Non-equilibrium quantum domain reconfiguration dynamics in a two-dimensional electronic crystal and a quantum annealer
Jaka Vodeb, Michele Diego, Yevhenii Vaskivskyi, Leonard Logarić, Yaroslav A. Gerasimenko, V. V. Kabanov, Benjamin Lipovšek, Marko Topič, Dragan Mihailovic
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.
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.
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.
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.
False vacuum decay-the transition from a metastable quantum state to a true vacuum state-plays an important role in quantum field theory and non-equilibrium phenomena such as phase transitions and dynamical metastability. The non-perturbative nature of false vacuum decay and the limited experimental access to this process make it challenging to study, leaving several open questions regarding how true vacuum bubbles form, move and interact. Here we observe quantized bubble formation in real time, a key feature of false vacuum decay dynamics, using a quantum annealer with 5,564 superconducting flux qubits. We develop an effective model that captures both initial bubble creation and subsequent interactions, and remains accurate under dissipation. The annealer reveals coherent scaling laws in the driven many-body dynamics for more than 1,000 intrinsic qubit time units. This work provides a method for investigating false vacuum dynamics of large quantum systems in quantum annealers.
The study of non-equilibrium behaviors of quantum matter is one of the research directions at the frontiers of condensed matter physics and, in general, of theoretical and experimental physics. Understanding the mechanisms which prevent many quantum particles from reaching thermal equilibrium can ultimately shed light on the foundations of statistical physics and provide insight into the anomalous long-time collective behaviors observed in experiments. In this thesis, we present new theoretical developments in this direction. In the first part of the thesis we discuss the non-equilibrium dynamics of the two-dimensional quantum Ising model, the prototypical model of magnetism. In particular, we investigate the dynamics of interfaces separating different spin domains. In some regimes, we can provide an exact description of their unitary time evolution, but we also discuss the robustness of our predictions away from the exactly-solvable limit. Moreover, we address the same problem in the presence of disorder and provide a hydrodynamic interpretation of our findings. In the second part of the thesis, we investigate the localization properties of disordered quantum systems. In particular, we develop a renormalization-group picture of the Anderson localization transition in generic geometries. This provides a new framework to understand the phase diagram of such systems and their critical behavior beyond the usual finite-size scaling analysis. We also provide further insights on this topic both by studying resonances and their connection with observables and by employing unsupervised non-parametric learning techniques to probe disordered systems in an experimentally accessible form. The results presented in this thesis constitute a step forward in understanding the non-equilibrium phases and regimes of quantum matter and they pave the way to interesting future developments.
False vacuum decay is a potential mechanism governing the evolution of the early Universe, with profound connections to non-equilibrium quantum physics, including quenched dynamics, the Kibble-Zurek mechanism, and dynamical metastability. The non-perturbative character of the false vacuum decay and the scarcity of its experimental probes make the effect notoriously difficult to study, with many basic open questions, such as how the bubbles of true vacuum form, move and interact with each other. Here we utilize a quantum annealer with 5564 superconducting flux qubits to directly observe quantized bubble formation in real time -- the hallmark of false vacuum decay dynamics. Moreover, we develop an effective model that describes the initial bubble creation and subsequent interaction effects. We demonstrate that the effective model remains accurate in the presence of dissipation, showing that our annealer can access coherent scaling laws in driven many-body dynamics of 5564 qubits for over 1μs, i.e., more than 1000 intrinsic qubit time units. This work sets the stage for exploring late-time dynamics of the false vacuum at computationally intractable system sizes, dimensionality, and topology in quantum annealer platforms.