The work presented in this dissertation concerns dynamics of Rydberg atom lattices in the presence of noise and dissipation. Rydberg atoms possess a number of exaggerated properties, such as a strong van der Waals interaction. The interplay of that interaction, coherent driving and decoherence leads to intriguing non-equilibrium phenomena. Here, we study the non-equilibrium physics of driven atom lattices in the presence of decoherence caused by either laser phase noise or strong decay. In the first case, we compare between global and local noise and explore their effect on the number of excitations and the full counting statistics. We find that both types of noise give rise to a characteristic distribution of the Rydberg excitation number. The main method employed is the Langevin equation but for the sake of efficiency in certain regimes, we use a Markovian master equation and Monte Carlo rate equations, respectively. In the second case, we consider dissipative systems with more general power-law interactions. We determine the phase diagram in the steady state and analyse its generation dynamics using Monte Carlo rate equations. In contrast to nearest-neighbour models, there is no transition to long-range-ordered phases for realistic interactions and resonant driving. Yet, for finite laser detunings, we show that Rydberg atom lattices can undergo a dissipative phase transition to a long-range-ordered antiferromagnetic phase. We identify the advantages of Monte Carlo rate equations over mean field predictions. Having studied the dynamics of Rydberg atom lattices, we study an application of the strong interactions in such systems for quantum information processing. We investigate the coherent exchange of a single photon between a superconducting microwave cavity and a lattice of strongly interacting Rydberg atoms in the presence of local electric field fluctuations plaguing the cavity surface. We show that despite the increased sensitivity of Rydberg states to electric fields, as compared to ground state atoms, the Rydberg dipole-dipole interaction can be used to protect the system against the dephasing induced by the local noise. Using $1/f$ and laser phase noise models, we show that compared to the case with non-interacting atoms, our system exhibits longer coherence lifetimes and larger retrieval efficiency of the photon after storing into the atoms.
The work presented in this dissertation concerns dynamics of Rydberg atom lattices in the presence of noise and dissipation. Rydberg atoms possess a number of exaggerated properties, such as a strong van der Waals interaction. The interplay of that interaction, coherent driving and decoherence leads to intriguing non-equilibrium phenomena. Here, we study the non-equilibrium physics of driven atom lattices in the presence of decoherence caused by either laser phase noise or strong decay. In the first case, we compare between global and local noise and explore their effect on the number of excitations and the full counting statistics. We find that both types of noise give rise to a characteristic distribution of the Rydberg excitation number. The main method employed is the Langevin equation but for the sake of efficiency in certain regimes, we use a Markovian master equation and Monte Carlo rate equations, respectively. In the second case, we consider dissipative systems with more general power-law interactions. We determine the phase diagram in the steady state and analyse its generation dynamics using Monte Carlo rate equations. In contrast to nearest-neighbour models, there is no transition to long-range-ordered phases for realistic interactions and resonant driving. Yet, for finite laser detunings, we show that Rydberg atom lattices can undergo a dissipative phase transition to a long-range-ordered antiferromagnetic phase. We identify the advantages of Monte Carlo rate equations over mean field predictions. Having studied the dynamics of Rydberg atom lattices, we study an application of the strong interactions in such systems for quantum information processing. We investigate the coherent exchange of a single photon between a superconducting microwave cavity and a lattice of strongly interacting Rydberg atoms in the presence of local electric field fluctuations plaguing the cavity surface. We show that despite the increased sensitivity of Rydberg states to electric fields, as compared to ground state atoms, the Rydberg dipole-dipole interaction can be used to protect the system against the dephasing induced by the local noise. Using 1/f and laser phase noise models, we show that compared to the case with non-interacting atoms, our system exhibits longer coherence lifetimes and larger retrieval efficiency of the photon after storing into the atoms.
We study the non-equilibrium dynamics of driven spin lattices in the presence of decoherence caused by either laser phase noise or strong decay. In the first case, we discriminate between correlated and uncorrelated noise and explore their effect on the mean density of Rydberg states and the full counting statistics (FCS). We find that while the mean density is almost identical in both cases, the FCS differ considerably. The main method employed is the Langevin equation (LE) but for the sake of efficiency in certain regimes, we use a Markovian master equation and Monte Carlo rate equations, respectively. In the second case, we consider dissipative systems with more general power-law interactions. We determine the phase diagram in the steady state and analyse its generation dynamics using Monte Carlo rate equations. In contrast to nearest-neighbour models, there is no transition to long-range-ordered phases for realistic interactions and resonant driving. Yet, for finite laser detunings, we show that Rydberg lattices can undergo a dissipative phase transition to a long-range-ordered antiferromagnetic (AF) phase. We identify the advantages of Monte Carlo rate equations over mean field (MF) predictions.
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.
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.
While dissipative Rydberg gases exhibit unique possibilities to tune dissipation and interaction properties, very little is known about the quantum many-body physics of such long-range interacting open quantum systems. We theoretically analyze the steady state of a van der Waals interacting Rydberg gas in an optical lattice based on a variational treatment that also includes long-range correlations necessary to describe the physics of the Rydberg blockade, i.e., the inhibition of neighboring Rydberg excitations by strong interactions. In contrast to the ground state phase diagram, we find that the steady state undergoes a single first order phase transition from a blockaded Rydberg gas to a facilitation phase where the blockade is lifted. The first order line terminates in a critical point when including sufficiently strong dephasing, enabling a highly promising route to study dissipative criticality in these systems. In some regimes, we also find good quantitative agreement of the phase boundaries with previously employed short-range models, however, with the actual steady states exhibiting strikingly different behavior.
This thesis describes studies on a Rydberg-dressed ultracold atom system as a versatile platform for non-equilibrium physics research, atom-light interactions analysis and atomic sensing applications. This work includes a description of the experimental system, an ultracold potassium atom setup where we can prepare a gas of atoms in an optical dipole trap and precisely control their ground state properties. To excite the atoms to strongly-interacting Rydberg states, we set up and characterize a high-power and widely tunable excitation laser system, for driving both single and two-photon Rydberg excitations. Together this establishes a unique system for studying the effects of driving, long-range interactions and dissipation (due to the relatively short lifetime of excited states) on many-body dynamics. Using this setup we study the phase structure of a driven-dissipative system out of equilibrium , where exploiting the atom loss rate as an observable,we discover different power-laws depending on the system parameters (i.e driving,dissipation and interaction). We study further in detail a regime which shows loss rates much larger than those for single particles, and discover that due to the Rydberg population decay the system evolves to a self-organized critical state.Our key observations can be well described by effectively classical models for the many-body dynamics, which we understand as a consequence of rapid dephasing of atomic coherences. To quantify the coherence of the atom-light interactions, we realize a Rydberg dressed interferometer. This technique combines the precision of atomic clock transitions with the exaggerated properties of Rydberg atoms such as their long-range interactions and extreme response to electric fields. Using the interferometer, we are able to characterize the Rydberg-dressed ensemble, including the effects of population decay and dephasing both of which affect the coherence time. This enables us to identify power fluctuations in the excitation laser as the dominant effects limiting the coherence in the system, which will be used in the experiment for future improvements of the coherence time. As an additional application, we demonstrate that the Rydberg dressed interferometer can be used to precisely measure static electric fields down to 17 mV/cm which is comparable to state-of-the-art electrometers. These results together highlight the versatility of the Rydberg platform and pave the way towards a better understanding of long-range interacting systems out-of-equilibrium. This work paves the way to new studies of non-equilibrium phenomena and applications of many-body quantum systems which make use of both quantum coherent and dissipative interactions.
In the presence of strong dephasing noise the dynamics of Rydberg gases becomes effectively classical, due to the rapid decay of quantum superpositions between atomic levels. Recently a great deal of attention has been devoted to the stochastic dynamics that emerges in that limit, revealing several interesting features, including kinetically-constrained glassy behaviour, self-similarity and aggregation effects. However, the non-equilibrium physics of these systems, in particular in the regime where coherent and dissipative processes contribute on equal footing, is yet far from being understood. To explore this we study the dynamics of a small one-dimensional Rydberg lattice gas subject to dephasing noise by numerically integrating the quantum Master equation. We find indications that the main features observed in the strongly dissipative limit persist when the dissipation is not strong enough to annihilate quantum coherences at the dynamically relevant time scales. These features include a power law growth of the density of excitations and the existence of a time-dependent Rydberg blockade radius. Our results indicate that the power-law growth of density of excitations is characterised by an exponent which decreases as the dissipation becomes weaker.