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arXiv:1705.06532 · New Journal of Physics

Many-body dynamics of holes in a driven, dissipative spin chain of Rydberg superatoms

Fabian Letscher, David Petrosyan, Michael Fleischhauer

Published Oct 6, 2017• 13 citations
arXivHTMLPDF

Abstract

Strong, long-range interactions between atoms in high-lying Rydberg states can suppress multiple Rydberg excitations within a micron-sized trapping volume and yield sizable Rydberg level shifts at larger distances. Ensembles of atoms in optical microtraps then form Rydberg superatoms with collectively enhanced transition rates to the singly excited state. These superatoms can represent mesoscopic, strongly interacting spins. We study a regular array of such effective spins driven by a laser field tuned to compensate the interaction-induced level shifts between neighboring superatoms. During the initial transient, a few excited superatoms seed a cascade of resonantly facilitated excitation of large clusters of superatoms. Due to spontaneous decay, the system then relaxes to the steady state having nearly universal Rydberg excitation density . This state is characterized by highly non-trivial equilibrium dynamics of quasi-particles—excitation holes in the lattice of Rydberg excited superatoms. We derive an effective many-body model that accounts for hole mobility as well as continuous creation and annihilation of holes upon collisions with each other. We find that holes exhibit a nearly incompressible liquid phase with highly sub-Poissonian number statistics and finite-range density–density correlations.

DOI
10.1088/1367-2630/aa91c6

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Strong, long-range interactions between atoms in high-lying Rydberg states can suppress multiple Rydberg excitations within a micron-sized trapping volume and yield sizable Rydberg level shifts at larger distances. Ensembles of atoms in optical microtraps then form Rydberg superatoms with collectively enhanced transition rates to the singly excited state. These superatoms can represent mesoscopic, strongly interacting spins. We study a regular array of such effective spins driven by a laser field tuned to compensate the interaction-induced level shifts between neighboring superatoms. During the initial transient, a few excited superatoms seed a cascade of resonantly facilitated excitation of large clusters of superatoms. Due to spontaneous decay, the system then relaxes to the steady state having nearly universal Rydberg excitation density . This state is characterized by highly non-trivial equilibrium dynamics of quasi-particles—excitation holes in the lattice of Rydberg excited superatoms. We derive an effective many-body model that accounts for hole mobility as well as continuous creation and annihilation of holes upon collisions with each other. We find that holes exhibit a nearly incompressible liquid phase with highly sub-Poissonian number statistics and finite-range density–density correlations.
We study many-body correlations in the stationary state of a continuously driven, strongly interacting dissipative system. Specifically, we examine resonant optical excitations of Rydberg states of atoms interacting via long-range dipole-dipole and van der Waals potentials employing numerical and analytical techniques. Collection of atoms within a blockade distance form a ``superatom'' that can accommodate at most one Rydberg excitation. The superatom excitation probability saturates to 12\frac{1}{2}21​ for coherently driven atoms but is significantly higher in the presence of dephasing, approaching unity as the number of atoms increases. Using the exact numerical solution of the density-matrix equations for a small system, we demonstrate that strong dephasing of the optically driven dipoles renders the many-body problem amenable to semiclassical Monte Carlo simulations. We employ the Monte Carlo algorithm for a large number of atoms and find that in the steady state of a uniformly driven, extended one-dimensional system, the saturation of superatoms leads to quasicrystallization of Rydberg excitations whose correlations exhibit damped spatial oscillations. We show that the behavior of the system under the van der Waals interaction potential can be approximated by a rate-equations model based on a ``hard-rod'' interatomic potential, and by solving it we obtain the period and correlation length for the density wave of Rydberg excitations.
In an ensemble of laser-driven atoms involving strongly interacting Rydberg states, the steady-state excitation probability is usually substantially suppressed. In contrast, here we identify a regime in which the Rydberg excited fraction is enhanced by the interaction. This effect is associated with the buildup of many-body coherences induced by coherent multiphoton excitations between collective states. The excitation enhancement should be observable under currently existing experimental conditions and may serve as a direct probe for the presence of coherent multiphoton dynamics involving collective quantum states.
Owing to the unique physical characteristics of Rydberg atoms, which play an important role in quantum information and quantum computation, the theoretical and applied research of Rydberg atoms have become the hot spots of scientific research in recent years. With the large polarizability of Rydberg atoms, even a small electric field could cause a considerable electric dipole moment, resulting in a strong dipole-dipole interaction between Rydberg atoms. The multiple excitations of the Rydberg states are strongly inhibited because of the strong dipole interaction between atoms within a mesoscopic interaction (blockade) region. We call this phenomenon the dipole blockade effect. The dipole blockade effect makes it possible to build single-photon quantum devices, implement quantum gates, generate quantum entanglement, and simulate many-body quantum problems, etc. A Rydberg atomic ensemble in the same blockade region can be regarded as a superatom. In the same way, if these atoms trapped in two optical dipole traps, each sub-ensemble can be considered as a sub-superatom which is closely related to the superatom. According to the fact that two Rydberg sub-superatoms can be strongly correlated due to sharing no more than one excited Rydberg atom, we study correlated collective excitation and quantum entanglement between two Rydberg sub-superatoms in a steady state. With the superatom model, the problem of exponentially increasing system size with the number of atoms can be circumvented to a certain extent in studying many-body physics. By solving the two-body Lindblad’s master equation accurately, we obtain the analytical expressions for the collective excitation probabilities of the two sub-superatoms, and the concurrence measuring the bipartite entanglement between them. Our results show that they are all sensitive to the number of atoms in each Rydberg superatom: the bigger (including more atoms) the Rydberg superatom, the higher the collective Rydberg excitation probability is. And that the maximally entangled state can only be obtained with two equal-sized Rydberg superatoms. When this condition is fulfilled, the mesoscopic entanglement can be generated by adding the number of atoms in each Rydberg superatom. This may provide an attractive platform for studying the quantum-classical correspondence and have potential promising applications in quantum information processing.
The competition between resonant optical excitation of Rydberg states of atoms and their strong, long-range van der Waals interaction results in spatial ordering of Rydberg excitations in a two-dimensional lattice gas, as observed in a recent experiment of Schau\ss{} et al. [Nature (London) 491, 87 (2012)]. Here we use semiclassical Monte Carlo simulations to obtain stationary states for hundreds of atoms in finite-size lattices. We show the formation of regular spatial structures of Rydberg excitations in a system of increasing size, and find highly sub-Poissonian distribution of the number of Rydberg excitations characterized by a large negative value of the Mandel QQQ parameter which is nearly independent of the system size.
The glass phase and its quantum analog are prominent challenges of current non-equilibrium statistical mechanics and condensed matter physics. As a model system to study the transition from classical to quantum glassy dynamics, we propose a setup of laser driven three-level atoms trapped in an optical lattice. Tuning the strength of the laser driving to the intermediate level allows one to study the transition from a classical kinetically constrained model to the coherent regime. For strong driving, Rydberg excitations evolve analogously to defects in the one-spin facilitated model, a minimal model known to exhibit glassy dynamics. In our setup, the constraints result from the interplay between Rydberg interactions and the laser detuning from the Rydberg state. The emerging heterogeneous relaxation timescales are tuneable over several orders of magnitudes. In the opposite limit of weak driving of the intermediate level, we find an effective cluster model which describes the dynamics in a reduced subspace of the allowed number and positions of Rydberg excitations. This subspace is uniquely determined by the initial state and is characterized by a fixed number of clusters of Rydberg excitations. In addition, we investigate the influence of random fields on the classical relaxation. We find that the glassy dynamics can relax faster in the presence of weak random fields.
Non-equilibrium quantum dynamics represents an emerging paradigm for condensed matter physics, quantum information science, and statistical mechanics. Strongly interacting Rydberg atoms offer an attractive platform to examine driven-dissipative dynamics of quantum spin models with long-range order. Here, we explore the conditions under which stationary many-body entanglement persists with near-unit fidelity and high scalability. In our approach, coherent many-body dynamics is driven by Rydberg-mediated laser transitions, while atoms at the lattice boundary locally reduce the entropy of the many-body system. Surprisingly, the many-body entanglement is established by continuously evolving a locally dissipative Rydberg system towards the steady state, precisely as with optical pumping. We characterize the dynamics of multipartite entanglement in an one-dimensional lattice by way of quantum uncertainty relations, and demonstrate the long-range behavior of the stationary entanglement with finite-size scaling. Our work opens a route towards dissipative preparation of many-body entanglement with unprecedented scaling behavior.