We use trapped atomic ions forming a hybrid Coulomb crystal and exploit its phonons to study an isolated quantum system composed of a single spin coupled to an engineered bosonic environment. We increase the complexity of the system by adding ions and controlling coherent couplings and, thereby, we observe the emergence of thermalization: Time averages of spin observables approach microcanonical averages while related fluctuations decay. Our platform features precise control of system size, coupling strength, and isolation from the external world to explore the dynamics of equilibration and thermalization.
We use trapped atomic ions forming a hybrid Coulomb crystal and exploit its phonons to study an isolated quantum system composed of a single spin coupled to an engineered bosonic environment. We increase the complexity of the system by adding ions and controlling coherent couplings and, thereby, we observe the emergence of thermalization: Time averages of spin observables approach microcanonical averages while related fluctuations decay. Our platform features precise control of system size, coupling strength, and isolation from the external world to explore the dynamics of equilibration and thermalization.
The experimental control and observation of quantum many-body systems has become a reality with the advent of ultracold quantum matter. The high level of isolation of these experiments, together with the development of novel measurement techniques, has revived a fundamental debate concerning the thermal equilibration of isolated quantum systems, commonly named "quantum thermalization". In this thesis we make use of a quantum-gas microscope to explore the thermalizing dynamics of highly isolated systems of ultracold bosonic atoms in optical lattices. The ability to prepare and control quantum systems made up of hundreds of atoms makes it possible to explore regimes that represent a challenge for classical numeric simulations. A major part of this dissertation deals with Bose-Hubbard systems in the presence of quenched disorder. We begin by studying the microscopic properties of its phases near equilibrium, where by tuning the strength of the disorder, observe features consistent with the emergence of a so-called Bose-glass phase. We then continue by preparing states far from equilibrium and exploring their quantum many-body dynamics. In particular, we observe signatures of the phenomenon of "many-body localization", which implies a breakdown of quantum thermalization. In addition, we study whether localized systems can be thermalized via the coupling to a bath of few degrees of freedom, i.e. a quantum bath. We do so by preparing a mixture of two interacting atomic species, where one acts as the bath and the other as the localized system. We do observe delocalizing dynamics for large enough baths, though in regimes of weak coupling localization can survive for extremely long times. The second main topic of this thesis is the thermalization of periodically driven many-body systems, so-called Floquet thermalization. In these systems, the absence of energy conservation eventually brings any initial state into a featureless infinite-temperature one. However, for sufficiently high frequencies this thermalization process can take arbitrarily long times, which can enable the engineering of exotic long-lived prethermal states. We use the high isolation of our system, together with the high sensitivity of quantum-gas microscopy, to measure the heating rates for a range of driving frequencies and interaction regimes. Our results show a dramatic suppression of the heating as the frequency of the drive is increased, which is consistent with theoretical expectations.
The emergence of classical behavior and the origin of thermal equilibrium are two central problems in the foundations of physics. In the standard accounts, both phenomena are typically explained through interactions with an external environment: decoherence suppresses quantum interference, while coupling to a thermal bath drives relaxation toward equilibrium. Over the last decades, however, it has become clear that equilibration and thermalization can arise even in fully isolated quantum systems, in the operational sense that the expectation values of relevant observables remain close to equilibrium values for most of the time. Here, we ask whether the same intrinsic equilibration mechanism can also account for the emergence of classical behavior. Using rigorous bounds on equilibration in closed systems, we derive sufficient conditions under which a time-evolved pure state becomes, for most times, operationally indistinguishable from a classical mixture associated with a chosen physical property. We identify two complementary routes to such operational classicality: either the chosen property almost commutes with the system Hamiltonian or the observables used to probe the system lose access to the remaining coherence after equilibration. Our results show that classical behavior need not be confined to the energy basis and may emerge even when substantial coherence remains present in the equilibrium state. This establishes a direct connection between two foundational questions: the origin of thermalization in isolated quantum systems and the quantum-to-classical transition
Linear arrays of trapped and laser-cooled atomic ions are a versatile platform for studying strongly interacting many-body quantum systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser-mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatio-temporal resolution, decoupling from the external environment and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review, we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin models, effects that are heralded by the memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.
Quantum simulation provides important tools in studying strongly correlated many-body systems with controllable parameters. As a hybrid of two fundamental models in quantum optics and in condensed matter physics, the Rabi-Hubbard model demonstrates rich physics through the competition between local spin-boson interactions and long-range boson hopping. Here, we report an experimental realization of the Rabi-Hubbard model using up to 16 trapped ions and present a controlled study of its equilibrium properties and quantum dynamics. We observe the ground-state quantum phase transition by slowly quenching the coupling strength, and measure the quantum dynamical evolution in various parameter regimes. With the magnetization and the spin-spin correlation as probes, we verify the prediction of the model Hamiltonian by comparing theoretical results in small system sizes with experimental observations. For larger-size systems of 16 ions and 16 phonon modes, the effective Hilbert space dimension exceeds 2^{57}, whose dynamics is intractable for classical supercomputers.
Controlled quantum mechanical motion of trapped atomic ions can be used to simulate and explore collective quantum phenomena and to process quantum information. Groups of cold atomic ions in an externally applied trapping potential self-organize into "Coulomb crystals" due to their mutual electrostatic repulsion. The motion of the ions in these crystals is strongly coupled, and the eigenmodes of motion all involve multiple ions. While this enables studies of many-body physics, it limits the flexibility and tunability of the system as a quantum platform. Here, we demonstrate an array of trapped ions in individual trapping sites whose motional modes can be controllably coupled and decoupled by tuning the local applied confining potential for each ion. We show that a single motional quantum, or phonon, can be coherently shared among two or three ions confined at the vertices of an equilateral triangle 30 μm on a side. We can adiabatically tune the ion participation in the motional modes around a closed contour in configuration space, observing that the single-phonon wavefunction acquires a topological Berry phase if the contour encircles a conical intersection of motional eigenvalue surfaces. We observe this phase by single-phonon interference and study its breakdown as the motional mode tuning becomes non-adiabiatic. Our results show that precise, individual quantum control of ion motion in a two-dimensional array can provide unique access to quantum multi-body effects.
The detailed characterization of non-trivial coherence properties of composite quantum systems of increasing size is an indispensable prerequisite for scalable quantum computation, as well as for understanding non-equilibrium many-body physics. Here, we show how autocorrelation functions in an interacting system of phonons as well as the quantum discord between distinct degrees of freedoms can be extracted from a small controllable part of the system. As a benchmark, we show this in chains of up to 42 trapped ions, by tracing a single phonon excitation through interferometric measurements of only a single ion in the chain. We observe the spreading and partial refocusing of the excitation in the chain, even on a background of thermal excitations. We further show how this local observable reflects the dynamical evolution of quantum discord between the electronic state and the vibrational degrees of freedom of the probe ion.