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We investigate the quantum melting of one dimensional crystals that are realized in an atomic lattice in which ground state atoms are laser excited to two Rydberg states. We focus on a regime where both, intra- and inter-state density-density interactions as well as coherent exchange interactions contribute. We determine stable crystalline phases in the classical limit and explore their melting under quantum fluctuations introduced by the excitation laser as well as two-body exchange. We find that within a specific parameter range quantum fluctuations introduced by the laser can give rise to a devils staircase structure which one might associate with transitions in the classical limit. The melting through exchange interactions is shown to also proceed in a step-like fashion, in case of small crystals, due to the proliferation of Rydberg spinwaves.
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Spin models are the prime example of simplified manybody Hamiltonians used to model complex, real-world strongly correlated materials. However, despite their simplified character, their dynamics often cannot be simulated exactly on classical computers as soon as the number of particles exceeds a few tens. For this reason, the quantum simulation of spin Hamiltonians using the tools of atomic and molecular physics has become very active over the last years, using ultracold atoms or molecules in optical lattices, or trapped ions. All of these approaches have their own assets, but also limitations. Here, we report on a novel platform for the study of spin systems, using individual atoms trapped in two-dimensional arrays of optical microtraps with arbitrary geometries, where filling fractions range from 60 to 100% with exact knowledge of the initial configuration. When excited to Rydberg D-states, the atoms undergo strong interactions whose anisotropic character opens exciting prospects for simulating exotic matter. We illustrate the versatility of our system by studying the dynamics of an Ising-like spin-1/2 system in a transverse field with up to thirty spins, for a variety of geometries in one and two dimensions, and for a wide range of interaction strengths. For geometries where the anisotropy is expected to have small effects we find an excellent agreement with ab-initio simulations of the spin-1/2 system, while for strongly anisotropic situations the multilevel structure of the D-states has a measurable influence. Our findings establish arrays of single Rydberg atoms as a versatile platform for the study of quantum magnetism.
A defining property of particles is their behavior under exchange. In two dimensions anyons can exist which, opposed to fermions and bosons, gain arbitrary relative phase factors or even undergo a change of their type. In the latter case one speaks of non-Abelian anyons - a particularly simple and aesthetic example of which are Fibonacci anyons. They have been studied in the context of fractional quantum Hall physics where they occur as quasiparticles in the $k=3$ Read-Rezayi state, which is conjectured to describe a fractional quantum Hall state at filling fraction $ u=12/5$. Here we show that the physics of interacting Fibonacci anyons can be studied with strongly interacting Rydberg atoms in a lattice, when due to the dipole blockade the simultaneous laser excitation of adjacent atoms is forbidden. The Hilbert space maps then directly on the fusion space of Fibonacci anyons and a proper tuning of the laser parameters renders the system into an interacting topological liquid of non-Abelian anyons. We discuss the low-energy properties of this system and show how to experimentally measure anyonic observables.
Over the last decade, systems of individually-controlled neutral atoms, interacting with each other when excited to Rydberg states, have emerged as a promising platform for quantum simulation of many-body problems, in particular spin systems. Here, we review the techniques underlying quantum gas microscopes and arrays of optical tweezers used in these experiments, explain how the different types of interactions between Rydberg atoms allow a natural mapping onto various quantum spin models, and describe recent results that were obtained with this platform to study quantum many-body physics.
We theoretically investigate the dynamics of a gas of strongly interacting Rydberg atoms subject to a time-domain Ramsey interferometry protocol. The many-body dynamics is governed by an Ising-type Hamiltonian with long range interactions of tunable strength. We analyze and model the contrast degradation and phase accumulation of the Ramsey signal and identify scaling laws for varying interrogation times, ensemble densities, and ensemble dimensionalities.
The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a two-dimensional cloud of atoms dressed to Rydberg states, where excitations propagate by dipolar exchange interaction, while the Rydberg blockade phenomenon naturally gives rise to a characteristic length scale, suppressing the hopping on short distances. Then, the system becomes independent of the atoms spatial arrangement and can be described by a continuum model. We demonstrate the appearance of a topological band structure in the continuum characterized by a Chern number $C=2$ and show that edge states appear at interfaces tunable by the atomic density.
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