Non-equilibrium quantum domain reconfiguration dynamics in a two-dimensional electronic crystal: experiments and quantum simulations
Jaka Vodeb, Michele Diego, Yevhenii Vaskivskyi, Leonard Logarić, Yaroslav A. Gerasimenko, V. V. Kabanov, Benjamin Lipovšek, Marko Topič, Dragan Mihailovic
Relaxation dynamics of complex many-body quantum systems brought out of equilibrium and subsequently trapped into metastable states is a very active field of research from both the theoretical and experimental point of view with implications in a wide array of topics from macroscopic quantum tunnelling and nucleosynthesis to non-equilibrium superconductivity and new energy-efficient memory devices. Understanding the dynamics of such systems is crucial for exploring fundamental aspects of many-body non-equilibrium quantum physics. In this work we investigate quantum domain reconfiguration dynamics in the electronic superlattice of a quantum material where classical dynamics is topologically constrained. The crossover from temperature to quantum fluctuation dominated dynamics in the context of environmental noise is investigated by directly observing charge reconfiguration with time-resolved scanning tunneling microscopy. The process is modelled using a programmable superconducting quantum simulator in which qubit interconnections correspond directly to the microscopic interactions between electrons in the quantum material. Crucially, the dynamics of both the experiment on the quantum material and the simulation is driven by spectrally similar pink noise. We find that the simulations reproduce the emergent time evolution and temperature dependence of the experimentally observed electronic domain dynamics remarkably well. The combined experiment and simulations lead to a better understanding of noise-driven quantum dynamics in open quantum systems. From a practical viewpoint, the results are important for understanding the origin of the retention time in non-volatile memory devices such as those based on 1T-TaS2.
Relaxation dynamics of complex many-body quantum systems brought out of equilibrium and subsequently trapped into metastable states is a very active field of research from both the theoretical and experimental point of view with implications in a wide array of topics from macroscopic quantum tunnelling and nucleosynthesis to non-equilibrium superconductivity and new energy-efficient memory devices. Understanding the dynamics of such systems is crucial for exploring fundamental aspects of many-body non-equilibrium quantum physics. In this work we investigate quantum domain reconfiguration dynamics in the electronic superlattice of a quantum material where classical dynamics is topologically constrained. The crossover from temperature to quantum fluctuation dominated dynamics in the context of environmental noise is investigated by directly observing charge reconfiguration with time-resolved scanning tunneling microscopy. The process is modelled using a programmable superconducting quantum simulator in which qubit interconnections correspond directly to the microscopic interactions between electrons in the quantum material. Crucially, the dynamics of both the experiment on the quantum material and the simulation is driven by spectrally similar pink noise. We find that the simulations reproduce the emergent time evolution and temperature dependence of the experimentally observed electronic domain dynamics remarkably well. The combined experiment and simulations lead to a better understanding of noise-driven quantum dynamics in open quantum systems. From a practical viewpoint, the results are important for understanding the origin of the retention time in non-volatile memory devices such as those based on 1T-TaS2.
Abstract Emergent metastability in non-equilibrium systems is a subject that touches everything from the origins of life1 to the quantum nature of the universe2. In condensed quantum matter, a good topical example is the metastability of topologically inhibited self-organization of electronic domains in a correlated electronic crystal in the aftermath of a symmetry-breaking phase transition3. Understanding the dynamics of such systems is crucial for developing new quantum technologies and exploring fundamental aspects of many-body non-equilibrium quantum mechanics. Here, a non-equilibrium state is set up by carrier injection in the quantum material (M), resulting in a domain structure, whose time-evolution is investigated by scanning tunneling microscopy. Demonstrating a new approach to modelling of emergent non-equilibrium quantum behavior, we use an array of 2008 qubits in a programmable noisy superconducting quantum simulator (NSQS) without error correction (P), in which mutual qubit interconnections correspond directly to the electronic interactions on the triangular lattice of the electronic crystal material. The success of the simulations critically depends on both the faithfulness of the model correspondence between the two systems and careful management of the decoherence pathways. Importantly, decoherence of both P and M is driven by noise with a characteristic 1/ν frequency spectrum. The simulations reveal how an emergent false vacuum state arises, describing the time evolution and temperature dependence of the observed electronic domain dynamics of M solely on the basis of microscopic electronic interactions. The parallel experiments demonstrate the potential of NSQSs for studying emergent non-equilibrium dynamics in complex many-body quantum systems.
Domains are homogeneous areas of discrete symmetry, created in nonequilibrium phase transitions. They are separated by domain walls, topological objects which prevent them from fusing together. Domains may reconfigure by thermally-driven microscopic processes, and in quantum systems, by macroscopic quantum tunnelling. The underlying microscopic physics that defines the system's energy landscape for tunnelling is of interest in many different systems, from cosmology and other quantum domain systems, and more generally to nuclear physics, matter waves, magnetism, and biology. A unique opportunity to investigate the dynamics of microscopic correlations leading to emergent behaviour, such as quantum domain dynamics is offered by quantum materials. Here, as a direct realization of Feynman's idea of using a quantum computer to simulate a quantum system, we report an investigation of quantum electron reconfiguration dynamics and domain melting in two matching embodiments: a prototypical two-dimensionally electronically ordered solid-state quantum material and a simulation on a latest-generation quantum simulator. We use scanning tunnelling microscopy to measure the time-evolution of electronic domain reconfiguration dynamics and compare this with the time evolution of domains in an ensemble of entangled correlated electrons in simulated quantum domain melting. The domain reconfiguration is found to proceed by tunnelling in an emergent, self-configuring energy landscape, with characteristic step-like time evolution and temperature-dependences observed macroscopically. The remarkable correspondence in the dynamics of a quantum material and a quantum simulation opens the way to an understanding of emergent behaviour in diverse interacting many-body quantum systems at the microscopic level.
Understanding the collective quantum dynamics of non-equilibrium many-body systems is an outstanding challenge in quantum science. In particular, dynamics driven by quantum fluctuations are important for the formation of exotic quantum phases of matter1, fundamental high-energy processes2, quantum metrology3,4 and quantum algorithms5. Here we use a programmable quantum simulator based on Rydberg atom arrays to experimentally study collective dynamics across a (2+1)-dimensional Ising quantum phase transition. After crossing the quantum critical point, we observe a gradual growth of correlations through coarsening of antiferromagnetically ordered domains6. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries, and find that the dynamics accelerate with proximity to the quantum critical point. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (‘Higgs’) mode7. These observations offer a viewpoint into emergent collective dynamics in strongly correlated quantum systems and non-equilibrium quantum processes. A programmable quantum simulator based on Rydberg atom arrays is used to study the collective dynamics of a quantum phase transition and observe the phenomenon of quantum coarsening.
In the last decade the non-equilibrium dynamics of isolated quantum systems has raised a huge interest for both its conceptual and practical implications. Simulation of quantum dynamics represents by now a very active research effort, with highly controllable quantum devices composed of hundreds of qubits already being realized in numerous setups. These offer the unprecedented possibility to access real-time quantum dynamics and strongly correlated quantum many-body states, opening numerous avenues not only for future quantum technologies, but also for long-standing theoretical problems. One of the most sought-after applications is the computation of real-time evolution in theories of fundamental interactions. Since Wilson's proposal in 1974, the equilibrium phase diagrams of lattice gauge theories have been successfully investigated with Monte Carlo simulations in a wide range of parameters. Nonequilibrium properties, on the other hand, cannot be accessed with conventional techniques. Thanks to the recent advances in numerics (e.g. tensor networks) and experiments (quantum simulation), new promising tools are now available for tackling these questions. Remarkable works have already demonstrated that applying these techniques to simple theories, such as one-dimensional quantum electrodynamics, can help to detect the signatures of confinement and pair creation. Despite these impressive achievements, investigating the non-equilibrium dynamics of gauge theories with quantum simulators turned out to be extremely challenging. This is mostly due to the complex constrained dynamics of these theories, which make their simulation with realistic atomic platforms particularly difficult. At the same time, the dynamical constraints can play a key role in determining novel interesting phenomena and peculiar non-equilibrium properties. These phenomena -- which include, for example, quantum scars, fractons, Hilbert space fragmentation -- can lead to anomalous dynamics, eventually evading the paradigm of thermalization, which predicts the relaxation of physical observable to their thermodynamic values. The aim of this thesis is twofold: first, we want to address through a combination of numerical and analytical tools some of the open questions regarding the non-equilibrium dynamics of quantum many-body systems with constrained Hilbert spaces, including lattice gauge theories. In addition, the work reported here is part of a large effort of the community towards the quantum simulation of complex phenomena of condensed matter and high-energy physics.
Abstract Metastable domain-wall networks in correlated materials can relax on timescales vastly longer than the microscopic processes that move their elementary constituents. Motivated by the slow domain-wall rearrangements observed in 1T-TaS 2 , we study a phenomenological spin model designed to isolate the interplay between local domain-wall hopping and environmental noise. The model contains discrete registry-like configurations, energetic costs for domain walls, and a transverse-field-induced hopping channel, and is implemented on a superconducting quantum annealer with more than 2000 logical degrees of freedom. A Schrieffer–Wolff analysis shows that the intrinsic hopping amplitude arises at second order in the transverse field and is therefore fast on device timescales. However, the measured reconfiguration rate saturates to a finite value at low effective temperature and depends only weakly on the hopping amplitude. This indicates that domain-wall motion is not limited by bare tunnelling, but by quasi-static longitudinal-field noise that detunes neighboring configurations and intermittently permits local hopping events. These results demonstrate how noise can slow domain-wall motion in a minimal quantum-simulation model and suggest a possible mechanism for ultra-slow relaxation in charge-ordered materials.
This thesis summarizes a course of investigation of various aspects of non-equilibrium dynamics in isolated quantum systems which can be controlled to the extent that one can speak of not just realizing but rather simulating a desired physical effect. The first subject considered concerns a general question of relaxation in a large class of physical models. It is rigorously proven that equilibration can occur for arbitrary local observables despite the entire system being perfectly isolated. Various mechanisms responsible for convergence to local equilibrium are highlighted. These involve in particular the memory loss of non-Gaussian correlations following an interaction quench, a notion of Gaussian ergodicity and a proof of the emergence of translation invariance of correlations due to the presence of this symmetry in the Hamiltonian governing the evolution. These results provide the long time and large system size asymptotics facilitating a thermodynamic limit, but at the same time are relevant for state-of-the-art quantum simulation experiments with large numbers of ultra-cold atoms: A related effect has been observed in a one-dimensional phononic quantum field simulator and additionally a method is provided to study relaxation dynamics of this type in optical lattice quantum simulators. Within the second theme explored in this thesis a novel quantum read-out method is proposed and applied in continuous field quantum simulators which allowed for the first time to measure experimentally various thermodynamical properties of one-dimensional quasi-condensates. In particular, tomographic results concerning thermal properties, non-commuting observables, momentum and time-resolved occupation numbers of phonons are presented. Finally, ideas for practical benchmarking of the dynamics of certain closed quantum systems are put forward, based on the concept of a fidelity witness. It is demonstrated that fidelity, despite being a sensitive measure for large systems, can be efficiently estimated for non-equilibrium dynamics in coherent quantum simulators implementing paradigmatic models of condensed matter physics. The method developed has already found an independent application in studies of variational quantum circuits aiming at achieving so-called quantum chemistry accuracy using the Sycamore quantum processor. The fact that all three themes of research laid out in this thesis have found an experimental realization hints at a prognosis for future developments in physics that it will become standard that quantum simulators will realize experimentally novel theoretical ideas on demand and the time between theoretical insights and experimental observations will be dramatically shortened.