We explore the evolution of a strongly interacting dissipative quantum Ising spin chain that is driven by a slowly varying time-dependent transverse field. This system possesses an extensive number of instantaneous (adiabatic) stationary states which are coupled through non-adiabatic transitions. We analytically calculate the generator of the ensuing slow dynamics and analyze the creation of coherences through non-adiabatic processes. For a certain choice of the transverse field shape, we show that the system solely undergoes transitions among classical basis states after each pulse. The concatenation of many of such pulses leads to an evolution of the spin chain under a many-body dynamics that features kinetic constraints. Our setting not only allows for a quantitative investigation of adiabatic theorems and non-adiabatic corrections in a many-body scenario. It also directly connects to many-body systems in the focus of current research, such as ensembles of interacting Rydberg atoms which are resonantly excited by a slowly varying laser pulse and subject to dephasing noise.
We explore the evolution of a strongly interacting dissipative quantum Ising spin chain that is driven by a slowly varying time-dependent transverse field. This system possesses an extensive number of instantaneous (adiabatic) stationary states which are coupled through non-adiabatic transitions. We analytically calculate the generator of the ensuing slow dynamics and analyze the creation of coherences through non-adiabatic processes. For a certain choice of the transverse field shape, we show that the system solely undergoes transitions among classical basis states after each pulse. The concatenation of many of such pulses leads to an evolution of the spin chain under a many-body dynamics that features kinetic constraints. Our setting not only allows for a quantitative investigation of adiabatic theorems and non-adiabatic corrections in a many-body scenario. It also directly connects to many-body systems in the focus of current research, such as ensembles of interacting Rydberg atoms which are resonantly excited by a slowly varying laser pulse and subject to dephasing noise.
Applications of quantum devices and simulators require an accurate understanding of their dynamics as well as the effects of environmental noise. While some sources of noise can be modeled as Markovian dissipation, coupling to resonators or vibrational modes often produces non-Markovian dynamics as well, making it difficult to characterize the system, particularly for interacting many-body systems. Here, we identify a broad class of exactly solvable many-body quantum systems with both non-Markovian dynamics and Markovian dissipation. We consider a prototypical model of spins coupled to lossy bosonic modes that mediate Ising-type interactions. We exclude a transverse field but allow local spin dissipation that need not commute with the interactions, including dephasing, relaxation, pumping, and even processes that generate coherences. Using an exact stochastic representation, we decouple the many-body dynamics into the evolution of individual spins, yielding exact spin observables and correlations without adiabatically eliminating the bosons. In the Markovian limit, our solutions describe Ising models with correlated dephasing and nonreciprocal interactions. An example of spin squeezing shows that both the achievable squeezing and its optimal preparation time depend strongly on the interplay between non-Markovian dynamics and Markovian dissipation.
Metastability in many-body quantum systems and its associated exponentially-long timescales have been the subject of considerable recent interest. Here, we focus on a class of driven-dissipative many-body open quantum systems described by a Lindbladian having hidden time-reversal symmetry (a form of quantum detailed balance). Examples include boundary-driven interacting spin chains, bosonic lattice models and driven-dissipative collective spin models. We suggest that for such systems, slow timescales in the vicinity of a dissipative first-order phase transition can be analytically predicted using a special purification of the non-equilibrium steady state. We show the accuracy of our conjecture through detailed studies of a dissipative transverse-field Ising model with collective and local decay, and a driven-dissipative nonlinear cavity model. Our results allow quantitative insights into metastability and slow dynamics for a range of systems, including cases where semiclassical or path-integral instanton approaches are intractable.
We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or "classical" observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated and complex due to dynamical constraints, inspired by kinetically constrained models (KCMs) of classical glasses. We show that in the quantum case the relaxation can be orders of magnitude slower than the classical one due to the presence of quantum coherences. Aspects of these idealized quantum KCMs become manifest in a strongly interacting Rydberg gas under electromagnetically induced transparency (EIT) conditions in an appropriate limit. Beyond revealing a link between this Rydberg gas and the rather abstract dissipative KCMs of quantum glassy systems, our study sheds light on the limitations of the use of classical rate equations for capturing the non-equilibrium behavior of this many-body system.
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.
We study the real-time dynamics of a quantum Ising chain driven periodically by instantaneous quenches of the transverse field between $+{\ensuremath{\Gamma}}_{0}$ and ${\ensuremath{\Gamma}}_{0}$ back and forth in equal intervals of time. Two interesting phenomena are reported and analyzed. (i) We observe dynamical many-body freezing (DMF), i.e., strongly nonmonotonic freezing of the response with respect to the driving parameters (pulse width and height) resulting from coherent suppression of dynamics of all quasiparticle modes. For certain combinations of the pulse height and the period, maximal freezing (DMF peaks) is observed, where a massive collapse of the entire Floquet spectrum occurs and the many-body system remains frozen extremely close to the initial state for all time. (ii) Second, away from the freezing peak, we observe the emergence of a distinct oscillation with a single nontrivial frequency, which can be much lower than the driving frequency. This remarkable slow oscillation involving many high-energy modes dominates the response in the limit of long observation time. We identify this slow oscillation as the unique survivor of destructive quantum interference between the many-body modes. The oscillation tends to decay algebraically with time to a constant value. All the key features are demonstrated analytically with numerical evaluations for specific results.
We investigate a quantum dynamical phase transition induced by the competition between local unitary evolution and dissipation in a qubit chain with a strong, on-site Z2 symmetry. While the steady-state of this evolution is always maximally-mixed, we show that the dynamical behavior of certain non-local observables on the approach to this steady-state is dictated by a quantum Ising model with a complex transverse-field (cTFIM). A crucial feature of our mapping to the cTFIM is an extensive number of local, weak, Z2 symmetries possessed by the dynamics, allowing us to investigate these observables analytically and uncover a dynamical phase transition as the relative rate of unitary evolution and dissipation is tuned. We show that the weak-dissipation limit corresponds to a cTFIM with a large magnitude of the imaginary transverse-field, for which the many-body "ground-state" (with smallest real eigenvalue) is gapless, exhibiting quasi-long-range correlations of the local magnetization with a continuously-varying exponent. Correspondingly, the dynamics of the non-local observables show oscillatory behavior with an amplitude decaying exponentially in time. The strong-dissipation limit corresponds to a gapped ferromagnetic phase of the cTFIM, and non-local observables show exponential decay on the approach to equilibrium. This transition in (1+1)-dimensions has a peculiar, "two-sided" nature appearing as either first- or second-order depending on the phase from which the transition is approached, an analytic result which is corroborated by numerical studies. In higher dimensions, we present a field-theoretic understanding of the first-order nature of this transition, when approaching from the ferromagnetic phase of the cTFIM, though the nature of the phase with large imaginary transverse-field remains to be understood.