1D Quantum Simulation Using a Solid State Platform
The motivation for this work is to develop a solid state quantum simulation platform. One potential candidate is the oxide heterostructure LaAlO3/SrTiO3, which exhibits nearly every phenomenon in the solid state and has key ingredients for quantum simulation including: strong, controllable, sign changing electron-electron interactions [1], and the ability to be controlled on the nanoscale [2]. The level of control that we have over the interface will allow us to create a lattice of sites for putting electrons that doesn’t have to bear any resemblance to the underlying lattice of the system, and create any arbitrary 1D or 2D lattice to simulate a wide range of interesting Hamiltonians.
The ultimate goal of this project is to create 2D lattices that can be used to simulate quantum systems that are difficult or impossible to model classically. An extensive amount of work has been done towards this goal in the field of cold atomic gases which can be very precisely controlled and are well described by the Hubbard model Hamiltonian, which describes the interactions of particles in a lattice. But it is difficult for these systems to reach temperatures where correlated ground states occur. A solid state quantum simulation platform would have to advantage of naturally supporting the solid state physics that cold atoms are attempting to simulate and study.
We began the project by trying to simulate 1D systems because they are more theoretically tractable. We will take advantage of the extreme nanoscale control that we have over the LaAlO3/SrTiO3 interface using conductive atomic force microscope lithography to create artificial 1D systems. Additionally, similar nanowire devices at the LaAlO3/SrTiO3 interface show a gate-tunable transition from attractive to repulsive electron-electron interactions which should allow us to simulate interesting quantum systems. Experimental simulations of 1D superlattices are currently underway and results from these experiments should help to create and constrain a model in order to better understand the system and how to develop the tools needed to preform solid state quantum simulation.
Cheng, G., Tomczyk, M., Tacla, A. B., Lee, H., Lu, S., Veazey, J. P., Huang, M., Irvin, P., Ryu, S., Eom, C.-B., Daley, A., Pekker, D. & Levy, J. "Tunable electron-electron Interactions in LaAlO3/SrTiO3 Nanostructures," arXiv:1602.06029 (2016).
http://arxiv.org/abs/1602.06029Cen, C., Thiel, S., Hammerl, G., Schneider, C. W., Anderson, K. E., Hellberg, C. S., Mannhart, J. & Levy, J. "Nanoscale Control of an Interfacial Metal-Insulator Transition at Room Temperature," Nature Materials 7, 298 (2008).
http://dx.doi.org/doi:10.1038/nmat2136