Topological quantum systems

Topological order emerges as a new kind of behavior of quantum matter, which complements Landau’s symmetry-based classification of matter in a striking fashion. One of the most intriguing theoretical avenues is the predicted existence in certain topological phases of Majorana fermions (MFs), a kind of excitation serves as its own antiparticle. This is unlike ordinary particles such as electrons with distinct antimatter counterparts (positrons). We explore various physical systems (such as quantum wires, coupled oscillators, and spin lattices) to demonstrate non-trivial topological properties.

One challenge for topological quantum information processing is that two such devices cannot exchange quantum information unless they are on the same piece of material. This prevents such systems from communicating via quantum networks and thereby severely limits their capability. (Just imagine how inconvenient life would be if our computers could not access the Internet!) We investigate the coherent interface between topological systems and conventional quantum systems (e.g., atoms, photons, and etc.). For example, we may use conventional quantum systems to assist in the investigation of topological systems. This will not only enable us to transfer quantum information between different parts of topological quantum devices (e.g., via photons as illustrated), but also allow us to connect the two fields of topological and conventional quantum research.

Selected Publications:

  1. Demonstrating non-Abelian statistics of Majorana fermions using twist defects,” H. Zheng, A. Dua and L. Jiang, Phys. Rev. B 92, 245139 (2015).
  2. Topological Properties of Linear Circuit Lattices,” V. V. Albert, L. I. Glazman and L. Jiang, Phys. Rev. Lett. 114, 173902 (2015).
  3. Topologically protected quantum state transfer in a chiral spin liquid,” N. Y. Yao, C. R. Laumann, A. V. Gorshkov, H. Weimer, L. Jiang, J. I. Cirac, P. Zoller and M. D. Lukin, Nature Commun. 4, 1585 (2013).
  4. Interface between Topological and Superconducting Qubits,” L. Jiang, C. L. Kane and J. Preskill, Phys. Rev. Lett. 106, 130504 (2011).
  5. Majorana Fermions in Equilibrium and Driven Cold-Atom Quantum Wires,” L. Jiang, T. Kitagawa, J. Alicea, A. Akhmerov, D. Pekker, G. Refael, J. I. Cirac, E. Demler, M. D. Lukin and P. Zoller, Phys. Rev. Lett. 106, 220402 (2011).
  6. Unconventional Josephson signatures of Majorana bound states,” L. Jiang, D. Pekker, J. Alicea, G. Refael, Y. Oreg and F. von Oppen, Phys. Rev. Lett. 107, 236401 (2011).
  7. Anyonic interferometry and protected memories in atomic spin lattices,” L. Jiang, G. K. Brennen, A. Gorshkov, K. Hammerer, M. Hafezi, E. Demler, M. D. Lukin and P. Zoller, Nature Phys. 4, 482-488 (2008).