Exploring structural phase transitions of ion crystals

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Abstract

Phase transitions have been a research focus in many-body physics over past decades. Cold ions, under strong Coulomb repulsion, provide a repealing paradigm of exploring phase transitions in stable confinement by electromagnetic field. We demonstrate various conformations of up to sixteen laser-cooled ⁴⁰Ca ⁺ ion crystals in a home-built surface-electrode trap, where besides the usually mentioned structural phase transition from the linear to the zigzag, two additional phase transitions to more complicated two-dimensional configurations are identified. The experimental observation agrees well with the numerical simulation. Heating due to micromotion of the ions is analysed by comparison of the numerical simulation with the experimental observation. Our investigation implies very rich and complicated many-body behaviour in the trapped-ion systems and provides effective mechanism for further exploring quantum phase transitions and quantum information processing with ultracold trapped ions.

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Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins.

Joseph Britton, Brian Sawyer, Adam Keith … (2012)

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed-matter systems, potentially including high-temperature superconductivity. However, many properties of exotic, strongly correlated spin systems, such as spin liquids, have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N ≈ 30 particles. Feynman predicted that a quantum simulator--a special-purpose 'analogue' processor built using quantum bits (qubits)--would be inherently suited to solving such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach, but simulations allowing controlled, tunable interactions between spins localized on two- or three-dimensional lattices of more than a few tens of qubits have yet to be demonstrated, in part because of the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction, J(i,j), on a naturally occurring, two-dimensional triangular crystal lattice of hundreds of spin-half particles (beryllium ions stored in a Penning trap). This is a computationally relevant scale more than an order of magnitude larger than previous experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J(i,j) proportional variant d(-a)(i,j), where 0 ≤ a ≤ 3 and d(i,j) is the distance between spin pairs. These power laws correspond physically to infinite-range (a = 0), Coulomb-like (a = 1), monopole-dipole (a = 2) and dipole-dipole (a = 3) couplings. Experimentally, we demonstrate excellent agreement with a theory for 0.05 ≲ a ≲ 1.4. This demonstration, coupled with the high spin count, excellent quantum control and low technical complexity of the Penning trap, brings within reach the simulation of otherwise computationally intractable problems in quantum magnetism.

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Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins

Joseph Britton, Brian Sawyer, Adam Keith … (2012)

The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed matter systems, potentially including high-temperature superconductivity. However, many properties of exotic strongly correlated spin systems (e.g., spin liquids) have proved difficult to study, in part because calculations involving N-body entanglement become intractable for as few as N~30 particles. Feynman divined that a quantum simulator - a special-purpose "analog" processor built using quantum particles (qubits) - would be inherently adept at such problems. In the context of quantum magnetism, a number of experiments have demonstrated the feasibility of this approach. However, simulations of quantum magnetism allowing controlled, tunable interactions between spins localized on 2D and 3D lattices of more than a few 10's of qubits have yet to be demonstrated, owing in part to the technical challenge of realizing large-scale qubit arrays. Here we demonstrate a variable-range Ising-type spin-spin interaction J_ij on a naturally occurring 2D triangular crystal lattice of hundreds of spin-1/2 particles (9Be+ ions stored in a Penning trap), a computationally relevant scale more than an order of magnitude larger than existing experiments. We show that a spin-dependent optical dipole force can produce an antiferromagnetic interaction J_ij ~ 1/d_ij^a, where a is tunable over 0

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Quantum computations on a topologically encoded qubit.

D. Nigg, M. Müller, E. A. Martínez … (2014)

The construction of a quantum computer remains a fundamental scientific and technological challenge because of the influence of unavoidable noise. Quantum states and operations can be protected from errors through the use of protocols for quantum computing with faulty components. We present a quantum error-correcting code in which one qubit is encoded in entangled states distributed over seven trapped-ion qubits. The code can detect one bit flip error, one phase flip error, or a combined error of both, regardless on which of the qubits they occur. We applied sequences of gate operations on the encoded qubit to explore its computational capabilities. This seven-qubit code represents a fully functional instance of a topologically encoded qubit, or color code, and opens a route toward fault-tolerant quantum computing. Copyright © 2014, American Association for the Advancement of Science.

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Journal

Journal ID (nlm-ta): Sci Rep

Journal ID (iso-abbrev): Sci Rep

Title: Scientific Reports

Publisher: Nature Publishing Group

ISSN (Electronic): 2045-2322

Publication date (Electronic): 11 February 2016

Publication date Collection: 2016

Volume: 6

Electronic Location Identifier: 21547

Affiliations

[1 ]State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences , Wuhan, 430071, China

[2 ]University of the Chinese Academy of Sciences , Beijing 100049, China

Author notes

[a ] liangchen@ 123456wipm.ac.cn

[b ] zhoufei@ 123456wipm.ac.cn

[c ] mangfeng@ 123456wipm.ac.cn

Article

Publisher Item ID: srep21547

DOI: 10.1038/srep21547

PMC ID: 4749997

PubMed ID: 26865229

SO-VID: caa67468-3ec7-42f9-b807-eaad83a06f8c

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This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Exploring structural phase transitions of ion crystals

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Fracture and Structural Integrity

Most cited references 25

Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins.

Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins

Quantum computations on a topologically encoded qubit.

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