Exploring the non-equilibrium dynamics of kinetically constrained spin systems: Rydberg quantum simulation and artificial dissipation

This thesis discusses the non-equilibrium dynamics of one-dimensional quantum many-body systems. In particular, we investigate two distinct situations in which interesting dynamical properties arise, i.e., when the quantum evolution is subject to kinetic constraints or competes with an artificial dissipation through stochastic resets. Both topics have attracted considerable interest in the last decade, as they offer a playground to theoretically investigate the long-standing question of how isolated quantum systems evolve under non-equilibrium conditions. From the experimental point of view, the recent technological progress in the control and manipulation of ultracold atomic gases has led to new breakthroughs in the domains of quantum simulation and quantum computation. Key for the latter applications is the utilization of atomic Rydberg states in which atoms, trapped in optical tweezers, interact via state-dependent electrostatic dipolar forces. These strong interactions make Rydberg systems ideal for the realization of kinetic constraints, which cause a restriction of the connectivity between many-body states in the Hilbert space. A prominent example of a kinetic constraint is the Rydberg blockade, in which an excited Rydberg atom prevents the surrounding atoms to be excited to the Rydberg state. This effect has been largely exploited to implement controlled gates and complex many-body dynamics. Much less explored is the opposite situation, called the facilitation (or anti-blockade) constraint, where the interactions shift the otherwise detuned laser in resonance. In this case only atoms at the correct distance to an already excited atom are resonantly driven by the laser, thereby creating an “avalanche” of excitations. The first part of the thesis is devoted to the study of the facilitation dynamics in Rydberg chains. The facilitation constraint favours the dynamical creation of contiguous Rydberg excitations. We find that the resulting Rydberg excitation “cluster” develops long-range interactions that cause the onset of Bloch oscillations, preventing the system from reaching an ergodic stationary state. Contrary to the blockade constraint, facilitation is more challenging to implement in current Rydberg quantum simulators. The reason for this difficulty is that facilitation is particularly affected by mechanical effects and position disorder. These two problems originate respectively from the mechanical forces that displace the atoms from their initial positions and the spreading of the atomic wave functions in the optical traps. The interplay between the electronic degrees of freedom and the vibrational ones leads to a coupling between the (internal) Rydberg dynamics and the (external) atomic motion. We find that such spin-phonon coupling inhibits the facilitation mechanism, suppressing the expansion of the excitation cluster. This vibronic interaction can be also exploited to explore molecular physics in Rydberg atom arrays. We show this by considering a system composed of three atoms trapped in optical tweezers that form an equilateral triangle. We find that the atomic vibrations in the traps break the electronic degeneracy and generate a structural Jahn-Teller distortion, paving the way towards the exploration of molecular physics at the exaggerated length scales typical of Rydberg systems. The second part of the thesis investigates the effects of stochastic resetting on the stationary properties of quantum many-body spin systems. Stochastic resetting is a process that interrupts the dynamics of a system at random times and resets it to a certain state. Then the dynamics restarts again. This process leads very generally to a non-equilibrium stationary state. When the choice of the reset state is determined by the outcome of a measurement taken immediately before resetting, we find that resetting induces an emergent non-Markovian open dynamics, described by a generalized Lindblad equation. We also show that stochastic resetting can generate quantum correlation and collective behaviour even in a non-interacting system, showing its potential for quantum sensing applications. The structure of the thesis is as follows. In the first chapter we introduce the topics covered in the thesis and provide useful references for the reader. In the second chapter we review the physics of Rydberg systems, including their single-body properties and their interactions. We also explain how Rydberg quantum simulators are used for the implementation of kinetic constraints. In the third chapter we review the physics of stochastic resetting and the main mathematical techniques used in the thesis. In the fourth chapter we summarize the original results contained in the thesis. The fifth chapter is dedicated to the conclusions and an outlook on possible future research directions

Molecular Dynamics in Rydberg Tweezer Arrays: Spin-Phonon Entanglement and Jahn-Teller Effect

Atoms confined in optical tweezer arrays constitute a platform for the implementation of quantum computers and simulators. State-dependent operations are realized by exploiting electrostatic dipolar interactions that emerge, when two atoms are simultaneously excited to high-lying electronic states, so-called Rydberg states. These interactions also lead to state-dependent mechanical forces, which couple the electronic dynamics of the atoms to their vibrational motion. We explore these vibronic couplings within an artificial molecular system in which Rydberg states are excited under so-called facilitation conditions. This system, which is not necessarily self-bound, undergoes a structural transition between an equilateral triangle and an equal-weighted superposition of distorted triangular states (Jahn-Teller regime) exhibiting spin-phonon entanglement on a micrometer distance. This highlights the potential of Rydberg tweezer arrays for the study of molecular phenomena at exaggerated length scales.Comment: Accepted version in PRL. 7+4 pages, 4 figure

Phonon dressing of a facilitated one-dimensional Rydberg lattice gas

We study the dynamics of a one-dimensional Rydberg lattice gas under facilitation (anti-blockade) conditions which implements a so-called kinetically constrained spin system. Here an atom can only be excited to a Rydberg state when one of its neighbors is already excited. Once two or more atoms are simultaneously excited mechanical forces emerge, which couple the internal electronic dynamics of this many-body system to external vibrational degrees of freedom in the lattice. This electron-phonon coupling results in a so-called phonon dressing of many-body states which in turn impacts on the facilitation dynamics. In our theoretical study we focus on a scenario in which all energy scales are sufficiently separated such that a perturbative treatment of the coupling between electronic and vibrational states is possible. This allows to analytically derive an effective Hamiltonian for the evolution of consecutive clusters of Rydberg excitations in the presence of phonon dressing. We analyze the spectrum of this Hamiltonian and show -- by employing Fano resonance theory -- that the interaction between Rydberg excitations and lattice vibrations leads to the emergence of slowly decaying bound states that inhibit fast relaxation of certain initial states.Comment: 26 pages, 5 figure

Molecular Dynamics in Rydberg Tweezer Arrays: Spin-Phonon Entanglement and Jahn-Teller Effect

Atoms confined in optical tweezer arrays constitute a platform for the implementation of quantum computers and simulators. State-dependent operations are realized by exploiting electrostatic dipolar interactions that emerge, when two atoms are simultaneously excited to high-lying electronic states, so-called Rydberg states. These interactions also lead to state-dependent mechanical forces, which couple the electronic dynamics of the atoms to their vibrational motion. We explore these vibronic couplings within an artificial molecular system in which Rydberg states are excited under so-called facilitation conditions. This system, which is not necessarily self-bound, undergoes a structural transition between an equilateral triangle and an equal-weighted superposition of distorted triangular states (Jahn-Teller regime) exhibiting spin-phonon entanglement on a micrometer distance. This highlights the potential of Rydberg tweezer arrays for the study of molecular phenomena at exaggerated length scales

Phonon dressing of a facilitated one-dimensional Rydberg lattice gas

We study the dynamics of a one-dimensional Rydberg lattice gas under facilitation (antiblockade) conditions which implements a so-called kinetically constrained spin system. Here an atom can only be excited to a Rydberg state when one of its neighbors is already excited. Once two or more atoms are simultaneously excited mechanical forces emerge, which couple the internal electronic dynamics of this many-body system to external vibrational degrees of freedom in the lattice. This electron-phonon coupling results in a so-called phonon dressing of many-body states which in turn impacts on the facilitation dynamics. In our theoretical study we focus on a scenario in which all energy scales are sufficiently separated such that a perturbative treatment of the coupling between electronic and vibrational states is possible. This allows to analytically derive an effective Hamiltonian for the evolution of clusters of consecutive Rydberg excitations in the presence of phonon dressing. We analyze the spectrum of this Hamiltonian and show — by employing Fano resonance theory — that the interaction between Rydberg excitations and lattice vibrations leads to the emergence of slowly decaying bound states that inhibit fast relaxation of certain initial states

Coherent Spin-Phonon Scattering in Facilitated Rydberg Lattices

We investigate the dynamics of a one-dimensional spin system with facilitation constraint that can be studied using Rydberg atoms in arrays of optical tweezer traps. The elementary degrees of freedom of the system are domains of Rydberg excitations that expand ballistically through the lattice. Because of mechanical forces, Rydberg excited atoms are coupled to vibrations within their traps. At zero temperature and large trap depth, it is known that virtually excited lattice vibrations only renormalize the timescale of the ballistic propagation. However, when vibrational excitations are initially present—i.e., when the external motion of the atoms is prepared in an excited Fock state, coherent state or thermal state—resonant scattering between spin domain walls and phonons takes place. This coherent and deterministic process, which is free from disorder, leads to a reduction of the power-law exponent characterizing the expansion of spin domains. Furthermore, the spin domain dynamics is sensitive to the coherence properties of the atoms’ vibrational state, such as the relative phase of coherently superimposed Fock states. Even for a translationally invariant initial state the latter manifests macroscopically in a phase-sensitive asymmetric expansion

Enhancing Ozone Monitoring with Low-Cost Sensors and Deep Neural Network: A Novel Approach

Ozone is a crucial component of the Earth’s atmosphere, playing a critical role in protecting the planet from harmful ultraviolet radiation. However, its concentration can vary greatly across different regions with significant impacts on human health and environment equilibrium. The aim of this work was to calibrate a low-cost sensing platform, based on chemoresistive gas sensors, to monitor the environmental concentration of O3. The ongoing on-field calibration is performed with a deep neural network using the concentration of O3 collected by the local environmental protection agencies through certified tools as the gold standard

Emergent Bloch Oscillations in a Kinetically Constrained Rydberg Spin Lattice

We explore the relaxation dynamics of elementary spin clusters in a kinetically constrained spin system. Inspired by experiments with Rydberg lattice gases, we focus on the situation in which an excited spin leads to a "facilitated" excitation of a neighboring spin. We show that even weak interactions that extend beyond nearest neighbors can have a dramatic impact on the relaxation behavior: they generate a linear potential, which under certain conditions leads to the onset of Bloch oscillations of spin clusters. These hinder the expansion of a cluster and more generally the relaxation of many-body states towards equilibrium. This shows that non-ergodic behavior in kinetically constrained systems may occur as a consequence of the interplay between reduced connectivity of many-body states and weak interparticle interactions. We furthermore show that the emergent Bloch oscillations identified here can be detected in experiment through measurements of the Rydberg atom density, and discuss how spin-orbit coupling between internal and external degrees of freedom of spin clusters can be used to control their relaxation behavior. Introduction.-Kinetically constrained quantum systems have become an important setting for the investigation of complex dynamical many-body phenomena, both from the theoretical and the experimental point of view. In particular, constrained spin systems have turned out to constitute useful models for the study of slow relaxation, ergodicity breaking and the emergence of glassy physics [1-16]. In terms of experimental platforms a significant role is currently being played by Rydberg gases, in which atoms are excited to high-lying and strongly interacting states. This allows to implement effective quantum spin models with highly controllable state-dependent interactions that pave the way towards realizing a host of kinetic constraints [17-28]. Kinetic constraints impose restrictions on the connectiv-ity between many-body states that break the Hilbert space into disconnected sectors [29-32]. Ultimately, this may lead to the absence of thermalization and the emergence of non-ergodic behavior. This mechanism is different to ergodicity breaking stemming from disorder, occurring in many-body localized systems where it is caused by the emergence of local conservation laws [33]. Ergodic-ity breaking (in a disorder-free setting) may also occur when imposing externals fields: Refs. [34-42] show that for the case of a transverse field quantum Ising model, where an additionally applied longitudinal field leads to the confinement of excitations. This inhibits propagation of quasi-particles and thus prevents relaxation towards an ergodic steady state. In this work we investigate the dynamics of a disorder-free, translationally invariant many-body quantum spin system under a so-called facilitation constraint. As shown in Fig. 1, this can be realized with Rydberg atoms held in a lattice. We show that relaxation towards an ergodic stationary state is inhibited by the onset of Bloch osci

Emergent quantum correlations and collective behavior in non-interacting quantum systems subject to stochastic resetting

We investigate the dynamics of a non-interacting spin system, undergoing coherent Rabi oscillations, in the presence of stochastic resetting. We show that resetting generally induces long-range quantum and classical correlations both in the emergent dissipative dynamics and in the non-equilibrium stationary state. Moreover, for the case of conditional reset protocols-where the system is reinitialized to a state dependent on the outcome of a preceding measurement-we show that, in the thermodynamic limit, the spin system can feature collective behavior which results in a phenomenology reminiscent of that occurring in non-equilibrium phase transitions. The discussed reset protocols can be implemented on quantum simulators and quantum devices that permit fast measurement and readout of macroscopic observables, such as the magnetisation. Our approach does not require the control of coherent interactions and may therefore highlight a route towards a simple and robust creation of quantum correlations and collective non-equilibrium states, with potential applications in quantum enhanced metrology and sensing. Introduction.-Understanding and exploiting the interplay between coherent unitary evolution and measurement in quantum systems has been a central topic since the early days of quantum mechanics [1, 2]. Recent research in this direction is closely linked to the physics of open quantum systems [3-6], where interactions among quantum particles compete with the coupling to the surrounding environment. Modern experiments allow to externally control and even artificially engineer open system dynamics. This can, e.g., be achieved through so-called feedback protocols [7-12], which rely on the continuous monitoring of a system followed by some action conditioned on the output of a detector. This procedure can generate non-equilibrium steady states (NESS) that feature non-trivial quantum correlations [13-16]. Another approach that relies on externally imposed interventions in order to create effectively open system dynamics is stochastic resetting [17]. In its simplest form it amounts to resetting a system to its initial state at random times. This procedure has been originally studied for classical diffusive systems [18-21], search processes [18, 19, 22-25] and active systems [26-32], and also here interesting NESS have been shown to emerge [33-44]. Similar observations have been made recently in the context of quantum systems [45-55]. However, it remains an open question whether resetting can induce non-trivial NESS, that may display emergent quantum correlations or even non-equilibrium phase transition behavior