Critical behaviour of dissipative quantum systems

A.M. Kowalski, Angel Ricardo Plastino, Araceli N. Proto

Mikhail Gennag'evich Vasin

The non-equilibrium dynamics of the critical behaviour of the Boson system undergoing the second order quantum phase transition is discussed. The analysis is carried out using the Keldysh technique of the non-equilibrium dynamics description. The critical behaviour close to the quantum critical point has been shown to be multi-critical. Crossover among three different critical regimes (modes) is possible: adiabatic quantum mode (AQM), dissipative classical mode (classical critical dynamics mode (CCDM) and dissipative quantum critical mode (QCDM). As a result, the observed critical behavior can essentially depend on the conditions of approaching the critical point.

Thomas Vojta, José A. Hoyos, Chetan Kotabage

S. Helmrich

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.

Iver Bakken Sperstad

This thesis presents seven research papers on topics in condensed-matter theory. Five of the papers report on Monte Carlo studies of quantum phase transitions in various (d+1)-dimensional statistical mechanics models featuring Caldeira-Leggettlike dissipation. The principal motivation for these studies was to investigate a particular bond-dissipative (2+1)-dimensional XY model of circulating currents in cuprate high-temperature superconductors. It has been proposed that quantum critical fluctuations associated with a local quantum critical point described by this model can explain the marginal-Fermi-liquid behaviour of the normal state of these compounds. We present simulation results for this model for both compact and noncompact phase variables and show unambiguously that the quantum critical point in the compact case is not local. If the phases are taken to be noncompact variables, the model is also a model of resistively shunted Josephson junction arrays. The results in this case reveal a more complicated phase diagram, but we have not been able to establish critical behaviour consistent with the scenario of local quantum criticality.\n\nThe study of extended quantum dissipative models is also motivated by the general effect on condensed-matter systems of the coupling to environmental degrees of freedom. Their influence on quantum critical phenomena is characterized by the dynamical critical exponent z, a measure of spatiotemporal anisotropy, the value of which can be estimated by naive scaling arguments. We confirm by numerical means that such scaling estimates give correct results to a good approximations (with a few reservations), irrespective of system dimensionality, order parameter symmetry, or whether the variables are compact or noncompact. Corrections to the naive scaling estimates have to be invoked for strongly super-Ohmic dissipation for d = 1 due to relatively large values of the anomalous scaling dimension η.\n\nThe two last research papers are concerned with the superconducting pairing state of the recently discovered class of iron-based high-temperature superconductors. Here, we calculate possible signatures of the proposed s±-wave pairing state in conductance-spectroscopy and Josephson-effect experiments.