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arXiv:2202.04902 · Physical Review Research

Composite spin approach to the blockade effect in Rydberg atom arrays

Lei Pan, Hui Zhai

Published Sep 6, 2022• 21 citations
arXivHTMLPDF

Abstract

The Rydberg blockade induces strongly correlated many-body effects in Rydberg atom arrays, including rich ground-state phases and many-body scar states in the excitation spectrum.In this Letter, we propose a composite spin representation that can provide a unified description for major features in this system.The composite spin combines Rydberg excitation and the auxiliary fermions, which are introduced to implement the Rydberg blockade constraint automatically.First, we focus on the PXP model describing one-dimensional arrays with the Rydberg blocking radius being a lattice spacing.Using composite spins, the ground state is simply a polarized product state of composite spins, and the magnon excitations of these composite spins can accurately describe the many-body scar states and signal the quantum phase transition driven by detuning.Then, we show that Rydberg atom arrays with different blocking radii can share a universal description in terms of the composite spin representation, and the difference between different blockade radii can be absorbed in the formation of composite spins.Hence, our scheme provides a universal physical picture of the blockade effect in Rydberg atom arrays.

DOI
10.1103/physrevresearch.4.l032037

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•Jul 8, 2015•0 citations
The Rydberg blockade induces strongly correlated many-body effects in Rydberg atom arrays, including rich ground-state phases and many-body scar states in the excitation spectrum.In this Letter, we propose a composite spin representation that can provide a unified description for major features in this system.The composite spin combines Rydberg excitation and the auxiliary fermions, which are introduced to implement the Rydberg blockade constraint automatically.First, we focus on the PXP model describing one-dimensional arrays with the Rydberg blocking radius being a lattice spacing.Using composite spins, the ground state is simply a polarized product state of composite spins, and the magnon excitations of these composite spins can accurately describe the many-body scar states and signal the quantum phase transition driven by detuning.Then, we show that Rydberg atom arrays with different blocking radii can share a universal description in terms of the composite spin representation, and the difference between different blockade radii can be absorbed in the formation of composite spins.Hence, our scheme provides a universal physical picture of the blockade effect in Rydberg atom arrays.
We find exponentially many exact quantum many-body scar states in a two-dimensional PXP model---an effective model for a two-dimensional Rydberg atom array in the nearest-neighbor blockade regime. Such scar states are remarkably simple valence bond solids despite being at an effectively infinite temperature, and thus strongly violate the eigenstate thermalization hypothesis. For a particular boundary condition, such eigenstates have integer-valued energies. Moreover, certain charge-density-wave initial states give rise to strong oscillations in the Rydberg excitation density after a quantum quench and towerlike structures in their overlaps with eigenstates.
We discuss a Rydberg atom chain with a tunable blockade radius from the gauge theoretic perspective. When the blockade radius is one lattice spacing, this system can be formulated in terms of the PXP model, and there is a Z2{\mathbb{Z}}_{2}Z2​ Ising phase transition known to be equivalent to a confinement--deconfinement transition in a gauge theory, the lattice Schwinger model. Further increasing the blockade radius, one can add a next-nearest neighbor (NNN) interaction into the PXP model. We discuss the interpretation of the NNN interaction in terms of the gauge theory and how a finite NNN interaction alters the deconfinement behavior and propose a corresponding experimental protocol. When the blockade radius reaches two lattice spacing, the model reduces to the PPXPP model. A novel gauge theory equivalent to the PPXPP model is formulated, and the phases in the two formulations are delineated. These results are readily explored experimentally in Rydberg quantum simulators.
We develop an analytical approach for the description of quantum many-body scars in PXP models. We show that the scarred dynamics in the PXP model on a complete bipartite graph can be interpreted as a one-dimensional chiral scattering problem, and solve this problem analytically. The insights from this analysis allow us to predict that dynamical signatures of scars in PXP models can be enhanced by spin squeezing the initial states. We show numerically that this stabilization mechanism applies not only to the complete bipartite graph but also to one- and two-dimensional lattices, which are relevant for Rydberg atom array experiments. Moreover, our findings provide a physical motivation for Hamiltonian deformations reminiscent of those known to produce perfect scars.
The Rydberg blockade mechanism is an important ingredient in quantum simulators based on neutral atom arrays. It enables the emergence of a rich variety of quantum phases of matter, such as topological spin liquids. The typically isotropic nature of the blockade effect, however, restricts the range of natively accessible models and quantum states. In this work, we propose a method to systematically overcome this limitation, by developing gadgets, i.e., specific arrangements of atoms, that transform the underlying Rydberg blockade into more general constraints. We apply this technique to realize dimer models on square and triangular geometries. In these setups, we study the role of the quantum fluctuations induced by a coherent drive of the atoms and find signatures of U ( 1 ) and Z 2 quantum spin liquid states in the respective ground states. Finally, we show that these states can be dynamically prepared with high fidelity, paving the way for the quantum simulation of a broader class of constrained models and topological matter in experiments with Rydberg atom arrays.
We propose a scheme to simulate lattice spin models based on strong, long-range interacting Rydberg atoms stored in a large-spacing array of magnetic microtraps. Each spin is encoded in a collective spin state involving a single nS or Rydberg atom excited from an ensemble of ground-state alkali atoms prepared via Rydberg blockade. After the excitation laser is switched off, the Rydberg spin states on neighbouring lattice sites interact via general XXZ spin–spin interactions. To read out the collective spin states we propose a single Rydberg atom triggered avalanche scheme in which the presence of a single Rydberg atom conditionally transfers a large number of ground-state atoms in the trap to an untrapped state which can be readily detected by site-resolved absorption imaging. Such a quantum simulator should allow the study of quantum spin systems in almost arbitrary one-dimensional and two-dimensional configurations. This paves the way towards engineering exotic spin models, such as spin models based on triangular-symmetry lattices which can give rise to frustrated-spin magnetism.
Recent achievements in ultra-cold experiments have made quantum simulation of interacting many-body systems possible in a well controllable environment. Of many candidates as quantum simulators, Rydberg atoms have been extensively utilised due to its exaggerated and fascinating atomic properties. Example includes high susceptibility to electric fields and relatively long life time in comparison to atoms in low-lying states. The tunable interaction between Rydberg atoms have made them even more versatile in simulating quantum many-body systems, e.g. interacting spin-1/2 particles. We will start the thesis by reviewing these properties of Rydberg atoms and explain how they lead to the Rydberg lattice gases that of interest. Following the review of the essential knowledge of Rydberg atoms, we first study the ground states of interacting Rydberg lattice gases in both one-dimension and two-dimensions. The many-body system we are interested in is initially prepared in a Mott-insulator state, with each lattice site containing one atom that is laser coupled to its highly excited Rydberg state. The extremely huge van der Waals interactions between Rydberg atoms at close distance leads to an interesting Rydberg blockade effect. As we shall show, these strong interactions lead to rich phases and critical behaviours in the ground states of the many-body Hamiltonians that describes the systems. The aim of the first three chapters is to analyse these ground states in detail. Having investigated the static properties, we then move on to study the dynamical behaviour of a class of generic spin models which can in principal be realised by Rydberg lattice gases with tunable blockade radius. By deriving an effective master equation, and comparing it to the exact calculation, we will demonstrate how different pure initial states eventually evolve to the same equilibrium state and analysed in detail the time evolution and the steady state.