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arXiv:1809.05540 · Nature

Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator

Alexander Keesling, Ahmed Omran, Harry Levine, Hannes Bernien, Hannes Pichler, Soonwon Choi, Rhine Samajdar, Sylvain Schwartz, Pietro Silvi, Subir Sachdev A, P. Zoller, Manuel Endres, Markus Greiner, Vladan Vuletić, Mikhail D. Lukin

Published Apr 1, 2019• 533 citations
arXivHTMLPDF
DOI
10.1038/s41586-019-1070-1

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The experimental realization of the quantum Kibble-Zurek mechanism in arrays of trapped Rydberg atoms has brought the problem of commensurate-incommensurate transition back into the focus of active research. Relying on equilibrium simulations of finite intervals, direct chiral transitions at the boundary of the period-3 and period-4 phases have been predicted. Here, we study how these chiral transitions can be diagnosed experimentally with critical dynamics. We demonstrate that chiral transitions can be distinguished from the floating phases by comparing Kibble-Zurek dynamics on arrays with different numbers of atoms. Furthermore, by sweeping in the opposite direction and keeping track of the order parameter, we identify the location of conformal points. Finally, combining forward and backward sweeps, we extract all critical exponents characterizing the transition.
Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics are governed by the universal properties associated with the QPT. The resulting quantum criticality has been explored by probing linear response for systems near thermal equilibrium. While time dependent phenomena associated with classical phase transitions have been studied in various scientific fields, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is of fundamental importance both for exploring novel approaches to quantum information processing and realizing exotic new phases of matter. Here, we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations while crossing the QPT at variable speeds, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality, and observe corrections beyond simple QKZM predictions. This approach is subsequently used to investigate novel QPTs associated with chiral clock model providing new insights into exotic systems, and opening the door for precision studies of critical phenomena and applications to quantum optimization.
The Kibble–Zurek (KZ) mechanism has been extensively studied in various second-order phase transitions, yet the case of tricriticality—the point where second-order phase transition lines terminate—remains experimentally elusive. Here, we theoretically propose probing KZ scaling at tricritical points using Rydberg atom arrays arranged as two- and three-leg ladders, which realize the tricritical Ising and tricritical Potts universality classes. By slowly ramping the Rabi frequency and detuning, we extract two relevant tricritical exponents, ν and ν', both via conventional paths from the disordered to the ordered phase and via “tangential” paths confined entirely within the disordered phase. At faster speeds, ramping dynamics go beyond the standard KZ paradigm: data collapse analysis using the parent critical exponents (rather than the tricritical ones) reveals renormalization group flows toward the adjacent second-order critical line, and we identify it as a dynamical analog of Zamolodchikov’s c-theorem. Our protocol is readily implementable on existing Rydberg quantum simulators. This provides a direct route to measuring distinct tricritical exponents which can reveal an emergent spacetime supersymmetry constraint 1/ν − 1/ν' = 1. Moreover, this work deepens our theoretical understanding and opens new avenues for exploring beyond-KZ quantum dynamics with rich renormalization group structure. The Kibble-Zurek mechanism describes universal dynamics near criticality. Here, the authors extend it to tricriticality using Rydberg atom ladders, proposing ramping protocols that measure two tricritical exponents and reveal emergent supersymmetry and dynamical renormalization group flow.