1. Postdoctoral research assistant discussion

2. The Topological Protected and Non-Equilibrium States (TOPNES) program gathers many scientists, grouped at three different Universities, among which there are five postdoctoral fellows. Some are theoreticians, others are experimentalists, but we all have a common objective : elaborate a framework to understand and control quantum materials and devices. Although we have our own personal research, it is essential to collaborate to move forward with this common objective. To achieve this goal, we organized a group discussion during the last TOPNES advisory board meeting in May 2013 during which we all summarized our work, exchanges ideas and comments.

3. Eliot Kapit - Oxford University Quantum Simulation Architecture for Lattice Bosons in Arbitrary, Tunable External Gauge Fields Eliot described a lattice of asymmetrical qubit pairs, in one or two dimensions, with couplings arranged so that the motion of single-qubit excited states mimics the behavior of charged lattice bosons hopping in a magnetic field. He showed in particular that one can choose the parameters of the many-body circuit to reach a regime where the complex hopping phase between any two elements can be tuned to any value by simply adjusting the relative phases of two applied oscillating voltage signals. He also proposed specific realizations of their model using coupled three junction flux qubits or transmon qubits, in which one can reach the strongly interacting bosonic quantum Hall limit where one will find anyonic excitations. This model could also be studied in trapped ions, and the superconducting circuits could be used for topological quantum computation.

4. Chaitanya Joshi - University of St- Andrews Simulating dissipative driven quantum systems with Matrix Product States. Chaitanya discussed a possibility to simulate dissipative driven quantum systems using Matrix Product States. It was mentioned how Matrix Product States are an efficient representation when it comes to simulating 1-D quantum systems which otherwise is a mammoth looking task in terms of exponential increase in resources. The properties of non-equilibrium steady state were further discussed. Quantum correlations in the non-equilibrium steady state of Ising, X-Y and X-X model were also discussed. It was mentioned that non- equilibrium properties of these models are in stark contrast to their equilibrium counterparts.

5. Jesper Romers - Oxford University Unconventional superconductivity in Sr 2 RuO4 4 Jesper presented the main challenges on how to explain the complex and various experimental properties of the superconductor strontium ruthenate Sr 2 RuO4 4 (SRO) within a single theoretical framework. Indeed, although the spin triplet pairing is well-established experimentally, the form of the orbital part of the pairing wave function is still the subject of debate. There is hope though that SRO is an electronic analogue of the A phase of He-3, a chiral p- wave superconductor. If true, this state of matter would carry topologically protected edge modes and supports half quantum vortices with Majorana zero modes : the quintessential properties of topological superconductor. From a theoretical point of view, the problem is very rich given the fact that SRO is a layered two-dimensional system with three bands. Most theories assume the dominant contribution to the superconductivity comes from the 2D band - recent proposals however involve the other two quasi-1D bands. His original approach to solve this problem is to take into account all three energy bands as well as strong spin-orbit coupling, which is important in SRO.

6. Wei Guan - Edinburgh University The construction of a magneto optic Kerr microscope for topological systems Wei discussed the construction of the low-temperature magneto-optical Kerr effect microscope at University of Edinburgh. The initial motivation of this microscope is to image magnetic domain boundaries and vortices of novel superconductors and topological insulators. The main technical challenge is trying to achieve the highest possible resolution of magneto-optical imaging at extreme working conditions, such as low temperature at 100 mK, high magnetic field up to 14 T and through an diamond anvil cell providing high pressure. The research group at Edinburgh have worked out a solution to fit all the requirements and the bench test of this microscope shows some promising results.

7. Peter Kirton - University of St-Andrews Open problems related to photon condensation Peter talked about the current directions his research is taking and discussed some work in progress. Topics included: a Gross–Pitaevskii model for thermal lensing in the photon BEC, a description of the system above threshold using a variational polaron transform and a Keldysh Green's function approach to obtaining correlation functions of the photons.

8. Jean-Philippe Reid - University of St-Andrews & Cornell University Magnetoelectric effect of topological insulators Jean-Philippe’s project is to detect the main properties which define topological insulators. Although these materials are well defined theoretically, it is a real tour de force to design an experiment in order to identify the main properties of topological insulators. One possibility is to look for the magnetoelectric effect, which is an intrinsic property of topological insulators. This effect is the result of the coupling between the electrical and magnetic fields : by applying an electrical field, one should be able to detect a magnetic field... and vice versa. After discussing the origin of the magnetoelectric effect, Jean-Philippe described an elaborate experimental apparatus which can be used to detect this effect.