Formation of helical ion chains

When traversing a symmetry breaking second order phase transition at a finite rate, topological defects form whose number dependence on the quench rate is given by simple power laws. We propose a general approach for the derivation of such scaling laws that is based on the analytical transformation of the associated equations of motion to a universal form rather than employing plausible physical arguments. We demonstrate the power of this approach by deriving the scaling of the number of topological defects in both homogeneous and non-homogeneous settings. The general nature and extensions of this approach are discussed.

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“…This result is in perfect agreement with the analytical and numerical results presented in [27,30,31].…”

supporting

confidence: 82%

Universality in the Dynamics of Second-Order Phase Transitions

2016

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“…Within this simplified picture, the transition between the two stages is supposed to be sharp at a certain value of the external parameter which sets the length scale of the correlations in the final state. The scaling laws predicted by the adiabatic-impulse approximation have been investigated theoretically in a number of classical settings [18][19][20][21][22][23][24] and found to be in good agreement with experimental results [25][26][27][28][29]. The quantum Kibble-Zurek (QKZ) scaling laws, on the other hand, have been studied in [10][11][12][13]24].…”

Section: Introductionmentioning

confidence: 58%

Quantum Kibble-Zurek physics in long-range transverse-field Ising models

2019

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We analyze the quantum phase transitions taking place in a one-dimensional transverse field Ising model with long-range couplings that decay algebraically with distance. We are interested in the Kibble-Zurek universal scaling laws emerging in non-equilibrium dynamics and in the potential for the unambiguous observation of such behavior in a realistic experimental setup based on trapped ions. To this end, we determine the phase diagram of the model and the critical exponents characterizing its quantum phase transitions by means of density-matrix renormalization group calculations and finite-size scaling theory, which allows us to obtain good estimates for different range of ferro-and antiferromagnetic interactions. Beyond critical equilibrium properties, we tackle a non-equilibrium scenario in which quantum Kibble-Zurek scaling laws may be retrieved. Here it is found that the predicted non-equilibrium universal behavior, i.e. the scaling laws as a function of the quench rate and critical exponents, can be observed in systems comprising an experimentally feasible number of spins. Finally, a scheme is introduced to simulate the algebraically decaying couplings accurately by means of a digital quantum simulation with trapped ions. Our results suggest that quantum Kibble-Zurek physics can be explored and observed in state-of-the-art experiments with trapped ions realizing long-range Ising models.

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“…We hope that the results presented here will find direct comparison with previous work, particularly with regards to ions confined in traps [1][2][3][4][5][6][7][8][9] as well as assemblies of magnetic particles in a channels [17]. This work should also be relevant to other systems in which buckling is a key feature: for example localised buckling has recently been observed in experiments involving an expanding (growing) elastic beam pinned to a substrate [18].…”

Section: P-4mentioning

confidence: 71%

“…In detail they depend on the interactions between the particles, the confining potential and any boundary conditions at the end of a finite sample. Previous observations have been made with ion traps [2][3][4][5][6][7][8].…”

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confidence: 99%

Equilibrium configurations of hard spheres in a cylindrical harmonic potential

Winkelmann¹,

Mughal²,

Weaire³

et al. 2019

EPL

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PACS 45.70.-n -Granular systems PACS 47.57.-s -Complex fluids and colloidal systems PACS 61.50.Ah -Theory of crystal structure, crystal symmetry; calculations and modelingAbstract -A line of hard spheres confined by a transverse harmonic potential, with hard walls at its ends, exhibits a variety of buckled structures as it is compressed longitudinally. Here we show that these may be conveniently observed in a rotating liquid-filled tube (originally introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274 (2017)] to assemble ordered three dimensional structures at higher compressions). The corresponding theoretical model is transparent and easily investigated numerically, as well as by analytic approximations. Hence we explore a wide range of predicted structures occurring via bifurcation, of which the stable ones are also observed in our experiments. Qualitatively similar structures have previously been found in trapped ion systems.

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Formation of helical ion chains

Cited by 42 publications

References 65 publications

Universality in the Dynamics of Second-Order Phase Transitions

Universality in the Dynamics of Second-Order Phase Transitions

Quantum Kibble-Zurek physics in long-range transverse-field Ising models

Equilibrium configurations of hard spheres in a cylindrical harmonic potential

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