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arXiv:1412.3551 · Journal of Physics B Atomic Molecular and Optical Physics

Surface traps for freely rotating ion ring crystals

Po-Jen Wang, Tongcang Li, Crystal Noel, A Chuang, Xiang Zhang, Hartmut Häffner

Published Sep 16, 2015• 10 citations
arXivHTMLPDF

Abstract

Abstract Rings of trapped ions are an attractive system to study quantum-many body dynamics with closed boundary conditions as well as symmetry breaking. One of the biggest challenges towards such experiments is to sufficiently suppress rotational imperfections of the trapping potential and to allow for instance freely rotating ring structures. We show how to overcome this challenge with a surface trap design and perform numerical calculations to analyze the consequences of various imperfections in detail. We conclude that trap electrode imperfections, external stray electric fields, and local charging of the trap electrodes can be controlled sufficiently well to allow ion rings to rotate freely even near their rotational ground state.

DOI
10.1088/0953-4075/48/20/205002

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Abstract Rings of trapped ions are an attractive system to study quantum-many body dynamics with closed boundary conditions as well as symmetry breaking. One of the biggest challenges towards such experiments is to sufficiently suppress rotational imperfections of the trapping potential and to allow for instance freely rotating ring structures. We show how to overcome this challenge with a surface trap design and perform numerical calculations to analyze the consequences of various imperfections in detail. We conclude that trap electrode imperfections, external stray electric fields, and local charging of the trap electrodes can be controlled sufficiently well to allow ion rings to rotate freely even near their rotational ground state.
In this thesis, I present the design, implementation, and characterization of a novel, rotationally symmetric ion trap. Our compact design creates a toroidal trapping potential for charged atoms that has a radius that is much smaller than the height at which the ions are positioned above the surface of the trap. We trap ions at a height of 385~mu\\mumum and a radius of 45~mu\\mumum as expected from simulation. We demonstrate that this ring is rotationally symmetric with imperfections in the potential of much less than 3~mK. With two ions contained in a point Paul trap, we demonstrate the creation of a 100~kHz rotating ring using a rotating quadrupole. By releasing the quadrupole potential, we demonstrate the ability to create superpositions of rotational states using the modulation of the laser light produced by the classical rotation of the crystal in a symmetric potential. Superpositions of rotational states differing by up to four quanta are observed. With these rotational superpositions, we describe an experiment capable of observing the identical nature of two ions in a Coulomb crystal. By creating a rotational interferometer, one can coherently exchange two particles and observe their interference upon recombination. We describe what this interference signature would be and how particle indistinguishability would affect it. We present experimental efforts towards realizing this exchange and reflect on our unexpectedly short rotational superposition coherence times.
Scaling trapped-ion optical clocks to hundreds of ions remains a major challenge due to inhomogeneous frequency shifts in large ion crystals. Here, we propose a circular surface-trap architecture for a multi-ion optical clock with hundreds of ions. The rotational symmetry of the ion crystal suppresses the main sources of inhomogeneity, quadrupole shift.We investigate the feasibility of a clock based on a ring crystal of 400 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ions and propose a suitable experimental setup configuration. We have shown that circular configuration of ions leads to suppression by two orders of magnitude of the quadrupole shift comparing to the linear trap. Combined with stray-field compensation and dynamical decoupling techniques, this architecture provides a pathway toward multi-ion optical clocks with fractional frequency uncertainty at the 10−1810^{-18}10−18 level and an expected 20-fold improvement in frequency stability compared to single ion clocks.
Laser-cooled trapped ions platform is one of the best candidates for the development of future quantum computing. This has generated a major worldwide research effort aimed at scaling and integrating trapping devices. As part of this effort, we are developing miniature atomic ion traps in the laboratory: Paul linear surface traps manufactured in collaboration with Nanyang Technology University and the Microelectronics Institute of Singapore. An original feature of the manufacturing process is that all the electrical contacts of the trap electrodes are made through the Silicon substrate (TSV: through silicon vias). In this way, the wire-bondings usually soldered directly to the electrodes can be offset or completely eliminated [1]. This opens the way to complex architectures, in particular cylindrically symmetrical ring traps, which cannot be made with surface connections that would break the desired symmetry. The trapping and laser cooling of ions in cylindrically symmetrical linear Paul traps (called "ion storage rings" in their macroscopic version, diameters of around 100 mm) was demonstrated in pioneering work at Garching [2] and subsequently extended to microfabricated traps (multilayer technology) at Sandia National Labs (diameter 2.5 mm) [3] and Berkeley (diameter 95 μm) [4]. These devices are of interest because, in the absence of defects, they enable rotational symmetry for the trapped ions and thus periodic boundary conditions for the confined cold ion system (Coulomb crystal). They are also candidates for observing and manipulating the rotational quantum state of trapped ion ensembles [4]. We will present our latest results concerning the performance of TSV surface ring traps (diameters between 150 and 210 μm) manufactured in Singapore. In particular, we loaded these traps with Dopplercooled 88Sr+ ions (from a single ion to several hundreds). Laser cooling and image acquisition enable us to estimate the defects of the trapping potential with respect to perfect rotational symmetry. The application of DC voltages to a set of segmented electrodes then makes it possible to compensate for most of these defects, which nevertheless remain the major problem to be solved in order to achieve sub milikelvin free motion.
We crystallize up to 15 ^{40}Ca^{+} ions in a ring with a microfabricated silicon surface Paul trap. Delocalization of the Doppler laser-cooled ions shows that the translational symmetry of the ion ring is preserved at millikelvin temperatures. By characterizing the collective motion of the ion crystals, we identify homogeneous electric fields as the dominant symmetry-breaking mechanism at this energy scale. With increasing ion numbers, such detrimental effects are reduced. We predict that, with only a ten-ion ring, uncompensated homogeneous fields will not break the translational symmetry of the rotational ground state. This experiment opens a door towards studying quantum many-body physics with translational symmetry at the single-particle level.
Laser-cooled trapped ions platform is one of the best candidates for the development of future quantum computing. This has generated a worldwide research effort for scaling and integrating trapping devices. As part of this effort, we are developping cylindrically symmetrical linear Paul traps manufactured in collaboration with Nanyang Technology University and the Microelectronics Institute of Singapore. The electrical contacts of these traps electrodes are made through the Silicon substrate (TSV: through silicon vias), allowing not to break the desired symmetry with surface connections. The trapping and laser cooling of ions in ring traps was demonstrated at Garching [2] and subsequently extended to microfabricated traps at Sandia National Labs [3] and Berkeley [4]. In the absence of defects, these devices enable rotational symmetry for the trapped ions. They are also candidates for manipulating the rotational quantum state of trapped ion ensembles [4].We will present our results concerning the performance of TSV surface ring traps manufactured in Singapore. In particular, we loaded these traps with Doppler-cooled 88Sr+ ions and we estimate the defects of the trapping potential with respect to perfect rotational symmetry. The application of DC voltages to a set of segmented electrodes makes it possible to compensate for most of these defects for observing sub milikelvin free motion.[1] P. Zhao et al., Appl. Phys. Lett. 118, 124003 (2021).[2] I. Waki et al.,Phys. Rev. Lett. 68, 2007 (1992).[3] B. Tabakov et al., Phys. Rev. Applied 4, 031001 (2015). [4] E. Urban et al., Phys. Rev. Lett. 123, 133202 (2019)
Spontaneous symmetry breaking can lead to the formation of time crystals, as well as spatial crystals. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. We also study the effects of finite temperatures on the persistent rotation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.