Alexander W. Glaetzle

Time crystals in periodically driven systems have initially been studied assuming either the ability to quench the Hamiltonian between different many-body regimes, the presence of disorder or long-range interactions. Here we propose the simplest scheme to observe discrete time crystal dynamics in a one-dimensional driven quantum system of the Ising type with short-range interactions and no disorder. The system is subject only to a periodic kick by a global magnetic field, and no extra Hamiltonian quenching is performed. We analyze the emerging time crystal stabilizing mechanisms via extensive numerics as well as using an analytic approach based on an off-resonant transition model. Due to the simplicity of the driven Ising model, our proposal can be implemented with current experimental platforms including trapped ions, Rydberg atoms, and superconducting circuits.

We theoretically investigate trapped ions interacting with atoms that are coupled to Rydberg states. The strong polarizabilities of the Rydberg levels increases the interaction strength between atoms and ions by many orders of magnitude, as compared to the case of ground state atoms, and may be mediated over micrometers. We calculate that such interactions can be used to generate entanglement between an atom and the motion or internal state of an ion. Furthermore, the ion could be used as a bus for mediating spin-spin interactions between atomic spins in analogy to much employed techniques in ion trap quantum simulation. The proposed scheme comes with attractive features as it maps the benefits of the trapped ion quantum system onto the atomic one without obviously impeding its intrinsic scalability. No ground state cooling of the ion or atom is required and the setup allows for full dynamical control. Moreover, the scheme is to a large extent immune to the micromotion of the ion. Our findings are of interest for developing hybrid quantum information platforms and for implementing quantum simulations of solid state physics.

We propose a trapped ion scheme en route to realize spin Hamiltonians on a Kagome lattice which, at low energies, are described by emergent Z2 gauge fields, and support a topological quantum spin liquid ground state. The enabling element in our scheme is the hexagonal plaquette spin-spin interactions in a 2D ion crystal. For this, the phonon-mode spectrum of the crystal is engineered by standing-wave optical potentials or by using Rydberg excited ions, thus generating localized phonon-modes around a hexagon of ions selected out of the entire two-dimensional crystal. These tailored modes can mediate spin-spin interactions between ion-qubits on a hexagonal plaquette when subject to state-dependent optical dipole forces. We discuss how these interactions can be employed to emulate a generalized Balents-Fisher-Girvin model in minimal instances of one and two plaquettes. This model is an archetypical Hamiltonian in which gauge fields are the emergent degrees of freedom on top of the classical ground state manifold. Under realistic situations, we show the emergence of a discrete Gauss's law as well as the dynamics of a deconfined charge excitation on a gauge-invariant background using the two-plaquettes trapped ions spin-system. The proposed scheme in principle allows further scaling in a future trapped ion quantum simulator, and we conclude that our work will pave the way towards the simulation of emergent gauge theories and quantum spin liquids in trapped ion systems.