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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Trapped Ions, Entanglement, and Quantum Computing

C. J. Myatt, B. E. King, D. Kielpinski, Dietrich G. Leibfried, Q. A. Turchette, C. S. Wood, Wayne M. Itano, Christopher R. Monroe, David J. Wineland

Published May 1, 1998• 1 citation
OpenAlex

Abstract

A miniature, elliptical ring rf (Paul) ion trap has been used in recent esperiments toward realizing a quantum computer in a trapped ion system. With the combination of small spatial dimensions and high rf drive potentials, around 500 V amplitude, we have achieved secular oscillation frequencies in the range of 5-20 MHz. The equilibrium positions of pairs of ions that arc crystallized in this trap lie along the long &\\is of the ellipse. By adding a static potential to the trap, the micromotion of two crystallized ions may be reduced relative to the case of pure rf confinement. The presence of micromotion reduces the strength of internal transitions in the ion, an effect that is characterized by a Debye-Waller factor, in analogy with the reduction of Bragg scattering at finite temperature in a cvstal lattice. We have demonstrated the dependence of the rates of internal transitions on the amplitude of micromotion, and we propose a scheme to use this effect to differentially address the ions.

Related papers

Trapped ions, entanglement, and quantum computing

Christopher J. Myatt, B. E. King, D. Kielpinski +6 more

A miniature, elliptical ring rf ion trap has been sued in recent experiments toward realizing a quantum computer in a trapped ion system. With the combination of small spatial dimensions and high rf drive potentials, around 500 V amplitude, we have achieved secular oscillation frequencies in the range of 5-20 MHz. The equilibrium positions of pairs of ions that are crystallized in this trap lie along the long axis of the ellipse. By adding a static potential to the trap, the micromotion of two crystallized ions may be reduced relative to the case of pure rf confinement. The presence of micromotion reduces the strength of internal transitions in the ion, an effect that is characterized by a Debye-Waller factor, in analogy with the reduction of Bragg scattering at finite temperature in a crystal lattice. We have demonstrated the dependence of the rates of internal transitions on the amplitude of micromotion, and we propose a scheme to use this effect to differentially address the ions.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 15, 1998•2 citations

Elliptical ion traps for quantum computation

Ralph G. DeVoe

Summary form only given. The Cirac-Zoller model of quantum computation assumes that ions are confined in a linear ion trap. However, no experimental test of quantum computation or even of Raman cooling has yet been performed in a linear trap; instead the NIST group has used a miniature Paul trap in which a slight asymmetry or ellipticity is introduced to define an axis of crystallization. In this paper the case of arbitrary ellipticity is considered and two results for the crystal size and micromotion amplitude are derived. The first relation is a linear crystal stability condition, which shows that the maximum number of ions which can be confined is uniquely related to the ellipticity by a 7/3 power law. The second result shows that the micromotion in elliptical traps is far smaller than one would expect naively, specifically that the micromotion amplitude depends approximately on the 1/5 power of the number of trapped ions.

Quantum Electronics and Laser Science Conference•Jan 20, 2003•0 citations

Elliptical ion traps and trap arrays for quantum computation

Ralph G. DeVoe

The properties of a rf quadrupole trap, the elliptical ion trap, are derived. Elliptical traps can confine large numbers of ions in the Lamb-Dicke regime due to a hitherto unrecognized mechanism unique to one-dimensional Coulomb crystals, implicit in the theories of Dubin and Schiffer. This follows from a linear crystal stability condition, which uniquely relates the crystal size to ellipticity, and a micromotion relation, which reveals a 1/5-root dependence on the number of trapped ions. Elliptical traps offer several advantages over linear traps in the Cirac-Zoller model of quantum computing, both for initial tests and as a potential method of creating a full-scale quantum computer. Numerical solutions of a one-electrode structure show that microscopic elliptical traps, each containing $\ensuremath{\approx}100$ ions, can be constructed at a density of 100 traps/${\mathrm{cm}}^{2},$ making possible arrays containing $>{10}^{6}$ ions in the Lamb-Dicke regime for precision spectroscopy or quantum computation.

Physical Review A•Aug 1, 1998•52 citations

Quantum Computation in Large Ion Crystals

Yukai Wu

Ion trap is one of the most promising candidates for quantum computing. High-fidelity gates have been demonstrated in small ion crystals and schemes like ion shuttling have been proposed for larger systems. This thesis discusses the possibility of direct quantum computing on a large ion crystal in a Paul trap, without any shuttling of the ions. We first review a scheme to entangle two ions in a small ion crystal mediated by the collective phonon modes and analyze the gate errors. The generalization to larger systems is divided into three parts. (1) We present numerical methods to solve all the normal modes of the ion crystal, including the micromotion, up to arbitrary precision. The stability of the crystal under infinitesimal perturbation is ensured when all the normal modes have real frequencies. For finite disturbance, direct molecular dynamics simulation will be needed; after discussing some potential problems in the simulation, we give a rule of thumb for the ion crystal to be stable at a given temperature. (2) We show that when designing an entangling gate between two nearby ions, all the ions far away can be neglected, so that only a small number of normal modes are relevant. Similarly, distant entangling gates can be applied in parallel and the crosstalk is shown to decay cubically with the distance between these gates. (3) Then we present numerical methods to include the solved micromotion into the design of the entangling gates efficiently, again up to arbitrary precision. Thus we conclude that the design and the implementing of entangling gates are scalable in a large ion crystal. Finally we consider a near-term application to simulate an all-to-all coupled Ising model in a small to medium-sized ion crystal.

•Jan 1, 2019•3 citations

Optimizing RF/DC Electrode Layouts in Ion Traps: Minimizing Micromotion Through Geometric Configuration for Enhanced Confinement and Laser Cooling Access

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Ion traps are a foundational technology in quantum information processing, precision spectroscopy and foundational physics tests. At the heart of their performance is the inhibition of micromotion, an oscillation of ions through imperfect trapping potentials, that restricts the laser cooling efficiency, coherence times, and the accuracy of measurements. The paper provides a systematic computational analysis of four different electrode geometries (Linear Paul, Segmented, Surface and Ring) in 24 different RF / DC configurations (C01-C24) and 13 performance parameters that comprise trap depth (0.62 1.48 eV), radial secular frequency (1,100 1 Multi-objective optimization with weighted scoring of these metrics indicates that Ring trap geometry scores the highest total (80.2/100), followed by Linear Paul (72.0), Segmented (67.0) and Surface (55.1) configurations. ANOVA (one-way) statistically verified the presence of statistically significant inter-geometry differences in micro-motions amplitude (F = 18.43, p < .001) and cooling efficiency (F = 22.17, p < .001), with Tukey HSD post-hoc revealed that the most significant difference was between the Ring and the Surface. The Pearson correlation analysis shows that RF drive voltage and micromotion amplitude (r = -0.94 to -0.99) and cooling efficiency and micromotion (r = -1.00) have near-perfect inverse correlations, which prove that the quality of confinement is regulated by electrode geometry, RF amplitude, and spacing. These results give quantitative design principles of next-generation ion traps in quantum computing and atomic clock. Keywords: ion trap, micromotion minimization, RF/DC electrode optimization, laser cooling, Mathieu stability, secular frequency, quantum computing

Annual Methodological Archive Research Review•Jan 30, 2026•0 citations

Dynamics of charged particles in a Paul radio-frequency quadrupole trap

John D. Prestage, Ann Katherine Williams, Lute Maleki +2 more

We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for ${\mathit{q}}_{\mathit{z}}$\ensuremath{\lesssim}0.6, whereas rapid heating is seen for ${\mathit{q}}_{\mathit{z}}$=0.8.

Physical Review Letters•Jun 10, 1991•65 citations
A miniature, elliptical ring rf (Paul) ion trap has been used in recent esperiments toward realizing a quantum computer in a trapped ion system. With the combination of small spatial dimensions and high rf drive potentials, around 500 V amplitude, we have achieved secular oscillation frequencies in the range of 5-20 MHz. The equilibrium positions of pairs of ions that arc crystallized in this trap lie along the long &\is of the ellipse. By adding a static potential to the trap, the micromotion of two crystallized ions may be reduced relative to the case of pure rf confinement. The presence of micromotion reduces the strength of internal transitions in the ion, an effect that is characterized by a Debye-Waller factor, in analogy with the reduction of Bragg scattering at finite temperature in a cvstal lattice. We have demonstrated the dependence of the rates of internal transitions on the amplitude of micromotion, and we propose a scheme to use this effect to differentially address the ions.
A miniature, elliptical ring rf ion trap has been sued in recent experiments toward realizing a quantum computer in a trapped ion system. With the combination of small spatial dimensions and high rf drive potentials, around 500 V amplitude, we have achieved secular oscillation frequencies in the range of 5-20 MHz. The equilibrium positions of pairs of ions that are crystallized in this trap lie along the long axis of the ellipse. By adding a static potential to the trap, the micromotion of two crystallized ions may be reduced relative to the case of pure rf confinement. The presence of micromotion reduces the strength of internal transitions in the ion, an effect that is characterized by a Debye-Waller factor, in analogy with the reduction of Bragg scattering at finite temperature in a crystal lattice. We have demonstrated the dependence of the rates of internal transitions on the amplitude of micromotion, and we propose a scheme to use this effect to differentially address the ions.
Summary form only given. The Cirac-Zoller model of quantum computation assumes that ions are confined in a linear ion trap. However, no experimental test of quantum computation or even of Raman cooling has yet been performed in a linear trap; instead the NIST group has used a miniature Paul trap in which a slight asymmetry or ellipticity is introduced to define an axis of crystallization. In this paper the case of arbitrary ellipticity is considered and two results for the crystal size and micromotion amplitude are derived. The first relation is a linear crystal stability condition, which shows that the maximum number of ions which can be confined is uniquely related to the ellipticity by a 7/3 power law. The second result shows that the micromotion in elliptical traps is far smaller than one would expect naively, specifically that the micromotion amplitude depends approximately on the 1/5 power of the number of trapped ions.
The properties of a rf quadrupole trap, the elliptical ion trap, are derived. Elliptical traps can confine large numbers of ions in the Lamb-Dicke regime due to a hitherto unrecognized mechanism unique to one-dimensional Coulomb crystals, implicit in the theories of Dubin and Schiffer. This follows from a linear crystal stability condition, which uniquely relates the crystal size to ellipticity, and a micromotion relation, which reveals a 1/5-root dependence on the number of trapped ions. Elliptical traps offer several advantages over linear traps in the Cirac-Zoller model of quantum computing, both for initial tests and as a potential method of creating a full-scale quantum computer. Numerical solutions of a one-electrode structure show that microscopic elliptical traps, each containing $\ensuremath{\approx}100$ ions, can be constructed at a density of 100 traps/cm2,{\mathrm{cm}}^{2},cm2, making possible arrays containing >106>{10}^{6}>106 ions in the Lamb-Dicke regime for precision spectroscopy or quantum computation.
Ion trap is one of the most promising candidates for quantum computing. High-fidelity gates have been demonstrated in small ion crystals and schemes like ion shuttling have been proposed for larger systems. This thesis discusses the possibility of direct quantum computing on a large ion crystal in a Paul trap, without any shuttling of the ions. We first review a scheme to entangle two ions in a small ion crystal mediated by the collective phonon modes and analyze the gate errors. The generalization to larger systems is divided into three parts. (1) We present numerical methods to solve all the normal modes of the ion crystal, including the micromotion, up to arbitrary precision. The stability of the crystal under infinitesimal perturbation is ensured when all the normal modes have real frequencies. For finite disturbance, direct molecular dynamics simulation will be needed; after discussing some potential problems in the simulation, we give a rule of thumb for the ion crystal to be stable at a given temperature. (2) We show that when designing an entangling gate between two nearby ions, all the ions far away can be neglected, so that only a small number of normal modes are relevant. Similarly, distant entangling gates can be applied in parallel and the crosstalk is shown to decay cubically with the distance between these gates. (3) Then we present numerical methods to include the solved micromotion into the design of the entangling gates efficiently, again up to arbitrary precision. Thus we conclude that the design and the implementing of entangling gates are scalable in a large ion crystal. Finally we consider a near-term application to simulate an all-to-all coupled Ising model in a small to medium-sized ion crystal.
Ion traps are a foundational technology in quantum information processing, precision spectroscopy and foundational physics tests. At the heart of their performance is the inhibition of micromotion, an oscillation of ions through imperfect trapping potentials, that restricts the laser cooling efficiency, coherence times, and the accuracy of measurements. The paper provides a systematic computational analysis of four different electrode geometries (Linear Paul, Segmented, Surface and Ring) in 24 different RF / DC configurations (C01-C24) and 13 performance parameters that comprise trap depth (0.62 1.48 eV), radial secular frequency (1,100 1 Multi-objective optimization with weighted scoring of these metrics indicates that Ring trap geometry scores the highest total (80.2/100), followed by Linear Paul (72.0), Segmented (67.0) and Surface (55.1) configurations. ANOVA (one-way) statistically verified the presence of statistically significant inter-geometry differences in micro-motions amplitude (F = 18.43, p < .001) and cooling efficiency (F = 22.17, p < .001), with Tukey HSD post-hoc revealed that the most significant difference was between the Ring and the Surface. The Pearson correlation analysis shows that RF drive voltage and micromotion amplitude (r = -0.94 to -0.99) and cooling efficiency and micromotion (r = -1.00) have near-perfect inverse correlations, which prove that the quality of confinement is regulated by electrode geometry, RF amplitude, and spacing. These results give quantitative design principles of next-generation ion traps in quantum computing and atomic clock. Keywords: ion trap, micromotion minimization, RF/DC electrode optimization, laser cooling, Mathieu stability, secular frequency, quantum computing
We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for qz{\mathit{q}}_{\mathit{z}}qz​\ensuremath{\lesssim}0.6, whereas rapid heating is seen for qz{\mathit{q}}_{\mathit{z}}qz​=0.8.