Broken Symmetry and Josephson-like Tunneling in Quantum Hall Bilayers

I review recent novel experimental and theoretical advances in the physics of quantum Hall effect bilayers. Of particular interest is a broken symmetry state which optimizes correlations by putting the electrons into a coherent superposition of the two different layers.Comment: to be published in Proc. 11th International Conf. on Recent Progress in Many-Body Theories, ed. R.F. Bishop, T. Brandes, K.A. Gernoth, N.R. Walet, and Y. Xian, to appear in the series "Advances in Quantum Many-Body Theory" (World Scientific). 12 pages, 4 figure

DC Transformer and DC Josephson(-like) Effects in Quantum Hall Bilayers

In the early days of superconductivity, Ivar Giaver discovered that it was possible to make a novel DC transformer by using one superconductor to drag vortices through another. An analogous effect was predicted to exist in quantum Hall bilayers and has recently been discovered experimentally by Eisenstein's group at Caltech. Similarly, new experiments from the Caltech group have demonstrated the existence of a Josephson-like `supercurrent' branch for electrons coherently tunnelling between the two layers.Comment: To Appear in Proceedings of the Nobel Symposium on Quantum Coherence, Goteborg, Sweden, December, 2001 (Physica Scripta) Revision: references update

Asymmetry gap in the electronic band structure of bilayer graphene.

A tight binding model is used to calculate the band structure of bilayer graphene in the presence of a potential difference between the layers that opens a gap U between the conduction and valence bands. In particular, a self consistent Hartree approximation is used to describe imperfect screening of an external gate, employed primarily to control the density n of electrons on the bilayer, resulting in a potential difference between the layers and a density dependent gap U(n). We discuss the influence of a finite asymmetry gap U(0) at zero excess density, caused by the screening of an additional transverse electric field, on observations of the quantum Hall effect

Superfluid-insulator transitions of two-species Bosons in an optical lattice

We consider a realization of the two-species bosonic Hubbard model with variable interspecies interaction and hopping strength. We analyze the superfluid-insulator (SI) transition for the relevant parameter regimes and compute the ground state phase diagram for odd filling at commensurate densities. We find that in contrast to the even commensurate filling case, the superfluid-insulator transition occurs with (a) simultaneous onset of superfluidity of both species or (b) coexistence of Mott insulating state of one species and superfluidity of the other or, in the case of unit filling, (c) complete depopulation of one species. The superfluid-insulator transition can be first order in a large region of the phase diagram. We develop a variational mean-field method which takes into account the effect of second order quantum fluctuations on the superfluid-insulator transition and corroborate the mean-field phase diagram using a quantum Monte Carlo study.Comment: 12 pages, 11 figure

Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes

Starting from the graphene lattice tight-binding Hamiltonian with an on-site U and long-range Coulomb repulsion, we derive an interacting continuum Dirac theory governing the low-energy behavior of graphene in an applied magnetic field. Initially, we consider a clean graphene system within this effective theory and explore integer quantum Hall ferromagnetism stabilized by exchange from the long-range Coulomb repulsion. We study in detail the ground state and excitations at nu = 0 and nu = \pm 1, taking into account small symmetry-breaking terms that arise from the lattice-scale interactions, and also explore the ground states selected at nu = \pm 3, \pm 4, and \pm 5. We argue that the ferromagnetic regime may not yet be realized in current experimental samples, which at the above filling factors perhaps remain paramagnetic due to strong disorder. In an attempt to access the latter regime where the role of exchange is strongly suppressed by disorder, we apply Hartree theory to study the effects of interactions. Here, we find that Zeeman splitting together with symmetry-breaking interactions can in principle produce integer quantum Hall states in a paramagnetic system at nu = 0, \pm 1 and \pm 4, but not at nu = \pm 3 or \pm 5, consistent with recent experiments in high magnetic fields. We make predictions for the activation energies in these quantum Hall states which will be useful for determining their true origin.Comment: 13 pages, 2 figure

Synthetic gauge fields and homodyne transmission in Jaynes-Cummings lattices

Many-body physics is traditionally concerned with systems of interacting massive particles. Recent studies of effective interactions between photons, induced in the circuit QED architecture by coupling the microwave field to superconducting qubits, have paved the way for photon-based many-body physics. We derive the magnitude and intrinsic signs of photon hopping amplitudes in such circuit QED arrays. For a finite, ring-shaped Jaynes-Cummings lattice exposed to a synthetic gauge field we show that degeneracies in the single-excitation spectrum emerge, which can give rise to strong correlations for the interacting system with multiple excitations. We calculate the homodyne transmission for such a device, explain the generalization of vacuum Rabi splittings known for the single-site Jaynes-Cummings model, and identify fingerprints of interactions beyond the linear response regime.Comment: 17 pages, 5 figure

Disorder and interactions in quantum Hall ferromagnets near ν=1\nu=1

We report on a finite-size Hartree-Fock study of the competition between disorder and interactions in a two-dimensional electron gas near Landau level filling factor $\nu=1$. The ground state at $\nu=1$ evolves with increasing disorder from a fully spin-polarized ferromagnet with a charge gap, to a partially spin-polarized ferromagnetic Anderson insulator, to a quasi-metallic paramagnet at the critical point between $i=0$ and $i=2$ quantum Hall plateaus. Away from $\nu=1$, the ground state evolves from a ferromagnetic Skyrmion quasiparticle glass, to a conventional quasiparticle glass, and finally to a conventional Anderson insulator. We comment on signatures of these different regimes in low-temperature transport and NMR lineshape and peak position data.Comment: 10 pages, 8 figures, submitted to PR

Circuit QED and engineering charge based superconducting qubits

The last two decades have seen tremendous advances in our ability to generate and manipulate quantum coherence in mesoscopic superconducting circuits. These advances have opened up the study of quantum optics of microwave photons in superconducting circuits as well as providing important hardware for the manipulation of quantum information. Focusing primarily on charge-based qubits, we provide a brief overview of these developments and discuss the present state of the art. We also survey the remarkable progress that has been made in realizing circuit quantum electrodynamics (QED) in which superconducting artificial atoms are strongly coupled to individual microwave photons.Comment: Proceedings of Nobel Symposium 141: Qubits for Future Quantum Informatio

Cooling in the single-photon strong-coupling regime of cavity optomechanics

In this paper we discuss how red-sideband cooling is modified in the single-photon strong-coupling regime of cavity optomechanics where the radiation pressure of a single photon displaces the mechanical oscillator by more than its zero-point uncertainty. Using Fermi's Golden rule we calculate the transition rates induced by the optical drive without linearizing the optomechanical interaction. In the resolved-sideband limit we find multiple-phonon cooling resonances for strong single-photon coupling that lead to non-thermal steady states including the possibility of phonon anti-bunching. Our study generalizes the standard linear cooling theory.Comment: 4 pages, 3 figure