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Physical Review A

Internal-state dephasing of trapped ions

S. Brouard, Jesús Plata

Published Jul 14, 2003• 11 citations
Publisher

Abstract

The effect of random fields on the internal dynamics of trapped ions is studied analytically. General characteristics of the dependence of the dephasing on the noise statistics are identified: the form of the initial decay of the coherences is determined by the probability distribution; effects of noise color, in particular, collapses and revivals rooted in spectral concentration of the fluctuations, are apparent in a transient regime; at large times, exponential decay sets in for widely different noise properties. The study is particularized to magnetic-field fluctuations: features distinctive of the linear and quadratic Zeeman shifts are traced. The scaling of the dephasing with the number of ions is analyzed; the implications for the realization of decoherence-free states are discussed.

DOI
10.1103/physreva.68.012311

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The effect of random fields on the internal dynamics of trapped ions is studied analytically. General characteristics of the dependence of the dephasing on the noise statistics are identified: the form of the initial decay of the coherences is determined by the probability distribution; effects of noise color, in particular, collapses and revivals rooted in spectral concentration of the fluctuations, are apparent in a transient regime; at large times, exponential decay sets in for widely different noise properties. The study is particularized to magnetic-field fluctuations: features distinctive of the linear and quadratic Zeeman shifts are traced. The scaling of the dephasing with the number of ions is analyzed; the implications for the realization of decoherence-free states are discussed.
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.
The effect of intensity fluctuations on laser-induced coupling of electronic and vibrational states of a trapped ion is studied analytically. Different types of noise relevant to the experiments are considered. The resulting decoherence phenomenology is shown to present nontrivial characteristics. Noise color leads to nonexponential decay of the coherences: after the initial decay, determined by the probability distribution, a transient period specific to the noise spectrum is apparent; at large times, exponential decay sets in for widely different noise properties. The detection of these features in the evolution of an initial coherent state of the vibrational mode is discussed.
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.
How a closed interacting quantum many-body system relaxes and dephases as a function of time is a fundamental question in thermodynamic and statistical physics. In this Letter, we analyze and observe the persistent temporal fluctuations after a quantum quench of a tunable long-range interacting transverse-field Ising Hamiltonian realized with a trapped-ion quantum simulator. We measure the temporal fluctuations in the average magnetization of a finite-size system of spin-1/2 particles. We experiment in a regime where the properties of the system are closely related to the integrable Hamiltonian with global spin-spin coupling, which enables analytical predictions for the long-time nonintegrable dynamics. The analytical expression for the temporal fluctuations predicts the exponential suppression of temporal fluctuations with increasing system size. Our measurement data is consistent with our theory predicting the regime of many-body dephasing.
The dynamics of the quantum Rabi model in the deep strong coupling regime is investigated in a trapped-ion setup. Recognizably, the main hallmark of this regime is the emergence of collapses and revivals, whose faithful observation is hindered under realistic magnetic dephasing noise. Here we discuss how to attain a faithful implementation of the quantum Rabi model in the deep strong coupling regime which is robust against magnetic-field fluctuations and at the same time provides a large tunability of the simulated parameters. This is achieved by combining standing wave laser configuration with continuous dynamical decoupling. In this manner the present work further supports the suitability of continuous dynamical decoupling techniques in trapped-ion settings to faithfully realize different interacting dynamics.
The dynamics of the quantum Rabi model (QRM) in the deep strong coupling regime is theoretically analyzed in a trapped-ion set-up. Recognizably, the main hallmark of this regime is the emergence of collapses and revivals, whose faithful observation is hindered under realistic magnetic dephasing noise. Here, we discuss how to attain a faithful implementation of the QRM in the deep strong coupling regime which is robust against magnetic field fluctuations and at the same time provides a large tunability of the simulated parameters. This is achieved by combining standing wave laser configuration with continuous dynamical decoupling. In addition, we study the role that amplitude fluctuations play to correctly attain the QRM using the proposed method. In this manner, the present work further supports the suitability of continuous dynamical decoupling techniques in trapped-ion settings to faithfully realize different interacting dynamics.