Part 1: Scattering theory in quantum opticsPart 2: Scaling up and understanding the limits of photonic inverse design
Dr. Rahul Trivedi
Stanford University, Stanford, USA
Max-Planck-Institut für Quantenoptik
Seminar room Theory Division - B 2.46
Part 1: Quantum optical systems can often be modelled as a low-dimensional quantum system (such atwo-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  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 . 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.
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 , 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).