Controlling systematic frequency uncertainties at the 
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 level in linear Coulomb crystals

Keller, Jonas; Burgermeister, T.; Kalincev, D.; Alexandre, Didier; Kulosa, A. P.; Nordmann, T.; Kiethe, Jan; Mehlstäubler, T. E.

doi:10.1103/physreva.99.013405

Cited by 74 publications

(80 citation statements)

References 75 publications

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“…Beyond a single ion, the extension to a crystal of many ions whose motions are linearized about their (periodically driven) equilibrium positions would be immediate using analytic expressions for a coupled Mathieu oscillators system [33,40], with applications ranging from the cooling of 1D chains of ions [41][42][43][44][45][46][47][48], to planar, 2D and 3D crystals in Paul and also Penning traps [49][50][51][52][53][54][55], and applications in quantum information processing [33,40,[56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73]. The extension of the theory to account for more than two electronic levels could be relevant for different types of ions [23,74].…”

Section: Discussionmentioning

confidence: 99%

Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps

et al. 2019

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We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.

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Section: Discussionmentioning

confidence: 99%

Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps

et al. 2019

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“…The smallest system with appreciable nonlinearity (and hence, possibly, chaotic motion) in the * haggaila@gmail.com earlier Paul traps was that of two ions, and it was studied in detail [9][10][11][12][13][14][15], within a time-independent approximation [16,17], including an analysis of all integrable cases [18][19][20][21]. Due to their importance in high-accuracy quantum applications, the effects of the periodic driving (known as the 'micromotion') are extensively studied in various regimes [22][23][24][25][26][27][28][29][30]. The nonlinear (and timedependent) regimes of motion in a surface trap, remain however largely unexplored.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Phase-space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions

et al. 2018

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We present a comprehensive phase-space treatment of the motion of charged particles in electrodynamic traps. Focusing on five-wire surface-electrode Paul traps, we study the details of integrable and chaotic motion of a single ion. We introduce appropriate phase-space measures and give a universal characterization of the trap effectiveness as a function of the parameters. We rigorously derive the commonly used (time-independent) pseudopotential approximation, quantify its regime of validity and analyze the mechanism of its breakdown within the time-dependent potential. The phase space approach that we develop gives a general framework for describing ion dynamics in a broad variety of surface Paul traps. To probe this framework experimentally, we propose and analyze, using numerical simulations, an experiment that can be realized with an existing four-wire trap. We predict a robust experimental signature of the existence of trapping pockets within a mixed regular and chaotic phase-space structure. Intricately rich escape dynamics suggest that surface traps give access to exploring microscopic Hamiltonian transport phenomena in phase space.

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“…Interesting extensions of the theory could include more general electronic level structures [14,45], and applying the action-angle framework to setups where power-law distributions in energy (in an averaged sense) were predicted for collisions of ions with neutral atoms [46][47][48][49]. The interplay of micromotion, noise and laser cooling is of significant importance for applications in quantum information processing and the operation of quantum gates and entanglement operations with trapped ions [19,22,26,[50][51][52][53][54][55][56][57][58][59][60][61][62][63][64]. In particular, as discussed above, the actions standing at the heart of the current work correspond exactly to the quantum mechanical phonons with a periodically-driven harmonic potential [65], in terms of Floquet-Lyapunov modes [22,24].…”

Section: Discussionmentioning

confidence: 99%

Tuning nonthermal distributions to thermal ones in time-dependent Paul traps

Landa

2019

Phys. Rev. A

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We study the probability distribution of an atomic ion being laser-cooled in a periodically-driven Paul trap using a Floquet approach to the semiclassical photon scattering dynamics. We show that despite the microscopic nonequilibrium forces, a stationary thermal-like exponential distribution can be obtained in the Hamiltonian action, or equivalently in the number of quanta (phonons) of the motion linearized about the zero of the potential. At the presence of additional stray electric fields, the ion is pushed from the origin of the potential and set into a large-amplitude driven oscillation, and above a threshold amplitude of such "excess micromotion", the action distribution of excitations about the driven oscillation broadens and becomes distinctly nonthermal. We find that by a proper choice of the laser detuning the distribution can be made exponential again, with a mean phonon number close to that of the Doppler cooling limit. We derive a relation allowing to deduce just from the experimentally observable photon scattering rate both the required detuning for optimal cooling and the final mean phonon number. These results are important for quantum information processing and other applications, and in particular the derived approach can be applied to crystals of trapped ions in planar configurations, where the driven motion of ions is unavoidable.

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Controlling systematic frequency uncertainties at the 10−19 level in linear Coulomb crystals

Cited by 74 publications

References 75 publications

Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps

Far-from-equilibrium noise-heating and laser-cooling dynamics in radio-frequency Paul traps

Phase-space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions

Tuning nonthermal distributions to thermal ones in time-dependent Paul traps

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