J. Smith

Linear arrays of trapped and laser cooled atomic ions are a versatile platform for studying emergent phenomena in strongly-interacting many-body systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatiotemporal resolution, decoupling from the external environment, and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin-models which are heralded by memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.

Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Analogous to crystals in space, the breaking of translation symmetry in time and the emergence of a "time crystal" was recently proposed, but later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems subject to a periodic drive can exhibit persistent time-correlations at an emergent sub-harmonic frequency. This new phase of matter has been dubbed a "discrete time crystal" (DTC). Here, we present the first experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization (MBL) conditions, and observe a sub-harmonic temporal response that is robust to external perturbations. Such a time crystal opens the door for studying systems with long-range spatial-temporal correlations and novel phases of matter that emerge under intrinsically non-equilibrium conditions.

The physics of interacting integer-spin chains has been a topic of intense theoretical interest, particularly in the context of symmetry-protected topological phases. However, there has not been a controllable model system to study this physics experimentally. We demonstrate how spin-dependent forces on trapped ions can be used to engineer an effective system of interacting spin-1 particles. Our system evolves coherently under an applied spin-1 XY Hamiltonian with tunable, long-range couplings, and all three quantum levels at each site participate in the dynamics. We observe the time evolution of the system and verify its coherence by entangling a pair of effective three-level particles (`qutrits') with 86% fidelity. By adiabatically ramping a global field, we produce ground states of the XY model, and we demonstrate an instance where the ground state cannot be created without breaking the same symmetries that protect the topological Haldane phase. This experimental platform enables future studies of symmetry-protected order in spin-1 systems and their use in quantum applications.

Frustration, or the competition between interacting components of a network, is often responsible for the complexity of many body systems, from social and neural networks to protein folding and magnetism. In quantum magnetic systems, frustration arises naturally from competing spin-spin interactions given by the geometry of the spin lattice or by the presence of long-range antiferromagnetic couplings. Frustrated magnetism is a hallmark of poorly understood systems such as quantum spin liquids, spin glasses and spin ices, whose ground states are massively degenerate and can carry high degrees of quantum entanglement. The controlled study of frustrated magnetism in materials is hampered by short dynamical time scales and the presence of impurities, while numerical modeling is generally intractable when dealing with dynamics beyond N~30 particles. Alternatively, a quantum simulator can be exploited to directly engineer prescribed frustrated interactions between controlled quantum systems, and several small-scale experiments have moved in this direction. In this article, we perform a quantum simulation of a long-range antiferromagnetic quantum Ising model with a transverse field, on a crystal of up to N = 16 trapped Yb+ atoms. We directly control the amount of frustration by continuously tuning the range of interaction and directly measure spin correlation functions and their dynamics through spatially-resolved spin detection. We find a pronounced dependence of the magnetic order on the amount of frustration, and extract signatures of quantum coherence in the resulting phases.