Talks

We report on the ab-plane optical properties of the magnetic field inducednormal state of underdoped La1.94Sr0.06CuO4  (Tc=5.5 K), the first such study. We apply strong magnetic fields (4 T and 16 T) along the c-axis. We find that a 4 T field is strong enough to destroy the superconducting condensate.  However at higher fields we observed a gap-like depression in the optical conductivity at low frequency along with parallel growth of a broad absorption peak at higher frequency just above the 5 meV gap. The loss of low frequency conductivity in the gap region is in good agreement with dc magneto resistance measurements on samples from the same batch.  The spectral weight loss in the depression at low frequency is recovered by the spectral weight in the broad peak. Significantly, this spectral weight equals the spectral weight of the superconducting condensate.  The broad peak tracks the SDW order seen by neutron scattering[1] and we suggest offers an optical signature of magnetism.

Chiral superconducting states have attracted an enormous amount of interest in recent years, due both to their intrinsic novelty as well as their potential for quantum information processing. They break both parity and time-reversal sym-metries and have been predicted to harbour Majorana fermions in vortex cores and along their edges.  A crucial challenge in the quest to find such states is identifying robust experimental probes of chirality.  In this talk, I will discuss an intrinsic, anomalous Hall effect that arises in multiband chiral superconductors. This effect arises from interband transitions involving time-reversal symmetry breaking chiral Cooper pairs. I will discuss the implications of this effect for the putative chiral p-wave superconductor, Sr2RuO4, and show that it can contribute significantly to Kerr rotation experiments. Since the magnitude of the effect depends on the structure of the order parameter across the bands, this result may also be used to distinguish between different models proposed for the superconducting state of Sr2RuO4.

We present large-scale quantum Monte Carlo simulations on a sign-problem free Bose-Hubbard model on the kagome lattice. This model supports a quantum Z2 spin liquid phase with fractional excitations and topological order, which can be characterized definitively through calculation of the topological entanglement entropy.  I will outline how the entanglement entropy can be measured in general using a direct implementation of the "replica trick", which allows for the study of entanglement scaling in a variety of other models amenable to study by QMC.  Finally, I will examine the kagome model's superfluid/spin-liquid transition, which is an example of an exotic deconfined quantum critical point called XY*, mediated by the fractional charges.  This fact is demonstrated in several universal quantities that we measure, and may also be reflected the scaling of entanglement entropy at the critical point.

Experiments where impurities were incorporated into helium nanodroplets have shown that the impurity freely rotates, and this has been attributed to the superfluidity of the nanodroplet [1]. Results from experiments with smaller helium clusters suggest that the onset of superfluidity is linked to system size and bosonic exchange effects [2]. We have used path integral techniques to investigate these systems and predict their spectroscopic behaviour in the microwave and the infrared regions of the spectrum. We are particularly interested in observing the superfluid response in clusters where the helium atoms have been substituted with parahydrogen molecules. Molecular hydrogen has been suggested as a potential candidate for the observation of superfluid response but this substance crystallizes before reaching a temperature low enough for superfluidity to appear. We will show theoretical and experimental results of a molecular superfluid response at the nanoscale via the formation of doped hydrogen clusters with a carbon dioxide probe molecule [3]. Properties such as density distributions, spectroscopic features, and effective rotational inertia can be extracted from the simulations. We will show new results for the case of asymmetric top molecules embedded in superfluid para-hydrogen clusters. A perspective on the current challenges of the field will be presented. [1] Grebenev, Toennies, and Vilesov, Science 279, 2083 (1998); Toennies and Vilesov, Angew. Chem.-Int. Edit. 43, 2622-2648 (2004). [2] Tang, Xu, McKellar and Jäger, Science 297, 2030 (2002) [3] Li, Le Roy, Roy, and McKellar, Phys. Rev. Lett. 105, 133401 (2010)

Charged colloidal particles present a controllable system for study a host of condensed matter/many body problems such as crystallization. 2D crystals are invariably hexagonal. Hexagons perfectly tile a flat plane but a soccer ball requires exactly 12 pentagons dispersed among the hexagons on its curved surface. Pentagons and hexagons are positive and negative topological charges, disclinations, sources for positive and negative curvature. But we have discovered that “Pleats”, grain boundaries which vanish on the surface (and play a similar role to fabric pleats) can provide a finer control of curvature. We experimentally investigate the generation of topological charge as flat surfaces are curved. For positive curvature, domes and barrels, there is one pentagon added for every 1/12 of a sphere. Negative curvature is different! For capillary bridges forming catenoids, pleats relieve the stress before heptagons appear on the surface. Pleats are important for controlling curvature from crystals on surfaces, to the shape of the spiked crown of the Chrysler building. Adding a particle to a flat surface produces an interstitial - usually an innocuous point defect. On a curved surface interstitials are remarkable, forming pairs or triplets of dislocations which can fission dividing the added particles into fractions which migrate to disclinations.    Work done with William Irvine, e.g. Nature 468, 947 (2010).

I will discuss string cosmology and the dynamics of multiple scalar fields in potentials that can become negative, and their features as (Early) Dark Energy models. The point of departure is the ``String Axiverse'', a scenario that motivates the existence of cosmologically light axion fields as a generic consequence of string theory. These fields can constitute part of the Dark Matter, suppressing structure formation in a manner similar to massive neutrinos. Future observations will constrain their existence to percent level accuracy. I couple such an axion to its corresponding modulus and give a detailed presentation of the rich cosmology of such a model, ranging from the setting of initial conditions on the fields during inflation, to the asymptotic future. A dynamical systems analysis reveals the existence of many fixed point attractors, repellers and saddle points, which I analyse in detail, and provide a geometric interpretation of. These fixed points can be used to bound the couplings in the model. A systematic scan of certain regions of parameter space reveals that the future evolution of the universe in this model can be rich, containing multiple epochs of accelerated expansion.

(Given time) I will also discuss the relevance of isocurvature perturbations in these models, and the motivation to study negative (terminal) vauca in the context of eternal inflation and the string landscape, as recently discussed by Susskind.

(based primarily on Marsh, Tarrant, Copeland and Ferreira (to appear) but also arXiv:1102.4851  arXiv:1110.0502)

Recent experiments have demonstrated that it is possible to create a synthetic magnetic field for neutral atoms in optical lattices using two-photon (Raman) processes. Motivated by exploring the interplay of such artificial magnetic fields and strong correlations for bosons, we have studied the Bose Hubbard model in the presence of pi-flux per plaquette. Using a variety of techniques, this model is shown to support a remarkable chiral Mott insulator phase on a 2-leg ladder. This state is a fully gapped insulator with staggered loop currents. We discuss physical insights as well experimental signatures of such a state for cold atoms as well as for Josephson junction arrays in a magnetic field.

We used time-of-flight inelastic neutron scattering to measure the excitation spectra from field-polarized states of exotic frustrated magnets. A knowledge of these spin-wave excitations in various directions in reciprocal space allows a robust determination of exchange parameters in suitable model Hamiltonians.  We have taken this approach with two pyrochlores, Er2Ti2O7 and Yb2Ti2O7, whose magnetic properties have until this point been somewhat puzzling.  The model we use is an effective spin-1/2 exchange Hamiltonian that incorporates the full anisotropy allowed by symmetry at the rare earth site.  Er2Ti2O7, an XY anti-ferromagnet on the pyrochlore lattice, is found to reach its unexpected ordered ground state via quantum-order-by-disorder.  Meanwhile, Yb2Ti2O7's effective Hamiltonian reveals the possibility of a Coulombic quantum spin liquid through what we have revealed to be "quantum spin ice" interactions.   I will focus on the experimental side of these collaborative studies.

The quantum spin liquid state is a prime example of an emergent phenomenon. Theory predicts that new particles such as spinons and gauge fields may emerge at low temperatures. However, for many years there have not been any examples in nature. The situation has changed in recent years in that a number of candidate materials have been discovered which may exhibit these exotic phenomena.

Joint work with Earl Campbell (FU-Berlin) and Hussain Anwar (UCL)   Magic state distillation is a key component of some high-threshold schemes for fault-tolerant quantum computation [1], [2]. Proposed by Bravyi and Kitaev [3] (and implicitly by Knill [4]), and improved by Reichardt [4], Magic State Distillation is a method to broaden the vocabulary of a fault-tolerant computational model, from a limited set of gates (e.g. the Clifford group or a sub-group[2])  to full universality, via the preparation of mixed ancilla qubits which may be prepared without fault tolerant protection.    Magic state distillation schemes have a close relation with quantum error correcting codes, since a key step in such protocols [5] is the projection onto a code subspace. Bravyi and Kitaev proposed two protocols; one based upon the 5-qubit code, the second derived from a punctured Reed-Muller code. Reed Muller codes are a very important family of classical linear code. They gained much interest [6] in the early years of quantum error correction theory, since their properties make them well-suited to the formation of quantum codes via the CSS-construction [7]. Punctured Reed-Muller codes (loosely speaking, Reed-Muller codewords with a bit removed) in particular lead to quantum codes with an unusual property, the ability to implement non-Clifford gates transversally [8].    Most work in fault-tolerant quantum computation focuses on qubits, but fault tolerant constructions can be generalised to higher dimensions [9]  - particularly readily for prime dimensions. Recently, we presented the first magic state distillation protocols [10] for non-binary systems, providing explicit protocols for the qutrit case (complementing a recent no-go theorem demonstrating bound states for magic state distillation in higher dimensions [11]). In this talk, I will report on more recent work [12], where the properties of punctured Reed-Muller codes are employed to demonstrate Magic State distillation protocols for all prime dimensions. In my talk, I will give a technical account of this result and present numerical investigations of the performance of such a protocol in the qutrit case. Finally, I will discuss the potential for application of these results to fault-tolerant quantum computation.     This will be a technical talk, and though some concepts of linear codes and quantum codes will be briefly revised, I will assume that listeners are familiar with quantum error correction theory (e.g. the stabilizer formalism and the CSS construction) for qubits.   [1] E. Knill. Fault-tolerant postselected quantum computation: schemes, quant-ph/0402171 [2] R. Raussendorf, J. Harrington and K. Goyal, Topological fault-tolerance in cluster state quantum computation, arXiv:quant-ph/0703143v1 [3] S. Bravyi and A. Kitaev. Universal quantum computation based on a magic states distillation, quant- ph/0403025 [4] B. W. Reichardt, Improved magic states distillation for quantum universality, arXiv:quant-ph/0411036v1 [5] E.T. Campbell and D.E. Browne, On the Structure of Protocols for Magic State Distillation, arXiv:0908.0838
[6] A. Steane, Quantum Reed Muller Codes, arXiv:quant-ph/9608026 [7] Nielsen and Chuang, Quantum Information and Computation, chapter 10 [8] E. Knill, R. Laflamme, and W. Zurek, Threshold accuracy for quantum computation, quant-ph/9610011 [9] D. Gottesman, Fault-Tolerant Quantum Computation with Higher-Dimensional Systems, quant-ph/9802007 [10] H. Anwar, E.T Campbell and D.E. Browne, Qutrit Magic State Distillation, arXiv:1202.2326 [11] V. Veitch, C. Ferrie, J. Emerson, Negative Quasi-Probability Representation is a Necessary Resource for Magic State Distillation, arXiv:1201.1256v3 [12] H. Anwar, E.T Campbell and D.E. Browne, in preparation

Majorana disappeared under mysterious circumstances in 1938 and the particle that bears his name remains elusive to experiments. There is growing interests in realizing the Majorana bound state in the Laboratory because it is expected to possess unusual properties such as non-abelian statistics. I shall discuss various proposals to produce  Majorana bound states and the associated topological superconductors which support them.