In this thesis, we consider the forms of non-equilibrium phenomena that can arise in atoms or polar molecules trapped in a deep optical lattice and coupled by dipolar internal degrees of freedom. We specifically focus on only two internal states, which results in the systems studied behaving as spin$-1/2$ models with long-range interactions. We first study a closed system with both static and resonant near-field dipole interactions under an external drive. By studying the uniform mean-field dynamics of the system, we find the dynamics are given by Rabi oscillations, with a bifurcation in the dynamics as a function of drive strength between small scale and large scale oscillations. Analysing the stability of these oscillations to small fluctuations reveals that interactions tend to cause the oscillations to decohere. However, we find parameter regimes where coherent oscillations can persist for high enough intensity drive. We then consider the effects of an environment on the non-equilibrium dynamics of the near-field dipole model. We find that within the mean-field approximation, an environment causes the system to relax to many novel steady state spin configurations, such as spin density waves, antiferromagnetism and long-time oscillations, as well as bistabilities between these phases. To assess the validity of the mean-field approximation, we compare our mean-field results to small quantum systems. We carry out a similar analysis on a system with far-field dipole interactions, where it is necessary to introduce nonlocal dissipation, which results in several decay modes into the environment. These decay modes lead to instabilities of many of the steady state phases that occurred in the near-field dipole system, leading to the emergence of more spin density wave and oscillatory phases. Finally, we examine the dynamics on the approach to steady state in a dissipative dipolar system by studying Rydberg atoms coupled to a photonic crystal waveguide, which mediates an effective dipole-dipole interaction between the atoms. We find that if two excitations exist in the system, then bound states can form, with nonlocal dissipation resulting in a momentum dependent decay rate of the bound states and also greater freedom in engineering the bound state energy dispersion.
In this thesis, we consider the forms of non-equilibrium phenomena that can arise in atoms or polar molecules trapped in a deep optical lattice and coupled by dipolar internal degrees of freedom. We specifically focus on only two internal states, which results in the systems studied behaving as spin−1/2 models with long-range interactions. We first study a closed system with both static and resonant near-field dipole interactions under an external drive. By studying the uniform mean-field dynamics of the system, we find the dynamics are given by Rabi oscillations, with a bifurcation in the dynamics as a function of drive strength between small scale and large scale oscillations. Analysing the stability of these oscillations to small fluctuations reveals that interactions tend to cause the oscillations to decohere. However, we find parameter regimes where coherent oscillations can persist for high enough intensity drive. We then consider the effects of an environment on the non-equilibrium dynamics of the near-field dipole model. We find that within the mean-field approximation, an environment causes the system to relax to many novel steady state spin configurations, such as spin density waves, antiferromagnetism and long-time oscillations, as well as bistabilities between these phases. To assess the validity of the mean-field approximation, we compare our mean-field results to small quantum systems. We carry out a similar analysis on a system with far-field dipole interactions, where it is necessary to introduce nonlocal dissipation, which results in several decay modes into the environment. These decay modes lead to instabilities of many of the steady state phases that occurred in the near-field dipole system, leading to the emergence of more spin density wave and oscillatory phases. Finally, we examine the dynamics on the approach to steady state in a dissipative dipolar system by studying Rydberg atoms coupled to a photonic crystal waveguide, which mediates an effective dipole-dipole interaction between the atoms. We find that if two excitations exist in the system, then bound states can form, with nonlocal dissipation resulting in a momentum dependent decay rate of the bound states and also greater freedom in engineering the bound state energy dispersion.
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.
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.
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.
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.
In this thesis we investigate theoretically two distinct systems of dipole-coupled atoms. In Part I we investigate light scattering from a system of N ultracold atoms, with laser induced electric dipole interactions. We derive the equations of motion in the Heisenberg picture for the atomic operators, for an arbitrary dipole transition. Then we take the specific case of a jl = 0 → ju = 1 transition and derive the second and third-order inter-atomic correlations. We solve the resulting set of linear equations for two and three atoms exactly, with particular focus on the exact two-atom system. We find a steady-state analytic solution for the two atoms in a specific geometric configuration, and use this to derive explicit expressions for the spatial and coherence properties of the far-field scattered light intensity, valid for the full range of system parameters. A comprehensive survey of the scattering behaviour is given, with key features precisely characterised, including subradiant scattering. We examine in detail a decorrelation approximation that has potential applications for larger systems of atoms that are intractable in a full quantum treatment. We introduce the concept of an effective driving field and show that it can provide a direct and intuitive physical interpretation of key aspects of the system behaviour, including subradiant scattering. Finally, we show that this effective field interpretation, and the decorrelation approximation, is readily extended to a three atom system. In Part II of this thesis we present our investigation of the quantum many-body dynamics of a large ensemble of bosonic S = 3 chromium atoms in a three-dimensional lattice. We implement an extended Bose-Hubbard model which includes the tunnelling, onsite spinor in- teractions and dipole-dipole interactions (giving interactions between atoms on neighbouring sites). We study the dynamics of the population of the different Zeeman levels as a function of lattice depth following a sudden spin rotation, and provide comparison to experimental res- ults. We are able to identify two distinct regimes: At low lattice depths, where atoms are in the superfluid regime, we observe the spin dynamics are strongly determined by the competi- tion between particle transport, onsite interactions and external magnetic field gradients. On the contrary, at high lattice depths, transport is largely frozen out and the spin populations are mainly driven by the long range dipolar interactions and quantum fluctuations.
We study an array of two-level systems arranged on a lattice and illuminated by an external plane wave which drives a dipolar transition between the two energy levels. In this setup, the two-level systems are coupled by dipolar interactions and subject to nonlocal dissipation, and so behave as an open many-body quantum system. We investigate the long-time dynamics of the system at the mean-field level and use this to determine a phase diagram as a function of external drive and detuning. We find a multitude of phases including antiferromagnetism, spin density waves, oscillations, and phase bistabilities. We investigate these phases in more detail and explain how nonlocal dissipation plays a role in the long-time dynamics. Furthermore, we discuss what features would survive in the full quantum description.