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Transport induced melting of crystals of Rydberg dressed atoms in a one dimensional lattice

Achim Lauer, Dominik Muth, Michael Fleischhauer

Published Aug 15, 2016• 16 citations
OpenAlex

Abstract

Abstract. We discuss the many-body physics of an ensemble of Rydberg dressed atoms with van der Waals dipole-dipole interactions in a one-dimensional lattice. Using a strong coupling expansion and numerical density-matrix renormalisation group simulations, we calculate the many-body phase diagram. A devil’s staircase structure emerges with Mott-insulating phases at any rational filling fraction. Closed analytic expressions are given for the phase boundaries in second order of the tunnelling amplitude and shown to agree very well with the numerical results. The transition point where the incompressible phases melt due to the kinetic energy term depends strongly on the denominator of the filling fraction and varies over many orders of magnitude between different phases.

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arXiv:1004.5595•Apr 30, 2010•0 citations
Abstract. We discuss the many-body physics of an ensemble of Rydberg dressed atoms with van der Waals dipole-dipole interactions in a one-dimensional lattice. Using a strong coupling expansion and numerical density-matrix renormalisation group simulations, we calculate the many-body phase diagram. A devil’s staircase structure emerges with Mott-insulating phases at any rational filling fraction. Closed analytic expressions are given for the phase boundaries in second order of the tunnelling amplitude and shown to agree very well with the numerical results. The transition point where the incompressible phases melt due to the kinetic energy term depends strongly on the denominator of the filling fraction and varies over many orders of magnitude between different phases.
We discuss the many-body physics of an ensemble of Rydberg dressed atoms with van der Waals dipole–dipole interactions in a one-dimensional lattice. Using a strong coupling expansion and numerical density-matrix renormalization group simulations, we calculate the many-body phase diagram. A devil's staircase structure emerges with Mott-insulating phases at any rational filling fraction. Closed analytic expressions are given for the phase boundaries in second order of the tunneling amplitude and are shown to agree very well with the numerical results. The transition point where the incompressible phases melt due to the kinetic energy term depends strongly on the denominator of the filling fraction and varies over many orders of magnitude between different phases.
We describe the zero-temperature phase diagram of a model 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.
Competing short- and long-range interactions represent distinguished ingredients for the formation of complex quantum many-body phases. Their study is hard to realize with conventional quantum simulators. In this regard, Rydberg atoms provide an exception as their excited manifold of states have both density-density and exchange interactions whose strength and range can vary considerably. Focusing on one-dimensional systems, we leverage the Van der Waals and dipole-dipole interactions of the Rydberg atoms to obtain the zero-temperature phase diagram for a uniform chain and a dimer model. For the uniform chain, we can influence the boundaries between ordered phases and a Luttinger liquid phase. For the dimerized case, a new type of bond-order-density-wave phase is identified. This demonstrates the versatility of the Rydberg platform in studying physics involving short- and long-ranged interactions simultaneously.
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 interstate 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 devil's staircase structure which one might associate with transitions in the classical limit. The melting through exchange interactions is shown to also proceed in a steplike fashion, in the case of small crystals, due to the proliferation of Rydberg spin waves.
Quantum fluctuations in frustrated systems can lead to the emergence of complex many-body phases. However, the role of quantum fluctuations in frustration-free lattices is less explored and could provide an interesting avenue for exploring new physics, and perhaps is easier to realize compared to frustrated lattice systems. Using Rydberg atoms with tunable interactions as a platform, we leverage strong van der Waals interactions and obtain a constrained model in one dimension with nonlocal fluctuations given by dipolar interactions alongside local fluctuations. The combined effect of such processes leads to intrinsically quantum-ordered Rydberg crystals through the order-by-disorder mechanism. Finite-size analyses indicate that combined fluctuations drive the transition from disordered to ordered phases, contrary to the expected direction. We provide a theoretical description to understand the physics of order-by-disorder in one-dimensional systems, which are typically seen only in higher dimensions.
We consider a single-component gas of dipolar bosons confined in a one-dimensional optical lattice, where the dipoles are aligned such that the long-ranged dipolar interactions are maximally repulsive. In the limit of zero inter-site hopping and sufficiently large on-site interaction, the phase diagram is a complete devil's staircase for filling fractions between 0 and 1: every commensurate state at a rational filling is stable over a finite interval in chemical potential, and for every chemical potential the system is in a gapped commensurate phase. We perturb away from this limit in two experimentally motivated directions involving the addition of hopping and a reduction of the onsite interaction. The addition of hopping alone yields a phase diagram, which we compute in perturbation theory in the hopping, where the commensurate Mott phases now compete with the superfluid. We capture the physics of the Mott-superfluid phase transitions via bosonization. In a finite trap, we argue using an LDA and simulated annealing that this results in regions of commensurate states separated by patches with dominant superfluid correlations. Further softening of the onsite interaction yields alternative commensurate states with double occupancies which can form a devil's staircase of their own; we describe these states and discuss the possible transitions between them. Adding a hopping term in this case produces one-dimensional "supersolids" which simultaneously exhibit discrete broken symmetries and superfluidity. The contents of this work was first published as a chapter in the doctoral thesis `On Exotic Orders in Strongly Correlated Systems' (Princeton University, 09/09, supervised by S. L. Sondhi), and constitutes a considerably more detailed version of [PRB 80: 174519 (2009)].