Darius Sadri

Here, we report the experimental observation of a dynamical quantum phase transition in a strongly interacting open photonic system. The system studied, comprising a Jaynes-Cummings dimer realized on a superconducting circuit platform, exhibits a dissipation-driven localization transition. Signatures of the transition in the homodyne signal and photon number reveal this transition to be from a regime of classical oscillations into a macroscopically self-trapped state manifesting revivals, a fundamentally quantum phenomenon. This experiment also demonstrates a small-scale realization of a new class of quantum simulator, whose well-controlled coherent and dissipative dynamics is suited to the study of quantum many-body phenomena out of equilibrium.

This article reviews the plane-wave/super Yang-Mills duality, which states that strings on a plane-wave background are dual to a particular large $R$-charge sector of $\mathcal{N}=4$, $D=4$ superconformal $\mathrm{U}(N)$ gauge theory. This duality is a specification of the usual anti--de Sitter/conformed field theory (AdS/CFT) correspondence in the ``Penrose limit.'' The Penrose limit of ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ leads to the maximally supersymmetric ten-dimensional plane wave (henceforth ``the'' plane wave) and corresponds to restricting to the large $R$-charge sector, the Berenstein-Maldacena-Nastase (BMN) sector, of the dual superconformal field theory. After reviewing the necessary background, the authors state the duality and review some of its supporting evidence. They discuss the suggestion by 't Hooft that Yang-Mills theories with gauge groups of large rank might be dual to string theories and the realization of this conjecture in the form of the AdS/CFT duality. Plane waves as exact solutions of supergravity and their appearance as Penrose limits of other backgrounds are considered, followed by an overview of string theory on the plane-wave background, discussing the symmetries and spectrum. The article then makes precise the statement of the proposed duality and classifies the BMN operators. It examines the gauge theory side of the duality, studying both quantum and nonplanar corrections to correlation functions of BMN operators and their operator-product expansions. The important issue of operator mixing and the resultant need for rediagonalization is stressed. Finally, the article studies strings on the plane wave via light-cone string field theory and demonstrates agreement between the one-loop correction to the string mass spectrum and the corresponding quantity in the gauge theory. A new presentation of the relevant superalgebra is given.

We introduce a model for amorphous grain boundaries in graphene and find that stable structures can exist along the boundary that are responsible for local density of states enhancements both at zero and finite $(\ensuremath{\sim}0.5\text{ }\text{eV})$ energies. Such zero-energy peaks, in particular, were identified in STS measurements [J. \ifmmode \check{C}\else \v{C}\fi{}ervenka, M. I. Katsnelson, and C. F. J. Flipse, Nat. Phys. 5, 840 (2009)] but are not present in the simplest pentagon-heptagon dislocation array model [O. V. Yazyev and S. G. Louie, Phys. Rev. B 81, 195420 (2010)]. We consider the low-energy continuum theory of arrays of dislocations in graphene and show that it predicts localized zero-energy states. Since the continuum theory is based on an idealized lattice scale physics it is a priori not literally applicable. However, we identify stable dislocation cores, different from the pentagon-heptagon pairs that do carry zero-energy states. These might be responsible for the enhanced magnetism seen experimentally at graphite grain boundaries.

Geometrically a crystal containing dislocations and disclinations can be envisaged as a ``fixed frame'' Cartan-Einstein space-time carrying torsion and curvature, respectively. We demonstrate that electrons in defected graphene are transported in the same way as fundamental Dirac fermions in a nontrivial $2+1$-dimensional space-time, with the proviso that the graphene electrons remember the lattice constant through the valley quantum numbers. The extra ``valley holonomy'' corresponds to modified Euclidean symmetry generators.