A major objective of the strong ongoing drive to realize quantum simulators of gauge theories is achieving the capability to probe collider-relevant physics on them. In this regard, a highly pertinent and sought-after application is the controlled collisions of elementary and composite particles, as well as the scattering processes in their wake. Here, we propose particle-collision experiments in a cold-atom quantum simulator for a 1 + 1 D (one spatial and one temporal dimension) U(1) lattice gauge theory with a tunable topological θ term, where we demonstrate an experimentally feasible protocol to impart momenta to elementary (anti)particles and their meson composites. We numerically benchmark the collisions of moving wave packets for both elementary and composite particles, uncovering a plethora of rich phenomena, such as oscillatory string dynamics in the wake of elementary (anti)particle collisions due to confinement. We also probe string inversion and entropy production processes across Coleman’s phase transition through far-from-equilibrium quenches. We further demonstrate how collisions of composite particles unveil their internal structure. Our work paves the way towards the experimental investigation of collision dynamics in state-of-the-art quantum simulators of gauge theories, and sets the stage for microscopic understanding of collider-relevant physics in these platforms. Published by the American Physical Society 2024
A major objective of the strong ongoing drive to realize quantum simulators of gauge theories is achieving the capability to probe collider-relevant physics on them. In this regard, a highly pertinent and sought-after application is the controlled collisions of elementary and composite particles, as well as the scattering processes in their wake. Here, we propose particle-collision experiments in a cold-atom quantum simulator for a 1 + 1 D (one spatial and one temporal dimension) U(1) lattice gauge theory with a tunable topological θ term, where we demonstrate an experimentally feasible protocol to impart momenta to elementary (anti)particles and their meson composites. We numerically benchmark the collisions of moving wave packets for both elementary and composite particles, uncovering a plethora of rich phenomena, such as oscillatory string dynamics in the wake of elementary (anti)particle collisions due to confinement. We also probe string inversion and entropy production processes across Coleman’s phase transition through far-from-equilibrium quenches. We further demonstrate how collisions of composite particles unveil their internal structure. Our work paves the way towards the experimental investigation of collision dynamics in state-of-the-art quantum simulators of gauge theories, and sets the stage for microscopic understanding of collider-relevant physics in these platforms. Published by the American Physical Society 2024
Abstract Simulating real-time evolution in theories of fundamental interactions represents one of the central challenges in contemporary theoretical physics. Cold-atom platforms stand as promising candidates to realize quantum simulations of non-perturbative phenomena in gauge theories, such as vacuum decay and hadron collisions, in prohibitive conditions for direct experiments. In this work, we demonstrate that present-day quantum simulators can imitate linear particle accelerators, giving access to S -matrix measurements of elastic and inelastic meson collisions in low-dimensional abelian gauge theories. Considering for definiteness a (1 + 1)-dimensional Z 2 -lattice gauge theory realizable with Rydberg-atom arrays, we present protocols to observe and measure selected meson–meson scattering processes. We provide a benchmark theoretical study of scattering amplitudes in the regime of large fermion mass, including an exact solution valid for arbitrary coupling strength. This allows us to discuss the occurrence of inelastic scattering channels, featuring the production of new mesons with different internal structures. We present numerical simulations of realistic wavepacket collisions, which reproduce the predicted cross section peaks. This work highlights the potential of quantum simulations to give unprecedented access to real-time scattering dynamics.
Understanding the non-equilibrium dynamics of gauge theories remains a fundamental challenge in high-energy physics. Indeed, most large scale experiments on gauge theories intrinsically rely on very far-from equilibrium dynamics, from heavy-ion to lepton and hadron collisions, which is in general extremely challenging to treat ab initio. Quantum simulation holds intriguing potential in tackling this problem and pioneering experiments have observed different characteristic features of gauge theories, such as string breaking and false vacuum decay. Here, using a programmable Rydberg atom array, we observe real-time scattering and freeze-out dynamics in a (1+1)-dimensional U(1) lattice gauge theory. Through spatiotemporal Hamiltonian engineering, we demonstrate dynamical confinement-deconfinement transitions, revealing string fragmentation and symmetry restoration during quenches. We track scattering processes with single-site resolution across a range of parameter regimes. Utilizing a double quench protocol, we observe dynamical freeze-out: upon quenching the Hamiltonian after scattering, despite the injection of an extensive energy, the system evolution -- in terms of both low-order correlations and entanglement -- freezes, effectively stabilizing a highly correlated equilibrium state -- a situation that reminisces that of collisions between heavy ions. Our work establishes a high-resolution approach for probing non-perturbative gauge dynamics, opening alternative pathways toward studying far-from-equilibrium phenomena in high-energy physics.
Abstract Understanding the non-equilibrium dynamics of gauge theories remains a fundamental challenge in high-energy physics. Indeed, most large scale experiments on gauge theories intrinsically rely on very far-from equilibrium dynamics, from heavy-ion to lepton and hadron collisions, which is in general extremely challenging to treat ab initio. Quantum simulation holds intriguing potential in tackling this problem and pioneering experiments have observed different characteristic features of gauge theories, such as string breaking and false vacuum decay. Here, using a programmable Rydberg atom array, we observe real-time scattering and freeze-out dynamics in a (1+1)-dimensional U(1) lattice gauge theory. Through spatiotemporal Hamiltonian engineering, we demonstrate dynamical confinement-deconfinement transitions, revealing string fragmentation and symmetry restoration during quenches. We track scattering processes with single-site resolution across a range of parameter regimes. Utilizing a double quench protocol, we observe dynamical freeze-out: upon quenching the Hamiltonian after scattering, despite the injection of an extensive energy, the system evolution---in terms of both low-order correlations and entanglement---freezes, effectively stabilizing a highly correlated equilibrium state---a situation that reminisces that of collisions between heavy ions. Our work establishes a high-resolution approach for probing non-perturbative gauge dynamics, opening alternative pathways toward studying far-from-equilibrium phenomena in high-energy physics.
Gauge theories form the foundation of modern physics, with applications ranging from elementary particle physics and early-universe cosmology to condensed matter systems.We perform quantum simulations of the unitary dynamics of a U(1) symmetric gauge field theory and demonstrate emergent irreversible behavior.The highly constrained gauge theory dynamics is encoded in a one-dimensional Bose-Hubbard simulator, which couples fermionic matter fields through dynamical gauge fields.We investigate global quantum quenches and the equilibration to a steady state well approximated by a thermal ensemble.Our work may enable the investigation of elusive phenomena, such as Schwinger pair production and string-breaking, and paves the way for simulating more complex higher-dimensional gauge theories on quantum synthetic matter devices.
In the last decade there has been an intense activity aimed at the quantum simulation of interacting many-body systems using cold atoms [1, 2]. The idea of quantum simulations traces back to Feynman [3], who argued that the ideal setting to study quantum systems would be a quantum experimental setup rather then a classical one - the latter one being fundamentally limited due to its hardware classical structure. This is a particularly important problem given the intrinsic complexity of interacting many-body problems, and the difficulties that arise when tackling them with numerical simulations - two paradigmatic examples being the sign(s) problem affecting Monte Carlo simulations of fermionic systems, and the real time dynamics in more than one spatial dimension. Ultracold atoms offer a very powerful setting for quantum simulations. Atoms can be trapped in tailored optical and magnetic potentials, also controlling their dimensionality. The inter-atomic interactions can be tuned by external knobs, such as Feshbach resonances. This gives a large freedom on model building and, with suitable mappings, they allow the implementation of desired target models. This allowed an impressive exploitation of quantum simulators on the context of condensed matter physics. The simulation of high-energy physics is an important line of research in this field and it is less direct. In particular it requires the implementation of symmetries like Lorentz and gauge invariance which are not immediately available in a cold atomic setting. Gauge fields are ubiquitous in physics ranging from condensed matter [4–6] and quantum computation [7, 8] to particle physics [9], an archetypical example being Quantum Chromodynamics (QCD) [10,11], the theory of strong nuclear forces. Currently open problems in QCD, providing a long-term goal of cold atomic simulations, include confinement/deconfinement and the structure of color superconducting phases at finite chemical potential [12]. Even though QCD is a very complicated theory (to simulate or study), it is possible to envision a path through implementation of simpler models. Furthermore, it is also expected that interesting physics is found on such “intermediate models” which may deserve attention irrespectively of the QCD study. A very relevant model in this regard is the Schwinger model (Quantum Electrodynamics in 1+1 dimensions) [13]. This theory exhibits features of QCD, such as confinement [14], and is at the very same time amenable to both theoretical studies and simpler experimental schemes. This model was the target of the first experimental realization of a gauge theory with a quantum simulator [15]. The work on this Thesis is, in part, motivated by the study of toy models which put in evidence certain aspects that can be found in QCD. Such toy models provide also intermediate steps in the path towards more complex simulations. The two main aspects of QCD which are addressed here are symmetry-locking and confinement. The other main motivation for this study is to develop a systematic framework, through dimensional mismatch, for theoretical understanding and quantum simulations of long-range theories using gauge theories. The model used to study symmetry-locking consists of a four-fermion mixture [16]. It has the basic ingredients to exhibit a non-Abelian symmetry-locked phase: the full Hamiltonian has an SU (2) × SU (2) (global) symmetry which can break to a smaller SU (2) group. Such phase is found in a extensive region of the phase diagram by using a mean-field approach and a strong coupling expansion. A possible realization of such system is provided by an Ytterbium mixture. Even without tuning interactions, it is shown that such mixture falls inside the the locked-symmetry phase pointing towards a possible realization in current day experiments. The models with dimensional mismatch investigated here have fermions in a lower dimensionality d + 1 and gauge fields in higher dimensionality D + 1. They serve two purposes: establish mappings to non-local theories by integration of fields [17] and the study of confinement [18]. In the particular case of d = 1 and D = 2 it is found that some general non-local terms can be obtained on the Lagrangian [17]. This is found in the form of power-law expansions of the Laplacian mediating either kinetic terms (for bosons) or interactions (for fermions). The fact that such expansions are not completely general is not surprising since constraints do exist, preventing unphysical features like breaking of unitarity. The non-local terms obtained are physically acceptable, in this regard, since they are derived from unitary theories. The above mapping is done exactly. In certain cases it is shown that it is possible to construct an effective long-range Hamiltonian in a perturbative expansion. In particular it is shown how this is done for non-relativistic fermions (in d = 1) and 3 + 1 gauge fields. These results are relevant in the context of state of the art experiments which implement models with long-range interactions and where theoretical results are less abundant than for the case of local theories. The above mappings establish a direct relation with local theories which allow theoretical insight onto these systems. Examples of this would consist on the application of Mermin- Wagner-Hohenberg theorem [19, 20] and Lieb-Robinson bounds [21], on the propagation of quantum correlations, to non-local models. In addition they can also provide a path towards implementation of tunable long-range interactions with cold atoms. Furthermore, in terms of quantum simulations, they are in between the full higher dimensional system and the full lower dimensional one. Such property is attractive from the point of view of a gradual increase of complexity for quantum simulations of gauge theories. Another interesting property of these models is that they allow the study of confinement beyond the simpler case of the Schwinger model. The extra dimensions are enough to attribute dynamics to the gauge field, which are no longer completely fixed by the Gauss law. The phases of the Schwinger model are shown to be robust under variation of the dimension of the gauge fields [18]. Both the screened phase, of the massless case, and the confined phase, of the massive one, are found for gauge fields in 2+1 and 3+1 dimensions. Such results are also obtained in the Schwinger- Thirring model. This shows that these phases are very robust and raises interesting questions about the nature of confinement. Robustness under Thirring interactions are relevant because it shows that errors on the experimental implementation will not spoil the phase. Even more interesting is the case of gauge fields in higher dimensions since confinement in the Schwinger model is intuitively atributed to the dimensionality of the gauge fields (creating linear potentials between particles). This Thesis is organized as follows. In Chapter 1, some essential background regarding quantum simulations of gauge theories is provided. It gives both a brief introduction to cold atomic physics and lattice gauge theories. In Chapter 2, it is presented an overview over proposals of quantum simulators of gauge potentials and gauge fields. At the end of this Chapter, in Section 2.3 it is briefly presented ongoing work on a realization of the Schwinger model that we term Half Link Schwinger model. There, it is argued, some of the generators of the gauge symmetry on the lattice can be neglected without comprimising gauge invariance. In Chapter 3, the results regarding the phase diagram of the fourfermion mixture, exhibiting symmetry-locking, is presented. In Chapter 4, the path towards controlling non-local kinetic terms and interactions is provided, after a general introduction to the formalism of dimensional mismatch. At the end the construction of effective Hamiltonians is described. Finally, Chapter 5 concerns the study of confinement and the robustness of it for 1+1 fermions. The first part regards the Schwinger-Thirring with the presence of a -term while, in the second part, models with dimensional mismatch are considered. The thesis ends with conclusions and perspectives of future work based on the results presented here.
String breaking is a fundamental concept in gauge theories, describing the decay of a flux string connecting two charges through the production of particle-antiparticle pairs. This phenomenon is particularly important in particle physics, notably in quantum chromodynamics, and plays a crucial role in condensed matter physics. However, achieving a theoretical understanding of this nonperturbative effect is challenging, as conventional numerical approaches often fall short and require substantial computational resources. On the experimental side, studying these effects necessitates advanced setups, such as high-energy colliders, which makes direct observation difficult. Here, we report an experimental investigation of the string breaking mechanism in a one-dimensional U(1) lattice gauge theory using an optical lattice quantum simulator. By deterministically preparing initial states of varying lengths with fixed charges at each end, and adiabatically tuning the mass and string tension, we observed in situ microscopic confined phases that exhibit either string or broken-string states. Further analysis reveals that string breaking occurs under a resonance condition, leading to the creation of new particle-antiparticle pairs. These findings offer compelling evidence of string breaking and provide valuable insights into the intricate dynamics of lattice gauge theories. Our work underscores the potential of optical lattices as controllable quantum simulators, enabling the exploration of complex gauge theories and their associated phenomena.