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Register a new userQuantum phases of Rydberg atoms on a kagome lattice
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We analyze the zero-temperature phases of an array of neutral atoms on the kagome lattice, interacting via laser excitation to atomic Rydberg states. Density-matrix renormalization group calculations reveal the presence of a wide variety of complex solid phases with broken lattice symmetries. In addition, we identify a novel regime with dense Rydberg excitations that has a large entanglement entropy and no local order parameter associated with lattice symmetries. From a mapping to the triangular lattice quantum dimer model, and theories of quantum phase transitions out of the proximate solid phases, we argue that this regime could contain one or more phases with topological order. Our results provide the foundation for theoretical and experimental explorations of crystalline and liquid states using programmable quantum simulators based on Rydberg atom arrays.
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Two-dimensional Rydberg atoms are modeled at low temperatures by means of the classical Monte Carlo method. The Coulomb repulsion of charged ions competing with the repulsive van der Waals long-range tail is modeled by a number of interaction potentials. We find that under specific conditions the usual triangular crystal becomes unstable with respect to more exotic lattices such as Kagome, flower, molecular crystal and rectangular chain packings. Ground-state configurations are obtained by means of the annealing procedure and their stability is additionally studied by the normal modes analysis. While commonly the square lattice is mechanically unstable due to softening of the shear modulus, we were able to find a specific set of parameters for which the square lattice can be made stable.
Quantum spin ice represents a paradigmatic example on how the physics of frustrated magnets is related to gauge theories. In the present work we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in optical lattices. The relevant interactions are obtained by weakly admixing van der Waals interactions between laser admixed Rydberg states to the atomic ground state atoms, exploiting the strong angular dependence of interactions between Rydberg p-states together with the possibility of designing step-like potentials. This allows us to implement Abelian gauge theories in a series of geometries, which could be demonstrated within state of the art atomic Rydberg experiments. We numerically analyze the family of resulting microscopic Hamiltonians and find that they exhibit both classical and quantum order by disorder, the latter yielding a quantum plaquette valence bond solid. We also present strategies to implement Abelian gauge theories using both s- and p-Rydberg states in exotic geometries, e.g. on a 4-8 lattice.
A large number of symmetry-protected topological (SPT) phases have been hypothesized for strongly interacting spin-1/2 systems in one dimension. Realizing these SPT phases, however, often demands fine-tunings hard to reach experimentally. And the lack of analytical solutions hinders the understanding of their many-body wave functions. Here we show that two kinds of SPT phases naturally arise for ultracold polar molecules confined in a zigzag optical lattice. This system, motivated by recent experiments, is described by a spin model whose exchange couplings can be tuned by an external field to reach parameter regions not studied before for spin chains or ladders. Within the enlarged parameter space, we find the ground state wave function can be obtained exactly along a line and at a special point, for these two phases respectively. These exact solutions provide a clear physical picture for the SPT phases and their edge excitations. We further obtain the phase diagram by using infinite time-evolving block decimation, and discuss the phase transitions between the two SPT phases and their experimental signatures.
In condensed matter, it is often difficult to untangle the effects of competing interactions, and this is especially problematic for superconductors. Quantum simulators may help: here we show how exploiting the properties of highly excited Rydberg states of cold fermionic atoms in a bilayer lattice can simulate electron-phonon interactions in the presence of strong correlation - a scenario found in many unconventional superconductors. We discuss the core features of the simulator, and use numerics to compare with condensed matter analogues. Finally, we illustrate how to achieve a practical, tunable implementation of the simulation using painted spot potentials.
We present a brief overview of the phases and dynamics of ultracold bosons in an optical lattice in the presence of a tilt. We begin with a brief summary of the possible experimental setup for generating the tilt. This is followed by a discussion of the effective low-energy model for these systems and its equilibrium phases. We also chart the relation of this model to the recently studied system of ultracold Rydberg atoms. Next, we discuss the non-equilibrium dynamics of this model for quench, ramp and periodic protocols with emphasis on the periodic drive which can be understood in terms of an analytic, albeit perturbative, Floquet Hamiltonian derived using Floquet perturbation theory (FPT). Finally, taking cue from the Floquet Hamiltonian of the periodically driven tilted boson chain, we discuss a spin model which exhibits Hilbert space fragmentation and exact dynamical freezing for wide range of initial states.
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