Sympathetic cooling of trapped ions for quantum logic

Kielpinski, David; King, B. E.; Myatt, C. J.; Sackett, C. A.; Turchette, Q. A.; Itano, Wayne M.; Monroe, Christopher; Wineland, D. J.; Wh, Zurek

doi:10.1103/physreva.61.032310

Cited by 149 publications

(166 citation statements)

References 16 publications

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“…For few-particle systems in quadrupole traps, this has lead to many applications ranging from high resolution spectroscopy and optical frequency standards [5,6] to quantum information [7,8,9] and tests on the possible variations of the fundamental constants [10,11]. While these effective harmonic traps allow focussing the ions at the center, a greater number of ions with reduced rf driven motion can be stored in higher-order confinements, with possible uses as microwave clocks for deep space navigation [12] or to control cold chemical reactions [13] of astrophysical relevance.…”

Section: Introductionmentioning

confidence: 99%

Crystallization of ion clouds in octupole traps: Structural transitions, core melting, and scaling laws

2009

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The stable structures and melting properties of ion clouds in isotropic octupole traps are investigated using a combination of semi-analytical and numerical models, with a particular emphasis at finite size scaling effects. Small-size clouds are found to be hollow and arranged in shells corresponding approximately to the solutions of the Thomson problem. The shell structure is lost in clusters containing more than a few thousands of ions, the inner parts of the cloud becoming soft and amorphous. While melting is triggered in the core shells, the melting temperature unexpectedly follows the rule expected for three-dimensional dense particles, with a depression scaling linearly with the inverse radius.

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Section: Introductionmentioning

confidence: 99%

Crystallization of ion clouds in octupole traps: Structural transitions, core melting, and scaling laws

2009

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“…Because of their importance to quantum computing, they have been studied in some detail [17,19] From the definition of the coupling matrix for the radial oscillations, B n,m , we see that it has identical eigenvectors to A n,m , but has different eigenvalues:…”

mentioning

confidence: 99%

“…The solutions to the equilibrium equations in this case have been investigated by various authors (see, for example, [16][17][18]); we denote the equilibrium position of the nth ion byr n ͑0, 0,z n ͒. Small oscillations of the ions about their equilibrium positions are described by the Lagrangian [17,19] …”

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confidence: 99%

Observation of Power-Law Scaling for Phase Transitions in Linear Trapped Ion Crystals

et al. 2000

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We report an experimental confirmation of the power-law relationship between the critical anisotropy parameter and ion number for the linear-to-zigzag phase transition in an ionic crystal. Our experiment uses laser cooled calcium ions confined in a linear radio-frequency trap. Measurements for up to ten ions are in good agreement with theoretical and numeric predictions. Implications on an upper limit to the size of data registers in ion trap quantum computers are discussed.PACS numbers: 32.80.Pj, 03.67. Lx, 52.25.Wz, Ions confined in linear radio-frequency traps, and cooled by laser radiation, will condense into a crystalline state. Such crystals are the most rarefied form of condensed matter known [1]. Besides being of inherent scientific interest for this reason, cold trapped ions have a growing number of applications, notably spectroscopy [2-4], frequency standards [3,5], and quantum computing [6,7]. The existence of different kinds of phase transitions of these crystals has been known for some time [8,9] and has been the subject of various theoretical and numeric studies [1,10,11]. Previous experimental work identified different crystal phases/configurations in a quadrupole ring trap [9]. Here we explicitly investigate the transition between two of these phases: the linear and the zigzag configurations. We report the first experimental confirmation of one of the key theoretical/numeric predictions for the linear-to-zigzag transition, namely, the existence of a power law relating the critical anisotropy parameter to the number of ions in the crystal. Further, we discuss the usefulness of this power-law expression in determining the ultimate size of a quantum logic register realizable using a single ion trap.The potential energy of a crystal of N identical ions of mass M and charge e confined in an effective threedimensional harmonic potential is U͑r 1 , r 2 , . . . , r N ͒ M͑2p͒ 2 2 N

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“…In a real experimental setup, the ions are subject to substantial background heating. For long-time quantum computation, to have the ions constantly remain at a certain temperature, it requires sympathetic cooling [31,32], in which case a subset of ions (cooling ions) are continuously laser cooled, bringing down the temperature of other ions (the computational ions) through the heat propagation enabled by the Coulomb interaction in the ion crystal. Sympathetic cooling has been studied for small systems with a few ions [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Sympathetic cooling in a large ion crystal

Lin

Duan

2015

Quantum Inf Process

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We analyze the dynamics and steady state of a linear ion array when some of the ions are continuously laser cooled. We calculate the ions' local temperature measured by its position fluctuation under various trapping and cooling configurations, taking into account background heating due to the noisy environment. For a large system, we demonstrate that by arranging the cooling ions evenly in the array, one can suppress the overall heating considerably. We also investigate the effect of different cooling rates and find that the optimal cooling efficiency is achieved by an intermediate cooling rate. We discuss the relaxation time for the ions to approach the steady state, and show that with periodic arrangement of the cooling ions, the cooling efficiency does not scale down with the system size.

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Sympathetic cooling of trapped ions for quantum logic

Cited by 149 publications

References 16 publications

Crystallization of ion clouds in octupole traps: Structural transitions, core melting, and scaling laws

Crystallization of ion clouds in octupole traps: Structural transitions, core melting, and scaling laws

Observation of Power-Law Scaling for Phase Transitions in Linear Trapped Ion Crystals

Sympathetic cooling in a large ion crystal

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