Complex Density Wave Orders and Quantum Phase Transitions in a Model of Square-Lattice Rydberg Atom Arrays

Abstract

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]

Quantum phases of Rydberg atoms on a kagome lattice

“…As δ/Ω is tuned toward large positive values, the fraction of atoms in |r increases but the geometric arrangement of the excitations is subject to the constraints stemming from the interactions between nearby Rydberg atoms. This competition between the detuning and the previously identified blockade mechanism results in socalled "Rydberg crystals" (37), in which Rydberg excitations are arranged regularly across the array, engendering symmetrybroken density-wave ordered phases (19). On the kagome lattice, the simplest such crystal that can be formed-while respecting the blockade restrictions-is constructed by having an atom in the excited state on exactly one out the three sublattices in the kagome unit cell.…”

“…Although both phases break the same symmetry, the stripe ordering is distinguished from the nematic by a substantial and equal density on two sublattices of the unit cell. The formation of these stripes can be attributed to quantum fluctuations (19), which help stabilize the phase in a narrow window as follows. The system optimizes the geometric packing in a configuration where all atoms on one sublattice are in the ground state, whereas those on the other two sublattices are each in a quantum superposition formed by the ground state with a coherent admixture of the Rydberg state.…”

“…In the search for QSLs, systems with frustration (11,12)which can be either of geometric origin or induced by furtherneighbor couplings-constitute a promising avenue of exploration. Motivated by this consideration, here, we investigate many-body states of neutral atom arrays, interacting via laser excitation to atomic Rydberg states (13), that have been found to display a variety of interesting correlated quantum phases in one and two dimensions (14)(15)(16)(17)(18)(19)(20). Specifically, we examine a realistic model of Rydberg atoms on the kagome lattice and perform density-matrix renormalization group (DMRG) computations to establish its rich phase diagram as a function of laser parameters and atomic distances.…”

Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain

“…Motivated by experimental progress in realizing two dimensional (2d) Rydberg atom array [58][59][60], in this work we show that the 2d effective model describing the nearest-neighbor Rydberg-blockaded array also exhibits scar states and anomalous dynamics, with both similarities and important differences from the 1d model. For the model on a square lattice with periodic boundary conditions, we find exponentially many exact scar eigenstates at finite energy density which are remarkably simply product states of dimers [valence bond solids (VBS)].…”

Raman sideband cooling in optical tweezer arrays for Rydberg dressing

“…The full control over spatial geometries and the mutual interactions makes Rydberg atoms in optical tweezers an excellent platform for quantum information [9][10][11][12][13][14][15][16][17][18][19][20], quantum simulation [21][22][23][24][25] and quantum metrology [8,[26][27][28][29]. Rydberg arrays naturally feature state dependent interactions, a fact that renders them particularly suited for implementing spin models, in which many fundamental many-body problems can be studied [30][31][32][33][34][35][36][37][38][39][40]. In contrast to direct excitation to Rydberg states, interactions between ground states can be induced by admixing Rydberg states via near-resonant coupling.…”