Quantum Simulation
There is considerable interest in developing quantum computational technologies that can simulate a series of physical phenomena inaccessible by classical computers. Mil et al. propose a modular scheme for quantum simulation of a U(1) lattice gauge theory based on heteronuclear spin-changing collisions in a mixture of two bosonic quantum gases isolated in single wells of a one-dimensional optical lattice. They engineered the elementary building block for a single well and demonstrate its reliable operation that preserves the gauge invariance. The potential for scalability of the proposed scheme opens up opportunities to address challenges in quantum simulating the continuum limit of the gauge theories.
Science , this issue p. [1128][1]
[1]: /lookup/doi/10.1126/science.aaz5312
Quantum Simulation
There is considerable interest in developing quantum computational technologies that can simulate a series of physical phenomena inaccessible by classical computers. Mil et al. propose a modular scheme for quantum simulation of a U(1) lattice gauge theory based on heteronuclear spin-changing collisions in a mixture of two bosonic quantum gases isolated in single wells of a one-dimensional optical lattice. They engineered the elementary building block for a single well and demonstrate its reliable operation that preserves the gauge invariance. The potential for scalability of the proposed scheme opens up opportunities to address challenges in quantum simulating the continuum limit of the gauge theories.
In the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is the quantum theory of electrons interacting with the electromagnetic field, based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. Although quantum computers suggest a way forward, large-scale digital quantum devices for complex simulations are difficult to build. We propose a scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. Using interspecies spin-changing collisions in an atomic mixture, we achieve gauge-invariant interactions between matter and gauge fields with spin- and species-independent trapping potentials. We experimentally realize the elementary building block as a key step toward a platform for quantum simulations of continuous gauge theories.
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.
Quantum simulations of high-energy physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge invariance and relativistic structure. In this paper we discuss these special requirements, and present a method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows us to include local gauge invariance as a fundamental symmetry of the atomic Hamiltonian, arising from natural atomic interactions and conservation laws (and not as a property of a low-energy sector). This allows us to implement elementary gauge invariant interactions for three lattice gauge theories: U(1) (compact QED), ZN and SU(N) (Yang-Mills), which can be used to build quantum simulators in 1+1 dimensions. We also present a loop method, which uses the elementary interactions as building blocks in the effective construction of quantum simulations for d+1 dimensional lattice gauge theories (d>1), but unlike in previous proposals, here gauge invariance and Gauss's law are natural symmetries, which do not have to be imposed as a constraint. We discuss in detail the quantum simulation of 2+1 dimensional compact QED and provide a numerical proof of principle. The simplicity of the already gauge-invariant elementary interactions of this model suggests it may be useful for future experimental realizations.
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.
We introduce a method for quantum simulation of U(1) lattice gauge theories coupled to matter, utilizing alkaline-earth(-like) atoms in state-dependent optical lattices.The proposal enables the study of both gauge and fermionic matter fields without integrating out one of them in one and two dimensions.We focus on a realistic and robust implementation that utilizes the long-lived metastable clock state available in alkaline-earth(-like) atomic species.Starting from an ab initio modeling of the experimental setting, we systematically carry out a derivation of the target U(1) gauge theory.This approach allows us to identify and address conceptual and practical challenges for the implementation of lattice gauge theories that-while pivotal for a successful implementation-have never been rigorously addressed in the literature: those include the specific engineering of lattice potentials to achieve the desired structure of Wannier functions and the subtleties involved in realizing the proper separation of energy scales to enable gauge-invariant dynamics.We discuss realistic experiments that can be carried out within such a platform using the fermionic isotope 173 Yb, addressing via simulations all key sources of imperfections, and provide concrete parameter estimates for relevant energy scales in both one-and two-dimensional settings.
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.