לוח שנה משולב

Consider the correspondence f(x,y) &#8594 f(X,Y), where f is a function, x,y &#8712 &#8476 are coordinates, and X,Y are linear operators on an auxiliary space that satisfy the commutation relation XY-YX=i &#8712 &#8465, for some real number &#949. Making sense of f(X,Y) can require great care.
In physics one encounters this problem with the phase space picture of quantum mechanics commonly used in quantum optics, where X,Y are conjugate position and momentum operators. Such notions also occur in the strong field limit of the Landau problem and its string theory equivalent for D-branes where X,Y are the position operators for coordinates in a spatial plane. In mathematics one finds these problems addressed by harmonic analysis on the Heisenberg group along with general pseudo-differential operators and symbol calculus.
The ubiquity of the f(x,y) &#8594 f(X,Y) question has led many researchers in many different fields to perennially rediscover some formulas and miss others. This talk will discuss a review paper which aims to help the disparate communities speak to one another and cover new ground. This talk will focus on explicit representations and useful formulas. We will emphasize otherwise unexpected correspondences between continuous PDE and lattice difference equations, the likes of which are often found in models of nonlinear optical waveguide array lattices.

Controlling the interaction of light and matter is the basis for diverse applications ranging from light technology to quantum information processing. Nowadays, many of these applications are based on nanophotonic structures. It turns out that the confinement of light in such nanostructures imposes an inherent link between its local polarization and its propagation direction, also referred to as spin–momentum locking of light [1]. Remarkably, this leads to chiral, i.e., propagation direction-dependent effects in the emission and absorption of light, and elementary processes of light–matter interaction are fundamentally altered. For example, when coupling plasmonic particles or atoms to evanescent fields, the intrinsic mirror symmetry of the particles’ emission can be broken. In our group, we observed this effect in the interaction between single rubidium atoms and the evanescent part of a light field that is confined by continuous total internal reflection in a whispering-gallery-mode microresonator [2]. In the following, this allowed us to realize chiral nanophotonic interfaces in which the emission direction of light into the structure is controlled by the polarization of the excitation light [3] or by the internal quantum state of the emitter [4], respectively. Moreover, we employed this chiral interaction to demonstrate an integrated optical isolator [5] as well as an integrated optical circulator [6] which operate at the single-photon level and which exhibit low loss. The latter are the first two examples of a new class of nonreciprocal nanophotonic devices which exploit the chiral interaction between single quantum emitters and transversally confined photons.

References
1 K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, Spin-orbit interactions of light, Nat. Photon. 9, 796 (2015).
[2] C. Junge, D. O'Shea, J. Volz, and A. Rauschenbeutel, Strong coupling between single atoms and non-transversal photons, Phys. Rev. Lett. 110, 213604 (2013).
[3] J. Petersen, J. Volz, and A. Rauschenbeutel, Chiral nanophotonic waveguide interface based on spin-orbit coupling of light, Science 346, 67 (2014).
[4] R. Mitsch, C. Sayrin, B. Albrecht, P. Schneeweiss, and A. Rauschenbeutel, Quantum state-controlled directional spontaneous emission of photons into a nanophotonic waveguide, Nature Commun. 5, 5713 (2014).
[5] C. Sayrin, C. Junge, R. Mitsch, B. Albrecht, D. O'Shea, P. Schneeweiss, J. Volz, and A. Rauschenbeutel, Nanophotonic Optical Isolator Controlled by the Internal State of Cold Atoms, Phys. Rev. X 5, 041036 (2015).
[6] M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeutel, Quantum optical circulator controlled by a single chirally coupled atom, Science 354, 1577 (2016).

Autism Spectrum Disorder is a heterogeneous condition characterized by deficits in social interactions and repetitive behaviors/restricted interests. Mouse models based on human disease-causing mutations provide the potential for understanding associated neuropathology and developing targeted treatments. Genetic, neurobiological and imaging data provide convergent evidence for the CNTNAP2 gene as a risk factor for autism and other developmental disorders. First, I will present data from my postdoctoral work demonstrating construct, face and predictive validity of a mouse knockout for the Cntnap2 gene, providing a tool for mechanistic and therapeutic research. In fact, through an in vivo drug screen in this model we found that administration of the neuropeptide oxytocin dramatically improves social deficits. Strikingly, reduced neuropeptide levels in this model seemed to account for the behavioral response. Last, I will present ongoing work in my lab evaluating the oxytocin system and related neurotransmitters in this model. Alterations in the oxytocin system and/or dysfunction in its related biological processes could potentially be more common in autism than previously anticipated.