Ab-Initio Calculations of Nonlinear Susceptibility and Multi-Phonon Mixing Processes in a 2DEG-Piezoelectric Heterostructure

Solid-state elastic-wave phonons are a promising platform for a wide range of quantum information applications. An outstanding challenge and enabling capability in harnessing phonons for quantum information processing is achieving strong nonlinear interactions between them. To this end, we propose a general architecture using piezoelectric-semiconductor heterostructures consisting of a piezoelectric acoustic material hosting phonon modes in direct proximity to a two-dimensional electron gas (2DEG). Each phonon in the piezoelectric material carries an electric field, which extends into the 2DEG. The fields induce polarization of 2DEG electrons, which in turn interact with other piezoelectric phononic electric fields. The net result is coupling between the various phonon modes. We derive, from first principles, the nonlinear phononic susceptibility of the system. We show that many nonlinear processes are strongly favored at high electron mobility, motivating the use of the 2DEG to mediate the nonlinearities. We derive in detail the first, second, and third-order susceptibilities and calculate them for the case of a lithium niobate surface acoustic wave interacting with a GaAs-AlGaAs heterostructure 2DEG. We show that, for this system, the strong third-order nonlinearity could enable single-phonon Kerr shift in an acoustic cavity that exceeds realistic cavity linewidths, potentially leading to a new class of acoustic qubit. We further show that the strong second-order nonlinearity could be used to produce a high-gain, traveling-wave parametric amplifier to amplify--and ultimately detect--the outputs of the acoustic cavity qubits. Assuming favorable losses in such a system, these capabilities, combined with the ability to efficiently transduce phonons from microwave electromagnetic fields in transmission lines, thus hold promise for creating all-acoustic quantum information processors.