Facilitation Dynamics and Localization Phenomena in Rydberg Lattice Gases with Position Disorder

Abstract

We explore the dynamics of Rydberg excitations in an optical tweezer array under antiblockade (or facilitation) conditions. Because of the finite temperature the atomic positions are randomly spread, an effect that leads to quenched correlated disorder in the interatomic interaction strengths. This drastically affects the facilitation dynamics as we demonstrate experimentally on the elementary example of two atoms. To shed light on the role of disorder in a many-body setting we show that here the dynamics is governed by an Anderson-Fock model, i.e., an Anderson model formulated on a lattice with sites corresponding to many-body Fock states. We first consider a one-dimensional atom chain in a limit that is described by a one-dimensional Anderson-Fock model with disorder on every other site, featuring both localized and delocalized states. We then illustrate the effect of disorder experimentally in a situation in which the system maps on a two-dimensional Anderson-Fock model on a trimmed square lattice. We observe a clear suppression of excitation propagation, which we ascribe to the localization of the manybody wave functions in Hilbert space. DOI: 10.1103/PhysRevLett.118.063606 Introduction.-Rydberg gases provide a versatile platform for studies of quantum few-body and many-body phenomena with applications ranging from quantum information processing [1] to simulations of complex condensed matter systems. The experimental degree of control has reached a stage which enables efficient entanglement creation [2] and implementation of quantum Ising models [3,4]. This opens pathways towards probing magnetic structures [5][6][7][8] as well as the exploration of open many-body quantum systems [9][10][11][12][13][14][15].Of particular interest is the so-called facilitation mechanism (or antiblockade), where the excitation of an atom to a Rydberg state is strongly enhanced in the vicinity of an already excited atom [16,17]. This effect is of broad relevance and exploited in the design of quantum gates [18,19], as well as in protocols for dissipative quantum state preparation [6]. In the many-body context it effectuates an aggregation mechanism, where an initial Rydberg excitation seed triggers a dynamical growth of excitation clusters [18,[20][21][22][23] and it enables the implementation of kinetic constraints [12,24,25] thereby connecting to the physics of glass-forming substances [26][27][28].Here we perform a theoretical and experimental study of the facilitated dynamics of Rydberg excitations in a onedimensional array of optical tweezers. In a first experiment conducted with only two of them, we establish that the uncertainty of the atomic positions introduces disorder

Optical Control of the Resonant Dipole-Dipole Interaction between Rydberg Atoms

“…Local operations are a crucial element of a quantum simulator and they have been used, for example, to perform one-qubit rotations for quantum state tomography [2], to engineer two-qubit quantum gates (see e.g. [3,4]), or to prepare peculiar initial states [5,6] and apply local noise [7] for studies of many-body localization. To achieve a local operation, one usually shifts the frequency of one targeted qubit in the system.…”

Non-adiabatic quantum state preparation and quantum state transport in chains of Rydberg atoms

“…Here we analyze in detail the limitations of the protocols when these assumptions are relaxed, namely when the blockade becomes non-perfect due to the finite interaction strength between nearest neighbors and when accounting for interactions beyond nearest neighbors, and due to the disorder in atomic positions coming from the finite temperature of the atoms and non-vanishing width of the optical traps. In the context of Rydberg gases, the disorder was shown to have a strong impact on the dynamics of spin excitations under the so-called 'anti-blockade' conditions [37]. We comment on other sources of imperfections, such as the influence of relaxation processes, at the end of this section.…”

“…) is given by the temperature T and the mass m of the atoms and the trap frequencies i w (see [37] for details).…”

“…Taking for our comparison parameters from recent experiments [37], in the following we set the trap separation to In figures 6-8 we show the fidelity for the GHZ, dimer-MPS and state transport protocols respectively (we take the initial state…”

“…Thus, we choose V 6.9 0 * W = ( ) , corresponding to the position of the leftmost maximum fidelity peak in each protocol (figures 3-5). Finally, we fix V 2 8.4 0 p =´MHz [37]. We can now estimate, with the help of the table 1 and the relations (17), the maximal number of atoms N max so that the total duration of each protocol is smaller than exp t .…”