Theory Seminar: Scattering theory in quantum optics & Scaling up and understanding the limits of photonic inverse design

Rahul Trivedi

July 30, 2019

Rahul Trivedi
Herbert-Walther Lecture Hall G0.25
Wed, 30. July 2019, 11:30 am

Abstract:

Part 1: Scattering theory in quantum optics

    Quantum optical systems can often be modelled as a low-dimensional quantum system (such a two-level system, Jaynes-Cummings system etc.) coupling to an electromagnetic bath. Within the Markovian approximation, calculating the propagator for this system is a computation that is equivalent to calculating the propagator corresponding to an effective non-hermitian hamiltonian. I will briefly sketch a proof of this result using the input-output formalism [1] along with its applications to understanding the dynamics of some paradigmatic systems [1, 2]. I will then go onto discuss the application of this technique in understanding photon transport through the multi-emitter cavity QED system [3]. In particular, I will focus on photon blockade induced by this system, and its dependence on the number of emitters interacting with the cavity mode.

    Part 2: Scaling up and understanding the limits of photonic inverse design

    Photonic inverse design has been immensely successful in producing compact, highly efficient and robust devices for applications in silicon photonics, metasurface optics, quantum optics etc. A typical photonic inverse design run requires a few hundred to thousands of electromagnetic simulations – performing these simulations is the limiting factor in scaling photonic inverse design to larger devices. In this part of my talk, I will present two approaches to accelerate electromagnetic simulations – (a) data-driven approach to augment iterative solutions of frequency-domain Maxwell’s equations [4], and (b) GPU accelerated implementation of the transfer-matrix algorithm for simulating a collection of electromagnetic scatterers. Finally, I will present some attempts at characterizing the fundamental performance limits on photonic devices by calculating the Lagrangian dual of the electromagnetic design problem.

        Rahul Trivedi, Kevin Fischer, Shanshan Xu, Shanhui Fan, and Jelena Vuckovic. "Few-photon scattering and emission from low-dimensional quantum systems." Physical Review B98, no. 14 (2018): 144112.
        Rahul Trivedi, Kevin Fischer, Sattwik Deb Mishra, and Jelena Vuckovic. "Point-coupling Hamiltonian for broadband linear optical devices." arXiv preprint arXiv:1907.02259 (2019).
        Rahul Trivedi, Marina Radulaski, Kevin A. Fischer, Shanhui Fan, and Jelena Vučković. "Photon Blockade in Weakly Driven Cavity Quantum Electrodynamics Systems with Many Emitters." Physical Review Letters 122, no. 24 (2019): 243602.
        Rahul Trivedi, Logan Su, Jesse Lu, Martin F. Schubert, and Jelena Vuckovic. "Data-driven acceleration of Photonic Simulations." arXiv preprint arXiv:1902.00090 (2019).