NBIA/QDev Seminar: Gunnar Möller

Gunnar Möller, Cambridge University
Creating Novel Quantum Phases by Artificial Magnetic Fields

Flat bands such as the Landau levels of charged particles in strong magnetic fields harbour some of the most exotic emergent phenomena known in condensed matter systems: incompressible quantum liquids supporting fractionalized quasiparticles with generalized exchange statistics. Thanks to their topological nature, these quasiparticle states are extremely robust to decoherence and thus provide an ideal basis for quantum computing.
Here, we address the question of whether the physics of the quantum Hall effect can be realized in different settings. Magnetic fields can be emulated by geometric phases that resemble the Aharonov-Bohm effect, or alternatively, by mimicking the Berry curvature of Landau-levels in reciprocal space. We review possible realizations of these ideas based on spin-orbit coupling in solid state systems or alternatively relying on light-matter coupled systems of cold atomic gases. We then focus on the question of classifying the resulting many-body states: We provide a formal proof that the phases of interacting particles in topological flat bands with Chern number C=1 can be adiabatically connected to fractional quantum Hall liquids [1], providing a formal proof of the equality of their respective topological orders. Furthermore, this proof robustly extends to the thermodynamic limit. Finally, we study bands of higher Chern index (C>1) and provide evidence for novel types of Hall states for the case of bosons in the Hofstadter lattice [2,3].
 
[1] T. Scaffidi & G. Möller, Phys. Rev. Lett. 109, 246805 (2012).
[2] G. Möller & N. R. Cooper, Phys. Rev. Lett. 103, 105303 (2009).
[3] L. Hormozi, G. Möller & S. H. Simon, Phys. Rev. Lett. 108, 256809 (2012).