This thesis reports the investigation of cooperative non-equilibrium dynamics in a thermal Rydberg ensemble. Cooperative behaviour arises due to resonant dipole-dipole interactions between highly excited Rydberg atoms. In order to transfer atomic population from the ground state to the Rydberg state in a caesium vapour, a three-photon excitation scheme is developed. This scheme has a number of benefits over traditional two-photon Rydberg excitation as each transition utilises in- expensive high-power diode lasers. The process of developing the excitation scheme produces a number of important results, including an excited-state polarisation spectroscopy technique and the observation of coherent three-photon electromagnetically induced transparency. The optical response and atomic dynamics of the interacting ensemble can be separated into two distinct phases. When the Rydberg number density is low and the interactions are negligible, the system can be described by the behaviour of a single atom. However, when the Rydberg number density is high, resonant dipole-dipole interactions result in a significant modification of the ensemble properties. This cooperative many-body phase cannot be described by the behaviour of a single atom. In the frequency domain, the interactions produce an excitation-dependent cooperative energy shift that is observed using probe transmission spectroscopy. In the time domain, the interactions result in a cooperative enhancement of the atomic decay rate that is analysed using fluorescence spectroscopy. At the transition between the single-body and many-body phase, a first-order non-equilibrium phase transition occurs. This is observed spatially along the length of the excitation region as a sharp switch in the emitted fluorescence. The first-order phase transition is also observed in the temporal response of the ensemble through critical slowing down. The divergence of the switching time to steady state follows a universal scaling law for phase transitions and the determined critical exponent is in excellent agreement with previous work on non-equilibrium phase transitions.
This thesis reports the investigation of cooperative non-equilibrium dynamics in a thermal Rydberg ensemble. Cooperative behaviour arises due to resonant dipole-dipole interactions between highly excited Rydberg atoms. In order to transfer atomic population from the ground state to the Rydberg state in a caesium vapour, a three-photon excitation scheme is developed. This scheme has a number of benefits over traditional two-photon Rydberg excitation as each transition utilises in- expensive high-power diode lasers. The process of developing the excitation scheme produces a number of important results, including an excited-state polarisation spectroscopy technique and the observation of coherent three-photon electromagnetically induced transparency. The optical response and atomic dynamics of the interacting ensemble can be separated into two distinct phases. When the Rydberg number density is low and the interactions are negligible, the system can be described by the behaviour of a single atom. However, when the Rydberg number density is high, resonant dipole-dipole interactions result in a significant modification of the ensemble properties. This cooperative many-body phase cannot be described by the behaviour of a single atom. In the frequency domain, the interactions produce an excitation-dependent cooperative energy shift that is observed using probe transmission spectroscopy. In the time domain, the interactions result in a cooperative enhancement of the atomic decay rate that is analysed using fluorescence spectroscopy. At the transition between the single-body and many-body phase, a first-order non-equilibrium phase transition occurs. This is observed spatially along the length of the excitation region as a sharp switch in the emitted fluorescence. The first-order phase transition is also observed in the temporal response of the ensemble through critical slowing down. The divergence of the switching time to steady state follows a universal scaling law for phase transitions and the determined critical exponent is in excellent agreement with previous work on non-equilibrium phase transitions.
This thesis presents several experiments investigating the regimes of behaviour of a proto-typical open quantum many-body system far away from equilibrium. The experimental platform is based on ultracold atoms laser-excited to Rydberg states, which we engineer to emulate a strongly interacting, driven-dissipative quantum spin system. The high degree of control over the relevant microscopic processes and their parameters, as well as the ability to widely tune interaction and driving strengths provides the means to address fundamental questions on how different regimes of dynamical behaviour emerge in complex open quantum systems and how they can be characterised. \n \nIn the first part, we discuss how control over the relevant properties of Rydberg spin systems, like temperature, density, long evolution times, strong interactions, tunable driving, and dissipation can be achieved. We introduce the new experimental apparatus developed during this thesis, which combines both single-photon and two-photon Rydberg excitation schemes with high atom densities and long excitation times using an optical dipole trap. Additionally, we investigate theoretically how long coherence times exceeding motional timescales combined with strong many-body interactions can be achieved in such a system. We identify an optimal parameter regime for two-photon excitation where such conditions can be generated with coherence times and interaction strengths comparable to what is achievable for single-photon excitation. \n \nIn the second part we explore the macroscopic non-equilibrium behaviour of our system and devise suitable observables for characterising different regimes of behaviour. We discover that the slow atom loss inherent to our system provides a convenient observable for the many-body state of the system. Focussing on evolution times where the effect of the atom loss on the evolution is small, we discover that the rate of atom loss exhibits powerlaw scaling with the driving strength over several orders of magnitude. The measured scaling exponents reveal the non-equilibrium phase structure of the many-body system and allow us to distinguish dissipation-dominated, paramagnetic and critical regimes, as well as an instability. In the observed critical regime, collectively enhanced driving dominates over dissipation, leading to scaling associated to the critical point of the non-dissipative equilibrium Rydberg spin system. Based on the known microscopic processes of our system, we perform classical many-body rate equation simulations, which agree well with the observed phase structure as well as the position and associated scaling exponents of the individual regimes. These findings open up new means to study and classify out of equilibrium systems based on slow particle loss and powerlaw scaling. \n \nIn the last part of this thesis we reveal a second type of criticality in our system, which is genuinely non-equilibrium in character and arises from an absorbing state phase transition. The critical state of this phase transition dominates the system evolution at late times where particle loss is no longer negligible. We identify self-organisation as the mechanism driving the system to this critical state, which we observe through powerlaw scaling of the non-equilibrium steady-state. These experiments establish Rydberg atoms as a well controlled platform for implementing and exploring models of absorbing state phase transitions and self-organised criticality with unprecedented access to the underlying microscopic properties of the system.
Abstract Far-from equilibrium dynamics that lead to self-organization are highly relevant to complex dynamical systems not only in physics, but also in life-, earth-, and social sciences. It is challenging however to find systems with sufficiently controllable parameters that allow quantitatively modelling of emergent properties. Here, we study a non-equilibrium phase transition and observe signatures of self-organized criticality in a dilute thermal vapour of atoms optically excited to strongly interacting Rydberg states. Electromagnetically induced transparency (EIT) provides excellent control over the population dynamics and enables high-resolution probing of the driven-dissipative dynamics, which also exhibits phase bistability. Increased sensitivity compared to previous work allows us to reconstruct the complete phase diagram including in the vicinity of the critical point. We observe that interaction-induced energy shifts and enhanced decay only occur in one of the phases above a critical Rydberg population. This limits the application of generic mean-field models, however a modified, threshold-dependent approach is in qualitative agreement with experimental data. Near threshold, we observe self-organized dynamics in the form of population jumps that return the density to a critical value.
High optical nonlinearities can be achieved at the single photon level by coupling the photon states to strongly interacting Rydberg excitations under the conditions of electromagnetically induced transparency. The nonlinear response in Rydberg quantum optics comes as a direct result of the long range dipole-dipole interactions via Rydberg blockade and interaction induced dephasing. In this thesis, Rydberg quantum optics experiments are performed with two spatially separated mediums with a nonlinear response at the single photon level. Two ultracold rubidium atomic clouds are tightly confined by a pair of in-vacuo aspheric lenses such that only a few Rydberg excitations can exist in each one of the clouds simultaneously. The long range character of the dipole-dipole interactions leads to the generation of quantum states of light. The effective photon-photon interactions are directly observed as an anti-correlation in the simultaneous photon retrieval as a result of the non resonant van der Waals interactions. The collective Rydberg excitations, stored in the non-overlapping mediums, experience an additional spatial non-uniform phase. In addition, we experimentally characterize the cooperative optical response of a cold atomic medium at a single photon level. This aims to exploit the enhancement of the spontaneous emissions decay rate (superradiance) as a dependence of the number of atoms involved in the ensemble. The observed atomic response in two different regimes gives a further understanding of the system dynamics and unlocks a promising potential route towards the implementation in scalable, multichannel quantum optical devices.
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 reflected 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.
This thesis explores the effects of decoherence and dephasing on single- and many- body dynamics of spin-systems. A particular realisation of the spin systems that the work focuses on are highly excited, Rydberg states of atoms. A software library ARC (Alkali Rydberg Calculator) for calculating properties of Rydberg states in alkali metals is presented, with particular attention to the multi- atom and multi-level effects that influence many-body dynamics in realistic systems, and properties related to terahertz imaging with alkali atom Rydberg states. Dressed-state electromagnetically induced transparency (EIT) is proposed as a way of preparing uniform-phase spin-waves in ladder excitation schemes, making the collective excitation storage insensitive to motional dephasing. Proof of concept dressed state EIT experiments are presented. Strong resonant dressing is also theoretically analysed as a way of preparing velocity superposition of spin-waves. The developed theoretical model is in a good agreement with existing experimental data on single-photon many-atom quantum beats in diamond excitation schemes. By modelling the strongly driven Rydberg ensembles, many-body dynamics of driven-dissipative spin systems is analysed. Working in the limit of strong dephasing, the effects of fluctuations, the shape of interaction potential, spatial correlations and motion on non-equilibrium phase diagrams and the occurrence of bistability are examined. An ensemble averaged mean field model is introduced as an exact solution for completely uncorrelated ensembles. It is shown that the van der Waals interaction does not allow the occurrence of bistability, for which a finite dipolar core is required. The short-range interaction potential shape is found to have a profound influence on non-equilibrium phase diagrams, controlling the size of fluctuations in the dynamics. For a frozen system, several methods for identifying and quantifying bistable phases are introduced, and phase diagrams are reconstructed. It is shown that the temperature of external degrees of freedom, i.e. spin motion, can drive a non-equilibrium transition into the bistable phase.
Far-from-equilibrium dynamics that lead to self-organization are highly relevant to complex dynamical systems not only in physics but also in life, earth, and social sciences.However, it is challenging to find systems with sufficiently controllable parameters that allow quantitatively modeling of emergent properties.Here, we study a nonequilibrium phase transition and observe signatures of self-organized criticality in a dilute thermal vapor of atoms optically excited to strongly interacting Rydberg states.Electromagnetically induced transparency provides excellent control over the population dynamics and enables highresolution probing of the driven-dissipative dynamics, which also exhibits phase bistability.Increased sensitivity compared to previous work allows us to reconstruct the complete phase diagram, including in the vicinity of the critical point.We observe that interaction-induced energy shifts and enhanced decay only occur in one of the phases above a critical Rydberg population.This case limits the application of generic mean-field models; however, a modified, threshold-dependent approach is in qualitative agreement with experimental data.Near threshold, we observe self-organized dynamics in the form of population jumps that return the density to a critical value.