Confinement and deconfinement, captivating attributes of high-energy elementary particles, have recently garnered wide attention in quantum simulations based on cold atoms. However, partial confinement, an intermediate state between the confinement and deconfinement, remains underexplored. The partial confinement encapsulates the phenomenon that the confining behavior of charged particles is contingent upon their relative positions. In this paper we demonstrate that the spin-1 quantum-link model provides an excellent platform for exploring partial confinement. We conduct a comprehensive investigation of the physics emerging from partial confinement in the context of both equilibrium and nonequilibrium dynamics. Potential experimental setups using cold atoms are also discussed. Our work offers a simple and feasible routine for the study of confinement-related physics in the state-of-the-art artificial quantum systems subject to gauge symmetries.
Confinement and deconfinement, captivating attributes of high-energy elementary particles, have recently garnered wide attention in quantum simulations based on cold atoms. However, partial confinement, an intermediate state between the confinement and deconfinement, remains underexplored. The partial confinement encapsulates the phenomenon that the confining behavior of charged particles is contingent upon their relative positions. In this paper we demonstrate that the spin-1 quantum-link model provides an excellent platform for exploring partial confinement. We conduct a comprehensive investigation of the physics emerging from partial confinement in the context of both equilibrium and nonequilibrium dynamics. Potential experimental setups using cold atoms are also discussed. Our work offers a simple and feasible routine for the study of confinement-related physics in the state-of-the-art artificial quantum systems subject to gauge symmetries.
Confinement is an intriguing phenomenon prevalent in condensed matter and high-energy physics. Exploring its effect on the far-from-equilibrium criticality of quantum many-body systems is of great interest from both a fundamental and a technological point of view. Here, we employ large-scale uniform matrix product state calculations to show that a qualitative change in the type of dynamical quantum phase transitions (DQPTs) accompanies the confinement-deconfinement transition in three paradigmatic models: the power-law interacting quantum Ising chain, the two-dimensional quantum Ising model, and the spin- S U ( 1 ) quantum link model. By tuning a confining parameter in these models, it is found that () DQPTs arise as a signature of (de)confinement. Whereas manifold DQPTs are associated with a sign change of the order parameter, their branch counterparts are not, but rather occur even when the order parameter exhibits considerably constrained dynamics. Our conclusions can be tested in modern quantum-simulation platforms, such as ion-trap setups and cold-atom experiments of gauge theories.
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.
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
The one-dimensional lattice Schwinger model has recently been realized by using bosons in optical lattices.This model contains both confinement and deconfinement phases, the phase diagram of which is controlled by the mass of the matter field and the topological angle.Since varying the mass of the matter field is straightforward experimentally, we propose how to tune the topological angle, allowing exploration of the phase diagram from both directions.We propose that direct experimental evidence of confinement and deconfinement can be obtained by measuring whether a physical charge is localized around a fixed gauge charge to screen it.We also discuss the PXP model realized in the Rydberg-atom array, which is equivalent to the lattice Schwinger model when all local gauge charges are fixed as zero.Although the gauge charges are fixed, we can alternatively probe confinement and deconfinement in the PXP model by studying the relative motion of a pair of a physical charge and an anticharge.Our scheme can be directly implemented in these two relevant experimental platforms of ultracold-atom quantum simulators.
Quantum link models (QLMs) are extensions of Wilson-type lattice gauge theories which realize exact gauge invariance with finite-dimensional Hilbert spaces. QLMs not only reproduce standard features of Wilson lattice gauge theories in equilibrium, but can also host new phenomena such as crystalline confined phases. The local constraints due to gauge invariance also provide kinetic restrictions that can influence substantially the real-time dynamics in these systems. We aim to characterize the nonequilibrium evolution in lattice gauge theories through the lens of dynamical quantum phase transitions, which provide general principles for real-time dynamics in quantum many-body systems. Specifically, we study quantum quenches for two representative cases, U(1) QLMs in (1+1)D and (2+1)D, for initial conditions exhibiting long-range order. Finally, we discuss the connection to the high-energy perspective and the experimental feasibility to observe the discussed phenomena in recent quantum simulator settings such as trapped ions, ultracold atoms, and Rydberg atoms.
Predicting the quantum dynamics of charged matter interacting with dynamical gauge fields poses an outstanding challenge in theoretical physics. Lacking a generally applicable computational method, quantum simulators offer a promising alternative. \n \nIn this thesis, we contribute to the quantum simulation of high-energy physics, focusing on the platform of ultracold atoms. Using Wilson fermions, we propose to improve implementations of lattice gauge theories based on mixtures of cold atoms in optical lattices. Numerical benchmarks indicate that this makes the realization of Schwinger pair production feasible with current technology. Our proposal is modular and an elementary building is demonstrated experimentally. We further identify dynamical topological transitions, which we discovered in the massive Schwinger model, as a suitable target for quantum simulators. Defining a gauge-invariant order parameter, these transitions are shown to persist beyond weak coupling. \n \nIn the second part of this thesis, we develop a framework for analyzing quantum simulators in terms of experimentally accessible irreducible correlation functions at equal times. We verify this approach numerically for the sine-Gordon model in thermal equilibrium, quantum simulated by two tunnel-coupled superfluids. Finally, we apply our analysis to the non-equilibrium dynamics of a spinor Bose gas, revealing suppressed effective interactions in a strongly-correlated infrared regime.