Hamiltonian Reconstruction through Polarimetry of High-Order Sidebands from Quasiparticles Recollisions*

In condensed matter systems, effective Hamiltonians describe the low-energy physics of quasiparticles. Engineering hybrid systems theorized to host interesting topological states requires knowledge of certain effective Hamiltonian parameters. Reconstructing these effective Hamiltonians from experimental data is difficult, as it normally involves fitting multiparameter theoretical models to a few experimentally measured quantities. We present Hamiltonian Reconstruction by Polarimetry of High-Order Sidebands (HaRPHOS) as a potential new method to meet this experimental challenge. HaRPHOS provides an optical method to create quasiparticle pairs, accelerate them out of equilibrium, and measure the polarization of emitted light from their recollisions. Information about the quasiparticles’ quantum mechanical phases, both dynamic and topological, is imprinted on the sideband polarizations. Recently, polarimetry of high-order sidebands has been used to reconstruct the Bloch wavefunctions of holes in gallium arsenide (GaAs) [1]. In this talk, we will discuss progress towards demonstrating HaRPHOS by reconstructing the Luttinger Hamiltonian for holes in GaAs, and prospects for applying HaRPHOS to other charged quasiparticles.