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Journal of Modern Optics

Decoherence of motional states of trapped ions

Christopher J. Myatt, B. E. King, Q. A. Turchette, Charles A. Sackett, D. Kielpinski, Wayne M. Itano, Christopher R. Monroe, David J. Wineland

Published Oct 1, 2000• 10 citations
Publisher

Abstract

We have studied the decoherence of motional-state superpositions of single trapped ions caused by their coupling to fluctuating fields. We illustrate these studies by showing how Schrödinger-cat state superpositions decohere in the presence of purposely-applied uniform stochastic electric fields and we compare these results to the decoherence caused by ambient fields in the experiments.

DOI
10.1080/09500340008235140

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•Jan 1, 2000•0 citations
We have studied the decoherence of motional-state superpositions of single trapped ions caused by their coupling to fluctuating fields. We illustrate these studies by showing how Schrödinger-cat state superpositions decohere in the presence of purposely-applied uniform stochastic electric fields and we compare these results to the decoherence caused by ambient fields in the experiments.
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)].
The decoherence of nonclassical motional states of a trapped 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ ion in a recent experiment is investigated theoretically. Sources of decoherence considered here destroy the characteristic coherent quantum dynamics of the system, but do not cause energy dissipation. Here they are first introduced phenomenologically, and then described using a microscopic Hamiltonian formulation. Theoretical predictions are compared to experimental results.
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.
We consider two different kinds of fluctuations in an ion trap potential: external fluctuating electrical fields, which cause statistical movement (``wobbling'') of the ion relative to the center of the trap, and fluctuations of the spring constant, which are due to fluctuations of the ac component of the potential applied in the Paul trap for ions. We write down master equations for both cases and, averaging out the noise, obtain expressions for the heating of the ion. We compare our results to previous results for far-off resonance optical traps and heating in ion traps. The effect of fluctuating external electrical fields for a quantum gate operation (controlled-NOT) is determined and the fidelity for that operation derived.
This thesis is concerned with various aspects of ion traps and their use as a quantum simulation and computation device. In its first part we investigate various sources of noise and decoherence in ion traps. As quantum information is very fragile, a detailed knowledge of noise and decoherence sources in a quantum computation device is essential. In the special case of an ion trap quantum computer we investigate the effects of intensity and phase noise in the laser, which is used to perform the gate operations. We then look at other sources of noise which are present without a laser being switched on. These are fluctuations in the trapping frequency caused by noise in the electric potentials applied to the trap and fluctuating electrical fields which will cause heating of the centre-of-mass vibrational state of the ions in the trap. For the case of fluctuating electrical fields we estimate the effect on a quantum gate operation. We then propose a scheme for performing quantum gates without having the ions cooled down to their motional ground state. The second part deals with various aspects of the use of ion traps as a device for quantum computation. We start with the use of ionic qubits as a measurement device for the centre-of-mass vibrational mode and investigate in detail the effect these measurements will have on the vibrational mode. If one wants to use quantum computation devices as systems to simulate quantum mechanics, it is of interest to know how to simulate say a k-level system with N qubits. We investigate the easiest case of this wider problem and look at how to simulate a three-level system (a so called trit) with two qubits in an ion trap quantum computer. We show how to get and measure a SU (3) geometric phase with this toy model. Finally we investigate how to simulate collective angular momentum models with a string of qubits in an ion trap. We assume that the ionic qubits are coupled to a thermal reservoir and derive a master equation for this case. We investigate the semiclassical limit of this master equation and, in the case for two qubits in the trap, determine the entanglement of the steady state. We also outline a way to find the steady state for the master equation using coherence vectors.