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arXiv:quant-ph/0109156 · Physical Review A

Decoherence in trapped ions due to polarization of the residual background gas

Roberto M. Serra, N. G. de Almeida, Wilson B. da Costa, M. H. Y. Moussa

Published Aug 17, 2001• 10 citations
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Abstract

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 ${}^{9}{\mathrm{Be}}^{+}$ 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.

DOI
10.1103/physreva.64.033419

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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 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.
The study of physical properties of Bose condensed gases has recently become a very active topic due to the experimental realization of Bose-Einstein condensation in the magnetically trapped gases of alkali atoms. In this paper we theoretically study the Rabi oscillation of a weakly interacting Bose gas in the regime of microwave electronic spin resonance. For a Bose gas above the critical temperature for Bose-Einstein condensation, the microwave radiation induced by the driving microwave field exhibits the ordinary Rabi oscillation damped by the inhomogeneous Doppler dephasing. For a Bose gas with a condensate, the microwave radiation is composed of two components. One is the strong coherent Rabi oscillation from the condensate. The other is a modulated Rabi oscillation due to the noncondensed part of the gas. We show that the modulation of Rabi oscillation of the noncondensed gas is directly relative to the elementary collective excitation of atoms in the gas.
We consider one source of decoherence for a single trapped ion due to intensity and phase fluctuations in the exciting laser pulses. For simplicity we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. This master equation is averaged over the noise, and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. Our results are in good qualitative agreement with recent experiments and predict that the decoherence rate will depend on vibrational quantum number in different ways depending on which vibrational excitation sideband is used.
Summary form only given.To model the decoherence in ion traps resulting from laser intensity and phase fluctuations, we assume that the stochastic processes involved are white noise processes, which enables us to give a simple master equation description of this source of decoherence. We discuss the effects those fluctuations have on gate operations in ion-trap quantum computation and briefly address possible detection and error correction mechanisms. The master equation is then averaged over the noise and is sufficient to describe the results of experiments that probe the oscillations in the electronic populations as energy is exchanged between the internal and electronic motion. We get solutions for the probability of the ion to be in the ground state for both intensity and phase fluctuations. Our results predict that the decoherence rate resulting from intensity fluctuations will depend on the vibrational quantum number in different ways depending on which vibrational excitation sideband is used. So the dependence of the decoherence rate for the second red sideband depends quadratically on the vibrational energy state |n> the ion is prepared in, whereas for the first sideband, this effect is linear in n. Due to this result, the second red (or any higher-order) sideband is a better choice for testing the dependence of decoherence on the excitation in the vibrational state experimentally than just the first-order sideband. Because those fluctuations in the exciting laser pulse are not the only source of decoherence, we briefly discuss fluctuations in the trap potential itself. These fluctuations lead to a wobbling trap center point, and we discuss the effects due to them.