String order in dipole-blockaded quantum liquids

We study the quantum melting of quasi-one-dimensional lattice models in which the dominant energy scale is given by a repulsive dipolar interaction. By constructing an effective low-energy theory, we show that the melting of crystalline phases can occur into two distinct liquid phases, having the same algebraic decay of density-density correlations, but showing a different non-local correlation function expressing string order. We present possible experimental realizations using ultracold atoms and molecules, introducing an implementation based on resonantly driven Rydberg atoms that offers additional benefits compared to a weak admixture of the Rydberg state.Comment: 6 pages, 4 figure

An Operational Definition of Topological Order

The unrivaled robustness of topologically ordered states of matter against perturbations has immediate applications in quantum computing and quantum metrology, yet their very existence poses a challenge to our understanding of phase transitions. In particular, topological phase transitions cannot be characterized in terms of local order parameters, as it is the case with conventional symmetry-breaking phase transitions. Currently, topological order is mostly discussed in the context of nonlocal topological invariants or indirect signatures like the topological entanglement entropy. However, a comprehensive understanding of what actually constitutes topological order is still lacking. Here we show that one can interpret topological order as the ability of a system to perform topological error correction. We find that this operational approach corresponding to a measurable observable does not only lay the conceptual foundations for previous classifications of topological order, but it can also be applied to hitherto inaccessible problems, such as the question of topological order for mixed quantum states arising in open quantum systems. We demonstrate the existence of topological order in open systems and their phase transitions to topologically trivial states, including topological criticality. Our results demonstrate the viability of topological order in nonequilibrium quantum systems and thus substantially broaden the scope of possible technological applications. We therefore expect our work to be a starting point for many future theoretical and experimental investigations, such as the application of our approach to fracton or Floquet topological order, or the direct experimental realization of the error correction protocol presented in our work for the development of future quantum technological devices.Comment: 7 pages, 5 figure

Time evolution of open quantum many-body systems

We establish a generic method to analyze the time evolution of open quantum many-body systems. Our approach is based on a variational integration of the quantum master equation describing the dynamics and naturally connects to a variational principle for its nonequilibrium steady state. We successfully apply our variational method to study dissipative Rydberg gases, finding excellent quantitative agreement with small-scale simulations of the full quantum master equation. We observe that correlations related to non-Markovian behavior play a significant role during the relaxation dynamics towards the steady state. We further quantify this non-Markovianity and find it to be closely connected to an information-theoretical measure of quantum and classical correlations.Comment: 5+3 pages, 8 figure

Dissipative Preparation of Antiferromagnetic Order in the Fermi-Hubbard Model

The Fermi-Hubbard model is one of the key models of condensed matter physics, which holds a potential for explaining the mystery of high-temperature superconductivity. Recent progress in ultracold atoms in optical lattices has paved the way to studying the model's phase diagram using the tools of quantum simulation, which emerged as a promising alternative to the numerical calculations plagued by the infamous sign problem. However, the temperatures achieved using elaborate laser cooling protocols so far have been too high to show the appearance of antiferromagnetic and superconducting quantum phases directly. In this work, we demonstrate that using the machinery of dissipative quantum state engineering, one can efficiently prepare antiferromagnetic order in present-day experiments with ultracold fermions. The core of the approach is to add incoherent laser scattering in such a way that the antiferromagnetic state emerges as the dark state of the driven-dissipative dynamics. In order to elucidate the development of the antiferromagnetic order we employ two complementary techniques: Monte Carlo wave function simulations for small systems and a recently proposed variational method for open quantum systems, operating in the thermodynamic limit. The controlled dissipation channels described in this work are straightforward to add to already existing experimental setups.Comment: 9 pages, 5 figure