We present a quantum simulation scheme for the Abelian-Higgs lattice gauge theory using ultracold bosonic atoms in optical lattices. The model contains both gauge and Higgs scalar fields, and exhibits interesting phases related to confinement and the Higgs mechanism. The model can be simulated by an atomic Hamiltonian, by first mapping the local gauge symmetry to an internal symmetry of the atomic system, the conservation of hyperfine angular momentum in atomic collisions. By including auxiliary bosons in the simulation, we show how the Abelian-Higgs Hamiltonian emerges effectively. We analyze the accuracy of our method in terms of different experimental parameters, as well as the effect of the finite number of bosons on the quantum simulator. Finally, we propose possible experiments for studying the ground state of the system in different regimes of the theory, and measuring interesting high energy physics phenomena in real time.
We present a quantum simulation scheme for the Abelian-Higgs lattice gauge theory using ultracold bosonic atoms in optical lattices. The model contains both gauge and Higgs scalar fields, and exhibits interesting phases related to confinement and the Higgs mechanism. The model can be simulated by an atomic Hamiltonian, by first mapping the local gauge symmetry to an internal symmetry of the atomic system, the conservation of hyperfine angular momentum in atomic collisions. By including auxiliary bosons in the simulation, we show how the Abelian-Higgs Hamiltonian emerges effectively. We analyze the accuracy of our method in terms of different experimental parameters, as well as the effect of the finite number of bosons on the quantum simulator. Finally, we propose possible experiments for studying the ground state of the system in different regimes of the theory, and measuring interesting high energy physics phenomena in real time.
Can high-energy physics be simulated by low-energy, non-relativistic, many-body systems such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure an atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective low-energy symmetry, or as an exact symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to a new type of (table-top) experiments which will be used to study various QCD (quantum chromodynamics) phenomena, such as the confinement of dynamical quarks, phase transitions and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing the quantum simulation of Abelian and non-Abelian lattice gauge theories in 1 + 1 and 2 + 1 dimensions using ultracold atoms in optical lattices.
Can high-energy physics be simulated by low-energy, non-relativistic, many-body systems such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in particular, they manifest neither local gauge invariance nor Lorentz invariance, which are crucial properties of the quantum field theories which are the building blocks of the standard model of elementary particles. However, it turns out, surprisingly, that there are ways to configure an atomic system to manifest both local gauge invariance and Lorentz invariance. In particular, local gauge invariance can arise either as an effective low-energy symmetry, or as an exact symmetry, following from the conservation laws in atomic interactions. Hence, one could hope that such quantum simulators may lead to a new type of (table-top) experiments which will be used to study various QCD (quantum chromodynamics) phenomena, such as the confinement of dynamical quarks, phase transitions and other effects, which are inaccessible using the currently known computational methods. In this report, we review the Hamiltonian formulation of lattice gauge theories, and then describe our recent progress in constructing the quantum simulation of Abelian and non-Abelian lattice gauge theories in 1 + 1 and 2 + 1 dimensions using ultracold atoms in optical lattices.
This thesis presents our recent studies on quantum simulation of the Abelian Higgs lattice gauge theory with quantum systems engineered with ultracold atoms in optical lattices and quantum equilibration and thermalization dynamics in the context of Joule expansion in cold atom systems.In the first part, we give proposals for the analog quantum simulation of lattice gauge theories with cold atoms in optical lattices with current experimental techniques, aiming at maximal simplicity on both the theoretical and experimental side. We search for the suitable platform for quantum simulation of the (1+1)-dimensional Abelian Higgs model, which is the scalar quantum electrodynamics replacing the fermionic fields by complex scalar fields. We use a discrete tensor reformulation to smoothly connect the space-time isotropic version used in most numerical lattice simulations to the continuous-time limit corresponding to the Hamiltonian formulation. We propose to use the Bose Hubbard model as a quantum simulator to probe the conformal Calabrese-Cardy scaling of its O(2) limit with a chemical potential. We also propose to use a physical multileg ladder of atoms trapped in optical lattices and interacting with Rydberg-dressed interactions to quantum simulate the model and measure the Polyakov loop. Numeric results from the Monte Carlo, the tensor renormalization group and the density matrix renormalization group techniques are cross-checked to support our proposals.In the second part of this thesis, we investigate the Joule expansion of nonintegrable quantum systems that contain bosons or spinless fermions in one-dimensional lattices. Initially a barrier confines the particles to be in half of the system in a thermal state described by the canonical ensemble and is removed at time t=0. We study the properties of the time-evolved density matrix, the diagonal ensemble density matrix and the corresponding canonical ensemble density matrix with an effective temperature determined by the total energy conservation. We discuss the equilibration and thermalization for the R\\'enyi entropy of subsystems, few-body observables and reduced density matrices in subsystems. We finally discuss the difference between bosons and fermions in finite size scaling of the effective temperature. We propose the Joule expansion as a way to dynamically create negative temperature states for fermion systems with repulsive interactions.
Lattice gauge theory has provided a crucial non-perturbative method in studying canonical models in high-energy physics such as quantum chromodynamics. Among other models of lattice gauge theory, the lattice gauge–Higgs model is a quite important one because it describes a wide variety of phenomena/models related to the Anderson–Higgs mechanism, such as superconductivity, the standard model of particle physics, and the inflation process of the early Universe. In this paper, we first show that atomic description of the lattice gauge model allows us to explore real-time dynamics of the gauge variables by using the Gross–Pitaevskii equations. Numerical simulations of the time development of an electric flux reveal some interesting characteristics of the dynamic aspect of the model and determine its phase diagram. Next, to realize a quantum simulator of the U(1) lattice gauge–Higgs model on an optical lattice filled by cold atoms, we propose two feasible methods: (i) Wannier states in the excited bands and (ii) dipolar atoms in a multilayer optical lattice. We pay attention to the constraint of Gauss's law and avoid nonlocal gauge interactions.
We present a theoretical study of quantum simulations of (1+1)-dimensional U(1) lattice gauge-Higgs models, which contain a compact U(1) gauge field and a Higgs matter field, by using ultracold bosonic gases on a one-dimensional optical lattice. Starting from the extended Bose-Hubbard model with on-site and nearest-neighbor interactions, we derive the U(1) lattice gauge-Higgs model as a low-energy effective theory. The derived gauge-Higgs model exhibits nontrivial phase transitions between the confinement and Higgs phases, and we discuss the relation with the phase transition in the extended Bose-Hubbard model. Finally, we study the real-time dynamics of an electric flux by the Gross-Pitaevskii equations and the truncated Wigner approximation. The dynamics is governed by a bosonic analog of the Schwinger mechanism---i.e., the shielding of an electric flux by a condensation of Higgs fields, which occurs differently in the Higgs and the confinement phases. These results, together with the obtained phase diagrams, shall guide experimentalists in designing quantum simulations of the gauge-Higgs models by using cold gases.
Recently, the possibility of quantum simulation of dynamical gauge fields was pointed out by using a system of cold atoms trapped on each link in an optical lattice. However, to implement exact local gauge invariance, fine-tuning the interaction parameters among atoms is necessary. In the present Letter, we study the effect of violation of the U(1) local gauge invariance by relaxing the fine-tuning of the parameters and showing that a wide variety of cold atoms is still a faithful quantum simulator for a U(1) gauge-Higgs model containing a Higgs field sitting on sites. The clarification of the dynamics of this gauge-Higgs model sheds some light upon various unsolved problems, including the inflation process of the early Universe. We study the phase structure of this model by Monte Carlo simulation and also discuss the atomic characteristics of the Higgs phase in each simulator.