Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals

Pyka, Karsten; Keller, Jonas; Partner, Heather L.; Nigmatullin, Ramil; Burgermeister, T.; Meier, Dennis; Kuhlmann, Kristijan; Retzker, Alex; Plenio, Martin B.; Zurek, Wojciech H.; Campo, Adolfo del; Mehlstäubler, T. E.

doi:10.1038/ncomms3291

Cited by 283 publications

(265 citation statements)

References 43 publications

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“…Schemes for creating polariton topological insulators have been proposed [33][34][35][36]. While KZM, as a universal mechanism, has already been widely studied in various systems sharing some common properties with our proposal, such as zigzag ionic chains [37][38][39][40], where the phase transition and the topology correspond to physical arrangement of atoms, none of these possess the same key ingredients. A topologically non-trivial polaritonic chain therefore appears as an ideal system to study the complex interplay of topological ordering and KZM [41].…”

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confidence: 99%

Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

2016

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We consider a zigzag chain of coupled micropillar cavities, taking into account the polarization of polariton states. We show that the TE-TM splitting of photonic cavity modes yields topologically protected polariton edge states. During the strongly non-adiabatic process of polariton condensation, the Kibble-Zurek mechanism leads to a random choice of polarization, equivalent to dimerization of polymer chains. We show that dark-bright solitons appear as domain walls between polarization domains, analogous to the Su-Schrieffer-Heeger solitons in polymers. The soliton density scales as a power law with respect to the quenching parameter.As initially shown by Kibble [1] for the expansion and cooling of the early Universe, and then for liquid helium by Zurek [2], a system undergoing a second-order phase transition on a finite timescale develops domains with independent order parameters. The Kibble-Zurek mechanism (KZM) allows predicting the typical size of the domains and, therefore, the densities of the topological defects on their boundaries. Their scaling as a function of the quench rate is given by a power law, with the critical exponent of the transition being determined by its universality class [3].A very relevant system to study the KZM are the quantum fluids such as atomic Bose-Einstein condensates (BECs) formed by cooling. Indeed, quantum fluids support topological defects [4,5], their most famous example being a quantum vortex, which, contrary to a classical vortex, like a tornado, cannot disappear "by itself", via a continuous transformation. This property is due to the difference in vortex and ground state topologies, which is guaranteed by the irrotational nature of the fluid described by a complex wavefunction [6]. The nonadiabatic cooling of such a fluid allows the development of topological defects obeying the KZM scaling, as confirmed by experiments [7] and also predicted for multicomponent BECs [8,9]. However, solitons in 1D and half-vortices in 2D spinor BECs [4,5,10] are only quasitopological defects. Indeed, a dark soliton transforms into a grey and eventually disappears by simple acceleration, and a half-vortex can be unwound by a divergent magnetic field. Another system of interest to study the KZM are cavity exciton-polariton quantum fluids [11,12]. Because of the finite polariton lifetime, polariton condensation can be an out-of-equilibrium process driven by the condensation kinetics rather than by thermodynamics [12,13]. As previously pointed out [14,15], the establishment of a steady state by non-resonant pumping in an initially empty system cannot be an adiabatic process and is therefore equivalent to a quenching of the parameters of the system, leading to the appearance of topological defects.Another class of systems which possess topologically protected states are periodic lattices with topologically non-trivial band structures characterized by non-zero Chern numbers, or Zak phase, depending on their dimensionality. The most well-known examples of such systems are the topological insu...

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confidence: 99%

Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

2016

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“…Indeed, while some experiments aimed at measuring defect scaling laws were realized in systems that are well approximated as large and homogeneous systems, e.g. liquid crystals [9][10][11], liquid Helium [12,13], superconducting films [14,15] and multiferroics [16,17], the consequences of inhomogeneity and finite-size effects cannot be ignored in recent experiments on Bose-Einstein condensates [18][19][20] and ion crystals, [21,22] which can exhibit non-standard scaling. Hence it is important to develop an approach that does not appeal to physical intuition but exclusively relies on mathematical arguments in its derivation of scaling laws.…”

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Universality in the Dynamics of Second-Order Phase Transitions

2016

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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 in itself is a remarkable observation as a priori there is no reason to expect that nonequilibrium properties are fully determined by equilibrium properties only. Recently, three experiments have measured the Kibble-Zurek mechanism in trapped ions [30][31][32] and verified the predicted KibbleZurek scaling. Present and future experiments as well as theoretical works is expected to study the properties of these kinks [26,33].…”

Section: Martin B Plenio and Alex Retzkermentioning

confidence: 99%

Ion Traps as a testbed of classical and quantum statistical mechanics

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Annalen der Physik

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The development of statistical mechanics over the last century represents a major advance in the Natural Sciences. It is capable of describing a wide range of phenomena including the properties of phase transitions by reducing the complexity of quantum-many-body systems to simple general principles rooted in statistical methods that hold true in macroscopic systems. These principles apply to a broad range of physical theories, encompassing phenomena that are for example governed by classical, relativistic or quantum physics. While many of these predictions have been confirmed experimentally, the exploration, under highly controlled conditions, of the statistical mechanics of mesoscopic systems and the theoretical prediction of their behavior does still represent a challenge for both theory and experiment. A new avenue towards the controlled exploration of the classical and quantum statistical mechanics of mesoscopic systems has opened up

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Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals

Cited by 283 publications

References 43 publications

Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

Kibble-Zurek Mechanism in Topologically Nontrivial Zigzag Chains of Polariton Micropillars

Universality in the Dynamics of Second-Order Phase Transitions

Ion Traps as a testbed of classical and quantum statistical mechanics

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