop a method for reconstructing the quantum mechanical state of a trapped ion by bichromatically irradiating it on a weak electronic transition and subsequently probing a strong electronic transition for resonance fluorescence. Based on this recently proposed scheme [S. Wallentowitz and W. Vogel, Phys. Rev. Lett. 75, 2932 (1995)] the density matrix of the vibrational motion can be readily obtained either in a generalized position representation or in the number-state representation. The method allows to uniquely define an ultimate classical noise level by a reference measurement with an ion cooled to its vibrational ground-state. Disturbations of the measurement and their suppression are considered. Moreover, we study the effect of the back action of the measurement principle on the motional quantum state. It consists in the splitting of the state to be measured into two substates, giving rise to quantum interference effects. \textcopyright{} 1996 The American Physical Society.