## Materials for Nonlinear Optics

Our group’s experience experimenting with optical devices made with single atoms and atom clouds in vacuum chambers and numerically modeling networks of these devices has led us believe that even small circuits (fewer than 10 devices) of nonlinear optical devices could provide novel, practical functionality relevant for communication, sensing and computing. The expanding industrial and academic effort to integrate microscopic versions of existing optical device technologies with nanoscale electronics ‘on chip’ provides strong motivation for this research.

Power-dependent (nonlinear) absorption and refraction by atoms, molecules and materials is the key ingredient for devices that mediate interaction of multiple laser beams. For now the laser intensities usually needed to induce significant nonlinear optical interaction are impractically high for all but niche applications. This is a significant hurdle that must be overcome to achieve nonlinear optical devices that can be practically scaled to operate in a circuit.

To address this challenge we study materials we believe to be promising for construction of scalable, low-power nonlinear-optical devices. So far our focus has been on laser spectroscopy of materials falling into two categories.

### Two-dimensional Materials

An isolated atom’s optical response can be saturated by a single photon but is exquisitely sensitive to environmental perturbation and impractical to scale. Three dimensional solid materials are most practical for making mechanically robust and scalable optical devices. Unfortunately they tend to have very weak nonlinear optical responses. Two-dimensional bulk materials offer an interesting middle ground between these extreme cases. Lower dimensionality generally implies less dispersed optical responses and a tendency for optical excitations to pile up on top of each other and ‘feel each other’. Thus two dimensional are expected to have stronger nonlinear optical responses (relative to their linear response) than three-dimensional materials. Many experiments and theoretical studies conducted in recent years seem to confirm this in specific cases. Two dimensional materials are also promising for integration with on-chip optical waveguides made of other three—dimensional solids.

Our research has mostly consisted of laser ‘micro-spectroscopy’ (laser + microscope + spectrometer) of microscopic flakes of graphene, MoS_{2} and Bi_{2}Se_{3}.

### Correlated Materials with Phase Transitions

We are also interested in materials where electrons interact strongly with vibrations or other electrons. At sufficiently low temperatures these materials tend to display interesting phase transitions, in which collective behavior spontaneously breaks some physical symmetry (such as the equivalence of all crystal axes). We are interested in studying the nonlinear optical susceptibility of such materials near (second-order) phase transitions. We are also interested in leveraging techniques used in our other laser experiments to scientifically study these materials in new ways. Thus far our experimental efforts have been focused on spontaneous and stimulated Raman scattering in SrTiO_{3}.

### Bandstructure Calculations

The discovery of graphene has given rise to newfound interest in the properties of two-dimensional nanomaterials in general. One question that we would like to answer is how these molecules respond to electromagnetic waves, e.g. by calculating their linear and nonlinear electric susceptibilities. The methods used in this research derive from the intersection of condensed-matter physics and optics. The results will help us determine the potential usefulness of the materials for trapped-ion quantum computers, among other cutting-edge technological applications. A substance that I have been recently examining is monolayer molybdenum disulfide, which forms a honeycomb lattice similar to graphene but with site asymmetry (Mo vs S) generating Dirac point band gaps and intrinsic spin-orbit coupling. Moving forward, I plan to examine a broad range of optical properties for a variety of crystalline substances.

## Nonlinear Dynamics in Pulsed OPOs

Growing out of the Ising machine work, we have developed separate “multimode” theory of OPO Ising machines based on synchronously pumped OPOs. This is being done in collaboration with Profs. Yamamoto (JST) and Fejer (Stanford), who are interested in coherent computing and nonlinear optics, respectively. It turns out that pulsed OPO dynamics is a hard problem even classically, and it takes great computational power to solve even simple problems. We have developed GPU-based algorithms to speed up the simulation time, and recently proposed a set of “reduced models” that accurately describe the OPO behavior in most regimes, without the need for expensive and time-consuming numerical simulations. (Ref. [8])

Presently, we are extending this work to the broadband, “simultonic” limit of pulsed OPO dynamics. At the same time, we are using the more conventional analysis in Ref. [8] to study networks of pulsed OPOs, which can exhibit much richer nonlinear dynamics than a single OPO. One hope is that these “multimode” effects can be used as a feature to enhance OPO-network Ising machines (see above). We are also interested in applying this work to study broadband parametric oscillation in integrated silicon photonic circuits (see below).