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Journal of Optics B Quantum and Semiclassical Optics

Decoherence in non-classical states of a trapped ion

Adrián A. Budini, R. L. de Matos Filho, Nicim Zagury

Published Aug 1, 2002• 2 citations
Publisher

Abstract

We assume that the origin of decoherence of non-classical motional states of a trapped ion is due to the coupling of the vibronic modes with classical stochastic electric fields and to the finite lifetime of the electronic levels. Working in the dressed basis of the effective two-level Hamiltonian, we show that these interactions lead to a dispersive-like decoherence dynamics. The numerical results agree with the experimental data reported by Meekhof et al.

DOI
10.1088/1464-4266/4/4/340

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We assume that the origin of decoherence of non-classical motional states of a trapped ion is due to the coupling of the vibronic modes with classical stochastic electric fields and to the finite lifetime of the electronic levels. Working in the dressed basis of the effective two-level Hamiltonian, we show that these interactions lead to a dispersive-like decoherence dynamics. The numerical results agree with the experimental data reported by Meekhof et al.
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)].
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.
The dynamics of the interaction of a quantized cavity field and the vibronic degrees of freedom of a trapped ion is studied under realistic conditions by including cavity losses, spontaneous electronic transitions, and atomic nonlinearities. As long as spontaneous electronic transitions are negligible, analytical results are derived for describing the interaction of the trapped ion and the damped cavity field in the secular approximation. Under more general conditions, when the secular approximation breaks down and spontaneous emission effects become important, the dynamics of the system is studied by quantum-trajectory methods. As an example we demonstrate that, by exploiting the nonlinearities inherent in the dynamics of the system, one may prepare correlated vibronic states and vibrational Fock states. Moreover, we study the generation of an entangled Greenberger-Horne-Zeilinger state. Taking into account the decoherence due to electronic and cavity losses, the best fidelity is obtained under conditions far from the Lamb-Dicke regime.
The effect of ambient magnetic fields on the dynamics of a single trapped ion is studied analytically. We consider two electronic states with energy separation stochastically varied by magnetic-field perturbations and coupled to the vibrational modes by a laser. For Gaussian white noise, a master equation is derived and solved. The results obtained reveal how the effective Rabi frequencies and the decay rates depend on the noise strength and on the number state index. The detection of features specific to magnetic-field noise in the evolution of states that can be prepared under standard experimental conditions is discussed. A comparison with the effects of laser intensity and phase fluctuations is presented. Implications for the realization of logic gates are analyzed.