September 2014

Abstracts of the QSIT Lunch Seminar, Thursday September 4, 2014

Characterization and manipulation of frequency entangled qudits

Bänz Bessire, Institute of Applied Physics, University of Bern

Entanglement is nowadays a fundamental resource for quantum information processing and at the same time reveals the non-local structure of nature at its fundamental level. Entangling higher dimensional bipartite systems (qudits) has been shown to give more insights into the nature of entanglement compared to the simplest entanglement system composed of two qubits. For quantum key distribution, increasing the dimension of the alphabet by using qudits increases the effective bit rate of the protocol, still being secure.

We demonstrate here a new way to experimentally encode qudits in the energy spectrum of broadband entangled photons generated by parametric down-conversion and detected in coincidence by sum frequency generation. Taking into account experimental methods used to shape fs-laser pulses, the spectrum of the entangled photons is discretized into frequency bins. By controlling each frequency bin individually, the generation of maximally entangled qudits up to dimension four is verified through quantum state tomography. Subsequently, we measure a Bell parameter for entangled qubits and qutrits as a function of their degree of entanglement. In collaboration with the Cryptography and Quantum Information group at USI Lugano, the non-locality content of various qutrit states is further quantified by means of the distance to a local polytope and the non-local capacity. The latter quantifies the amount of classically shared information to simulate the correlation between two quantum systems and therefore directly identifies non-locality as an information resource.

_{Experimental realization of the topological Haldane model}

Remi Desbuquois, Quantum Optics Group, ETH Zurich

The Haldane model on the honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topologically distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band-structure, rather than being caused by an external magnetic field. Although an implementation in a material was considered unlikely, it has provided the conceptual basis for theoretical and experimental research exploring topological insulators and superconductors. Here we report on the experimental realisation of the Haldane model and the characterisation of its topological band-structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The model is based on breaking time-reversal symmetry as well as inversion symmetry. The former is achieved through the introduction of complex next-nearest-neighbour tunnelling terms, which we induce through circular modulation of the lattice position. For the latter, we create an energy offset between neighbouring sites. Breaking either of these symmetries opens a gap in the band-structure, which is probed using momentum-resolved interband transitions. We explore the resulting Berry-curvatures of the lowest band by applying a constant force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between both broken symmetries gives rise to a transition between topologically distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line experimentally and compare it to calculations using Floquet theory without free parameters. We verify that our approach, which allows for dynamically tuning topological properties, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realise spin-dependent topological Hamiltonians.