No abstract

Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations [1]. 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. While time-dependent phenomena associated with classical, thermally driven phase transitions have been extensively studied in systems ranging from the early universe to Bose Einstein Condensates [2-5], understanding critical real-time dynamics in isolated, non-equilibrium quantum systems is an outstanding challenge [6]. 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, we experimentally verify the quantum Kibble-Zurek mechanism (QKZM) [7-9] for an Ising-type QPT, explore scaling universality, and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models [10,11], providing new insights into exotic systems that have not been understood previously, and opening the door for precision studies of critical phenomena, simulations of lattice gauge theories [12,13] and applications to quantum optimization [14,15].The celebrated Kibble-Zurek mechanism [2, 3] describes nonequilibrium dynamics and the formation of topological defects in a second-order phase transition driven by thermal fluctuations, and has been experimentally verified in a wide variety of physical systems [4,5]. Recently, the concepts underlying the Kibble-Zurek description have been extended to the quantum regime [7][8][9]. Here, the typical size of the correlated regions, ξ, after a dynamical sweep across the QPT scales as a power-law Critical point gc Control parameter g Correlation length » Phase 1 Phase 2 » » jg ¡ gcj ¡º Time ¿ » jg ¡ gcj ¡zº Fast ramp Slow ramp 0 1 2 3 4 5 Detuning ¢= 1 2 3 4 Interaction range RB=a ²±²±²±²±²±²±² ²±±²±±²±±²±±² ²±±±²±±±²±±±² ℤ2 ℤ3 ℤ4 t ¢ -0.05 0 0.05 -0.1 0 0.1 Density-density correlator G(r) 0 4 8 12 16 20 Distance r (sites) -0.2 -0.1 0 0.1 a b c d Ω Ω FIG. 1: Quantum Kibble-Zurek mechanism (QKZM) and phase diagram. a, Illustration of the QKZM. As the control parameter approaches its critical value, the response time, τ , given by the inverse energy gap of the system, diverges. When the temporal distance to the critical point becomes equal to the response time, as marked by red crosses, the correlation length, b, stops growing due to nonadiabatic excitations. c, Numerically calculated ground-state phase diagram. Circles (diamonds) denote numerically obtained points along the phase boundaries calculated using (infinite-size) Density-Matrix Renormalization Group techniques (Methods). The shaded regions are a guide to the eye. Dashed lines show the experimental trajectories across the phase transitions determined by the pulse diagram shown...

Synthesizing topological order Topologically ordered matter exhibits long-range quantum entanglement. However, measuring this entanglement in real materials is extremely tricky. Now, two groups take a different approach and turn to synthetic systems to engineer the topological order of the so-called toric code type (see the Perspective by Bartlett). Satzinger et al . used a quantum processor to study the ground state and excitations of the toric code. Semeghini et al . detected signatures of a toric code–type quantum spin liquid in a two-dimensional array of Rydberg atoms held in optical tweezers. —JS

Recent experiments on a one-dimensional chain of trapped alkali atoms [Bernien et al., Nature 551, 579 (2017)] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous Z3 symmetry breaking is described by a constrained model of hard-core bosons proposed by Fendley et al. [Phys. Rev. B 69, 075106 (2004)]. By symmetry arguments, the transition is expected to be in the universality class of the Z3 chiral clock model with parameters preserving both time-reversal and spatial-inversion symmetries. We study the nature of the order-disorder transition in these models, and numerically calculate its critical exponents with exact diagonalization and density-matrix renormalization group techniques. We use finite-size scaling to determine the dynamical critical exponent z and the correlation length exponent ν. Our analysis presents the only known instance of a strongly coupled generic transition between gapped states with z = 1, implying an underlying nonconformal critical field theory.

We describe the zero-temperature phase diagram of a two-dimensional square-lattice array of neutral atoms, excited into Rydberg states and interacting via strong van der Waals interactions. Using the density-matrix renormalization group algorithm, we map out the phase diagram and obtain a rich variety of phases featuring complex density wave orderings, upon varying lattice spacing and laser detuning. While some of these phases result from the classical optimization of the van der Waals energy, we also find intrinsically quantum-ordered phases stabilized by quantum fluctuations. These phases are surrounded by novel quantum phase transitions, which we analyze by finite-size scaling numerics and Landau theories. Our work highlights Rydberg quantum simulators in higher dimensions as promising platforms to realize exotic many-body phenomena. arXiv:1910.09548v1 [cond-mat.str-el]