Prof Dieter Jaksch

Abstract:

We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules. The contraction property does not depend on specifics such as geometry, but rather originates from the non-trivial algebraic properties of the constituent tensors. We then generalise the resulting tensor network from a spin-1/2 lattice to a class of exactly contractible states on spin-S degrees of freedom, yielding the most efficient tensor network description of finite Abelian lattice gauge theories. We gain a new perspective on these states as examples of two-dimensional quantum states with algebraically contractible tensor network representations. The introduction of local perturbations to the network is shown to reduce the von Neumann entropy of string-like regions, creating an unentangled sub-system within the bulk in a certain limit. We also show how perturbations induce finite-range correlations in this system. This class of tensor networks is readily translated onto any lattice, and we differentiate between the physical consequences of bipartite and non-bipartite lattices on the properties of the corresponding quantum states. We explicitly show this on the hexagonal, square, kagome and triangular lattices.

Abstract:

We study the suitability of correlator product states for describing ground-state properties of two-dimensional spin models. Our ansatz for the many-body wave function takes the form of either plaquette or bond correlator product states and the energy is optimized by varying the correlators using Monte Carlo minimization. For the Ising model we find that plaquette correlators are best for estimating the energy while bond correlators capture the expected long-range correlations and critical behavior of the system more faithfully. For the antiferromagnetic Heisenberg model, however, plaquettes outperform bond correlators at describing both local and long-range correlations because of the substantially larger number of local parameters they contain. These observations have quantitative implications for the application of correlator product states to other more complex systems, and give important heuristic insights: in particular the necessity of carefully tailoring the choice of correlators to the system considered, its interactions and symmetries.

Abstract:

Competition between electron localization and delocalization in Mott insulators underpins the physics of strongly correlated electron systems. Photoexcitation, which redistributes charge, can control this many-body process on the ultrafast 1,2 timescale. So far, time-resolved studies have been carried out in solids in which other degrees of freedom, such as lattice, spin or orbital excitations 3-5 , dominate. However, the underlying quantum dynamics of bareg electronic excitations has remained out of reach. Quantum many-body dynamics are observed only in the controlled environment of optical lattices 6,7 where the dynamics are slower and lattice excitations are absent. By using nearly single-cycle near-infrared pulses, we have measured coherent electronic excitations in the organic salt ET-F 2 TCNQ, a prototypical one-dimensional Mott insulator. After photoexcitation, a new resonance appears, which oscillates at 25THz. Time-dependent simulations of the Mottg Hubbard Hamiltonian reproduce the oscillations, showing that electronic delocalization occurs through quantum interference between bound and ionized holong doublon pairs. © 2011 Macmillan Publishers Limited. All rights reserved.

Abstract:

We demonstrate the coherent storage and retrieval of sub-nanosecond low-intensity light pulses with spectral bandwidths exceeding 1 GHz in cesium vapor, using the novel, far off-resonant two-photon Raman memory protocol. © 2010 Optical Society of America.