45 research outputs found
Many-Body Effects in Rydberg Gases : Coherent Dynamics of Strongly Interacting Two-Level Atoms and Nonlinear Optical Response of a Rydberg Gas in EIT Conguration
Subject of this thesis is the theoretical investigation of ensembles of atoms that are coherently laser-excited to a Rydberg state. Rydberg excited atoms interact with each other over large distances, which leads to strongly correlated many-body dynamics, demanding powerful numerical tools for their modeling. The first part of the thesis deals with effective two-level atoms consisting of a ground and a Rydberg state only. For resonant laser excitation a modified scaling behavior of the excitation number is observed, which is caused by effects of finite system size and coarse graining of the medium due to the finite atomic density. For off-resonant excitation, ordered structures arise out of an initially homogeneous gas, which are reected in strongly peaked spatial correlations and modified excitation statistics. In the second part a fast decaying intermediate level is additionally taken into account. In this situation the phenomenon of electromagnetically induced transparency (EIT) is encountered. This effect is suppressed in the presence of strong interactions between the Rydberg atoms leading to an optical nonlinearity. A model predicting the properties of a cloud of Rydberg atoms in EIT configuration is developed. In both parts the models are validated by comparing their predictions to recent experimental observations
Semi-analytical model for nonlinear light propagation in strongly interacting Rydberg gases
Rate equation models are extensively used to describe the many-body states of
laser driven atomic gases. We show that the properties of the rate equation
model used to describe nonlinear optical effects arising in interacting Rydberg
gases can be understood by considering the excitation of individual
super-atoms. From this we deduce a simple semi-analytic model that accurately
describes the Rydberg density and optical susceptibility for different
dimensionalities. We identify the previously reported universal dependence of
the susceptibility on the Rydberg excited fraction as an intrinsic property of
the rate equation model that is rooted in one-body properties. Benchmarking
against exact master equation calculations, we identify regimes in which the
semi-analytic model is particularly reliable. The performance of the model
improves in the presence of dephasing which destroys higher order atomic
coherences.Comment: 7 pages, 4 figure
Dynamic formation of Rydberg aggregates at off-resonant excitation
The dynamics of a cloud of ultra-cold two-level atoms is studied at
off-resonant laser driving to a Rydberg state. We find that resonant excitation
channels lead to strongly peaked spatial correlations associated with the
buildup of asymmetric excitation structures. These aggregates can extend over
the entire ensemble volume, but are in general not localized relative to the
system boundaries. The characteristic distances between neighboring excitations
depend on the laser detuning and on the interaction potential. These properties
lead to characteristic features in the spatial excitation density, the Mandel
parameter, and the total number of excitations. As an application an
implementation of the three-atom CSWAP or Fredkin gate with Rydberg atoms is
discussed. The gate not only exploits the Rydberg blockade, but also utilizes
the special features of an asymmetric geometric arrangement of the three atoms.
We show that continuous-wave off-resonant laser driving is sufficient to create
the required spatial arrangement of atoms out of a homogeneous cloud.Comment: 8 pages, 7 figure
Full counting statistics of laser excited Rydberg aggregates in a one-dimensional geometry
We experimentally study the full counting statistics of few-body Rydberg
aggregates excited from a quasi-one-dimensional Rydberg gas. We measure
asymmetric excitation spectra and increased second and third order statistical
moments of the Rydberg number distribution, from which we determine the average
aggregate size. Direct comparisons with numerical simulations reveal the
presence of liquid-like spatial correlations, and indicate sequential growth of
the aggregates around an initial grain. These findings demonstrate the
importance of dissipative effects in strongly correlated Rydberg gases and
introduce a way to study spatio-temporal correlations in strongly-interacting
many-body quantum systems without imaging.Comment: 6 pages plus supplemen
Universal time-evolution of a Rydberg lattice gas with perfect blockade
We investigate the dynamics of a strongly interacting spin system that is
motivated by current experimental realizations of strongly interacting Rydberg
gases in lattices. In particular we are interested in the temporal evolution of
quantities such as the density of Rydberg atoms and density-density
correlations when the system is initialized in a fully polarized state without
Rydberg excitations. We show that in the thermodynamic limit the expectation
values of these observables converge at least logarithmically to universal
functions and outline a method to obtain these functions. We prove that a
finite one-dimensional system follows this universal behavior up to a given
time. The length of this universal time period depends on the actual system
size. This shows that already the study of small systems allows to make precise
predictions about the thermodynamic limit provided that the observation time is
sufficiently short. We discuss this for various observables and for systems
with different dimensions, interaction ranges and boundary conditions.Comment: 16 pages, 3 figure
Effective dynamics of strongly dissipative Rydberg gases
We investigate the evolution of interacting Rydberg gases in the limit of strong noise and dissipation. Starting from a description in terms of a Markovian quantum master equation we derive effective equations of motion that govern the dynamics on a "coarse-grained" timescale where fast dissipative degrees of freedom have been adiabatically eliminated. Specifically, we consider two scenarios which are of relevance for current theoretical and experimental studies --- Rydberg atoms in a two-level (spin) approximation subject to strong dephasing noise as well as Rydberg atoms under so-called electromagnetically induced transparency (EIT) conditions and fast radiative decay. In the former case we find that the effective dynamics is described by classical rate equations up to second order in an appropriate perturbative expansion. This drastically reduces the computational complexity of numerical simulations in comparison to the full quantum master equation. When accounting for the fourth order correction in this expansion, however, we find that the resulting equation breaks the preservation of positivity and thus cannot be interpreted as a proper classical master rate equation. In the EIT system we find that the expansion up to second order retains information not only on the "classical" observables, but also on some quantum coherences. Nevertheless, this perturbative treatment still achieves a non-trivial reduction of complexity with respect to the original problem
Exploring out-of-equilibrium quantum magnetism and thermalization in a spin-3 many-body dipolar lattice system
Understanding quantum thermalization through entanglement build-up in
isolated quantum systems addresses fundamental questions on how unitary
dynamics connects to statistical physics. Here, we study the spin dynamics and
approach towards local thermal equilibrium of a macroscopic ensemble of S = 3
spins prepared in a pure coherent spin state, tilted compared to the magnetic
field, under the effect of magnetic dipole-dipole interactions. The experiment
uses a unit filled array of 104 chromium atoms in a three dimensional optical
lattice, realizing the spin-3 XXZ Heisenberg model. The buildup of quantum
correlation during the dynamics, especially as the angle approaches pi/2, is
supported by comparison with an improved numerical quantum phase-space method
and further confirmed by the observation that our isolated system thermalizes
under its own dynamics, reaching a steady state consistent with the one
extracted from a thermal ensemble with a temperature dictated from the system's
energy. This indicates a scenario of quantum thermalization which is tied to
the growth of entanglement entropy. Although direct experimental measurements
of the Renyi entropy in our macroscopic system are unfeasible, the excellent
agreement with the theory, which can compute this entropy, does indicate
entanglement build-up.Comment: 12 figure
Theoretical description of adiabatic laser alignment and mixed-field orientation: the need for a non-adiabatic model
We present a theoretical study of recent laser-alignment and
mixed-field-orientation experiments of asymmetric top molecules. In these
experiments, pendular states were created using linearly polarized strong ac
electric fields from pulsed lasers in combination with weak electrostatic
fields. We compare the outcome of our calculations with experimental results
obtained for the prototypical large molecule benzonitrile (CHN) [J.L.
Hansen et al, Phys. Rev. A, 83, 023406 (2011)] and explore the directional
properties of the molecular ensemble for several field configurations, i.e.,
for various field strengths and angles between ac and dc fields. For
perpendicular fields one obtains pure alignment, which is well reproduced by
the simulations. For tilted fields, we show that a fully adiabatic description
of the process does not reproduce the experimentally observed orientation, and
it is mandatory to use a diabatic model for population transfer between
rotational states. We develop such a model and compare its outcome to the
experimental data confirming the importance of non-adiabatic processes in the
field-dressed molecular dynamics.Comment: 11 pages, 9 figure