238 research outputs found
Phonon dressing of a facilitated one-dimensional Rydberg lattice gas
We study the dynamics of a one-dimensional Rydberg lattice gas under
facilitation (anti-blockade) conditions which implements a so-called
kinetically constrained spin system. Here an atom can only be excited to a
Rydberg state when one of its neighbors is already excited. Once two or more
atoms are simultaneously excited mechanical forces emerge, which couple the
internal electronic dynamics of this many-body system to external vibrational
degrees of freedom in the lattice. This electron-phonon coupling results in a
so-called phonon dressing of many-body states which in turn impacts on the
facilitation dynamics. In our theoretical study we focus on a scenario in which
all energy scales are sufficiently separated such that a perturbative treatment
of the coupling between electronic and vibrational states is possible. This
allows to analytically derive an effective Hamiltonian for the evolution of
consecutive clusters of Rydberg excitations in the presence of phonon dressing.
We analyze the spectrum of this Hamiltonian and show -- by employing Fano
resonance theory -- that the interaction between Rydberg excitations and
lattice vibrations leads to the emergence of slowly decaying bound states that
inhibit fast relaxation of certain initial states.Comment: 26 pages, 5 figure
Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
The dynamics after a quantum quench is determined by the weights of the
initial state in the eigenspectrum of the final Hamiltonian, i.e., by the
distribution of overlaps in the energy spectrum. We present an analysis of such
overlap distributions for quenches of the anisotropy parameter in the
one-dimensional anisotropic spin-1/2 Heisenberg model (XXZ chain). We provide
an overview of the form of the overlap distribution for quenches from various
initial anisotropies to various final ones, using numerical exact
diagonalization. We show that if the system is prepared in the
antiferromagnetic N\'eel state (infinite anisotropy) and released into a
non-interacting setup (zero anisotropy, XX point) only a small fraction of the
final eigenstates gives contributions to the post-quench dynamics, and that
these eigenstates have identical overlap magnitudes. We derive expressions for
the overlaps, and present the selection rules that determine the final
eigenstates having nonzero overlap. We use these results to derive concise
expressions for time-dependent quantities (Loschmidt echo, longitudinal and
transverse correlators) after the quench. We use perturbative analyses to
understand the overlap distribution for quenches from infinite to small nonzero
anisotropies, and for quenches from large to zero anisotropy.Comment: 23 pages, 8 figure
Vibrational dressing in kinetically constrained Rydberg spin systems
Quantum spin systems with kinetic constraints have become paradigmatic for exploring collective dynamical behavior in many-body systems. Here we discuss a facilitated spin system which is inspired by recent progress in the realization of Rydberg quantum simulators. This platform allows to control and investigate the interplay between facilitation dynamics and the coupling of spin degrees of freedom to lattice vibrations. Developing a minimal model, we show that this leads to the formation of polaronic quasiparticle excitations which are formed by many-body spin states dressed by phonons. We investigate in detail the properties of these quasiparticles, such as their dispersion relation, effective mass, and the quasiparticle weight. Rydberg lattice quantum simulators are particularly suited for studying this phonon-dressed kinetically constrained dynamics as their exaggerated length scales permit the site-resolved monitoring of spin and phonon degrees of freedom
Lattice Gauge Theories and String Dynamics in Rydberg Atom Quantum Simulators
Gauge theories are the cornerstone of our understanding of fundamental interactions among elementary particles. Their properties are often probed in dynamical experiments, such as those performed at ion colliders and high-intensity laser facilities. Describing the evolution of these strongly coupled systems is a formidable challenge for classical computers and represents one of the key open quests for quantum simulation approaches to particle physics phenomena. In this
work, we show how recent experiments done on Rydberg atom chains naturally realize the real-time dynamics of a lattice gauge theory at system sizes at the boundary of classical computational methods. We prove that the constrained Hamiltonian dynamics induced by strong Rydberg interactions maps exactly onto the one of a U(1) lattice gauge theory. Building on this correspondence, we show that the recently observed anomalously slow dynamics corresponds to a string-inversion
mechanism, reminiscent of the string breaking typically observed in gauge theories. This underlies the generality of this slow dynamics, which we illustrate in the context of one-dimensional quantum electrodynamics on the lattice. Within the same platform, we propose a set of experiments that generically show long-lived oscillations, including the evolution of particle-antiparticle pairs, and discuss how a tunable topological angle can be realized, further affecting the dynamics following a quench. Our work shows that the state of the art for quantum simulation of lattice gauge theories is at 51 qubits and
connects the recently observed slow dynamics in atomic systems to archetypal phenomena in particle physics
Towards the Thermodynamics of Localization Processes
We study the entropy time evolution of a quantum mechanical model, which is
frequently used as a prototype for Anderson's localization. Recently Latora and
Baranger [V. Latora, M. Baranger, Phys. Rev.Lett. 82, 520(1999)] found that
there exist three entropy regimes, a transient regime of passage from dynamics
to thermodynamics, a linear in time regime of entropy increase, namely a
thermodynamic regime of Kolmogorov kind, and a saturation regime. We use the
non-extensive entropic indicator recently advocated by Tsallis [ C. Tsallis, J.
Stat. Phys. 52, 479 (1988)] with a mobile entropic index q, and we find that
with the adoption of the ``magic'' value q = Q = 1/2 the Kolmogorov regime
becomes more extended and more distinct than with the traditional entropic
index q = 1. We adopt a two-site model to explain these properties by means of
an analytical treatment and we argue that Q =1/2 might be a typical signature
of the occurrence of Anderson's localization.Comment: 13 pages, 8 figures submitted to Phys. Rev.
Machine learning time-local generators of open quantum dynamics
In the study of closed many-body quantum systems one is often interested in the evolution of a subset of degrees of freedom. On many occasions it is possible to approach the problem by performing an appropriate decomposition into a bath and a system. In the simplest case the evolution of the reduced state of the system is governed by a quantum master equation with a time-independent, i.e. Markovian, generator. Such evolution is typically emerging under the assumption of a weak coupling between the system and an infinitely large bath. Here, we are interested in understanding to which extent a neural network function approximator can predict open quantum dynamics-described by time-local generators-from an underlying unitary dynamics. We investigate this question using a class of spin models, which is inspired by recent experimental setups. We find that indeed time-local generators can be learned. In certain situations they are even time-independent and allow to extrapolate the dynamics to unseen times. This might be useful for situations in which experiments or numerical simulations do not allow to capture long-time dynamics and for exploring thermalization occurring in closed quantum systems
Efficient Parallel Statistical Model Checking of Biochemical Networks
We consider the problem of verifying stochastic models of biochemical
networks against behavioral properties expressed in temporal logic terms. Exact
probabilistic verification approaches such as, for example, CSL/PCTL model
checking, are undermined by a huge computational demand which rule them out for
most real case studies. Less demanding approaches, such as statistical model
checking, estimate the likelihood that a property is satisfied by sampling
executions out of the stochastic model. We propose a methodology for
efficiently estimating the likelihood that a LTL property P holds of a
stochastic model of a biochemical network. As with other statistical
verification techniques, the methodology we propose uses a stochastic
simulation algorithm for generating execution samples, however there are three
key aspects that improve the efficiency: first, the sample generation is driven
by on-the-fly verification of P which results in optimal overall simulation
time. Second, the confidence interval estimation for the probability of P to
hold is based on an efficient variant of the Wilson method which ensures a
faster convergence. Third, the whole methodology is designed according to a
parallel fashion and a prototype software tool has been implemented that
performs the sampling/verification process in parallel over an HPC
architecture
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