Related papers: Quantum Simulation of the Two-Dimensional Weyl Equ…
The Weyl equation describes chiral massless relativistic particles, called Weyl fermions, which have important relations to neutrinos. A direct observation of the dynamics of Weyl fermions in an experiment is difficult to achieve. This…
We present a numerical scheme for simulating the 2D quantum dynamics of a two-level particle gas with internal degrees of freedom such as spin, pseudo-spin, or a two-band electronic structure. We adopt the Wigner formulation of quantum…
Quantum simulation of interacting many-body spin systems is routinely performed with cold trapped ions, and systems with hundreds of spins have been studied in one and two dimensions. In the most common realizations of these platforms, spin…
We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the…
The presence of long-range quantum spin correlations underlies a variety of physical phenomena in condensed matter systems, potentially including high-temperature superconductivity. However, many properties of exotic strongly correlated…
We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and…
The computational difficulty of solving fully quantum many-body spin problems is a significant obstacle to understanding the behavior of strongly correlated quantum matter. Experimental ion-trap quantum simulation is a promising approach…
Quantum field theories provide fundamental models of complex interacting systems, from high-energy physics and cosmology to condensed matter. However, solving these models in non-perturbative and dynamical regimes is often extremely…
We study a single quantum particle in discrete spacetime evolving in a causal way. We see that in the continuum limit any massless particle with a two dimensional internal degree of freedom obeys the Weyl equation, provided that we perform…
Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner…
A collection of trapped atomic ions represents one of the most attractive platforms for the quantum simulation of interacting spin networks and quantum magnetism. Spin-dependent optical dipole forces applied to an ion crystal create…
We perform a non-perturbative analysis of the dynamics of a two-level quantum system subjected to repeated interactions with a bosonic environment when these interactions are intense and localized in time. We use the Weyl relations to…
Large-scale simulations of the spin dynamics in quantum dots subjected to trains of periodic laser pulses enable us to describe and understand related experiments. By comparing the data for different models to experimental results, we gain…
The Weyl-Wigner-Moyal formalism for quantum particle with discrete internal degrees of freedom is developed. A one to one correspondence between operators in the Hilbert space $L^{2}(\mathbb{R}^{3})\otimes{\mathcal{H}}^{(s+1)}$ and…
Quantum-mechanical wave equation for a particle with spin 1 is investigated in presence of external magnetic field in spaces with non-Euclidean geometry with constant positive curvature. Separation of the variable is performed; differential…
We present a route towards the quantum simulation of exotic quantum magnetism in ion traps by exploiting dual relations between different spin models. Our strategy allows one to start from Hamiltonians that can be realized with current…
The possible interpretations of a new continuum model for the two-dimensional quantum gravity for $d>1$ ($d$=matter central charge), obtained by carefully treating both diffeomorphism and Weyl symmetries, are discussed. In particular we…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
Two-dimensional crystals of trapped ions are a promising system with which to implement quantum simulations of challenging problems such as spin frustration. Here, we present a design for a surface-electrode elliptical ion trap which…
A custom-built and precisely controlled quantum system may offer access to a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analog quantum simulator…