Non-Abelian Anyon Superconductivity

Non-Abelian Anyons exist in certain spin models and may exist in Quantuam Hall systems at certain filling fractions. In this work we studied the ground state of dynamical SU(2) level-$\kappa$ Chern Simons non-Abelian anyons at finite density and no external magnetic field. We find that in the large-$\kappa$ limit the topological interaction induces a pairing instability and the ground state is a superconductor with $\it{d+id}$ gap symmetry. We also develop a picture of pairing for the special value $\kappa=2$ and argue that the ground state is a superfluid of pairs for all values of $\kappa$.Comment: 5 pages, no figure

Edge States and Interferometers in the Pfaffian and anti-Pfaffian States

We compute the tunneling current in a double point contact geometry of a Quantum Hall system at filling fraction $\nu=5/2$, as function of voltage and temeprature, in the weak tunneling regime. We quantitatively compare two possible candidates for the state at $\nu=5/2$: the Moore-Read Pfaffian state, and its particle-hole conjugate, the anti-Pfaffian. We find that both possibilities exhibit the same qualitative behavior, and both have an even-odd effect that reflects their non-Abelian nature, but differ quantitatively in their voltage and temperature dependance.Comment: 8 pages, 3 figures. Fixed typos, added refs 32-3

Holographic opto-fluidic microscopy.

Over the last decade microfluidics has created a versatile platform that has significantly advanced the ways in which micro-scale organisms and objects are controlled, processed and investigated, by improving the cost, compactness and throughput aspects of analysis. Microfluidics has also expanded into optics to create reconfigurable and flexible optical devices such as reconfigurable lenses, lasers, waveguides, switches, and on-chip microscopes. Here we present a new opto-fluidic microscopy modality, i.e., Holographic Opto-fluidic Microscopy (HOM), based on lensless holographic imaging. This imaging modality complements the miniaturization provided by microfluidics and would allow the integration of microscopy into existing on-chip microfluidic devices with various functionalities. Our imaging modality utilizes partially coherent in-line holography and pixel super-resolution to create high-resolution amplitude and phase images of the objects flowing within micro-fluidic channels, which we demonstrate by imaging C. elegans, Giardia lamblia, and Mulberry pollen. HOM does not involve complicated fabrication processes or precise alignment, nor does it require a highly uniform flow of objects within microfluidic channels

Lensfree super-resolution holographic microscopy using wetting films on a chip.

We investigate the use of wetting films to significantly improve the imaging performance of lensfree pixel super-resolution on-chip microscopy, achieving < 1 µm spatial resolution over a large imaging area of ~24 mm(2). Formation of an ultra-thin wetting film over the specimen effectively creates a micro-lens effect over each object, which significantly improves the signal-to-noise-ratio and therefore the resolution of our lensfree images. We validate the performance of this approach through lensfree on-chip imaging of various objects having fine morphological features (with dimensions of e.g., ≤0.5 µm) such as Escherichia coli (E. coli), human sperm, Giardia lamblia trophozoites, polystyrene micro beads as well as red blood cells. These results are especially important for the development of highly sensitive field-portable microscopic analysis tools for resource limited settings

The Effect of Landau Level-Mixing on the Effective Interaction between Electrons in the fractional quantum Hall regime

We compute the effect of Landau-level-mixing on the effective two-body and three-body pseudopotentials for electrons in the lowest and second Landau levels. We find that the resulting effective three-body interaction is attractive in the lowest relative angular momentum channel. The renormalization of the two-body pseudopotentials also shows interesting structure. We comment on the implications for the $\nu=5/2$ fractional quantum Hall state

Multi-channel Kondo Models in non-Abelian Quantum Hall Droplets

We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state which is spatially separated from it by an integer quantum Hall state. Near a resonance, the physics at energy scales below the level spacing of the edge states of the dot is governed by a $k$-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction $\nu=2+k/(k+2)$ or its particle-hole conjugate at $\nu=2+2/(k+2)$. The $k$-channel Kondo model is channel isotropic even without fine tuning in the former state; in the latter, it is generically channel anisotropic. In the special case of $k=2$, our results provide a new venue, realized in a mesoscopic context, to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction $\nu=5/2$.Comment: 4 pages, 1 figure; references updated, version to appear in PR

Odd-Even Crossover in a non-Abelian ν=5/2\nu=5/2 Interferometer

We compute the backscattered current in a double point-contact geometry of a Quantum Hall system at filling fraction $\nu=5/2$ as a function of bias voltage in the weak backscattering regime. We assume that the system is in the universality class of either the Pfaffian or anti-Pfaffian state. When the number of charge $e/4$ quasiparticles in the interferometer is odd, there is no interference pattern. However, the coupling between a charge $e/4$ quasiparticle and the edge causes it to be absorbed by the edge at low energies. Consequently, an interference pattern appears at low bias voltages and temperatures, as if there were an even number of quasiparticles in the interferometer. We relate this problem to that of a semi-infinite Ising model with a boundary magnetic field. Using the methods of perturbed boundary conformal field theory, we give an exact expression for this crossover of the interferometer as a function of bias voltage. Finally, we comment on the possible relevance of our results to recent interference experiments.Comment: Two figures added, along with a brief explanation of them. Abstract slightly edited, and one reference adde

Sagnac interference in Carbon nanotubes

The Sagnac interference mode arises when two interfering counterpropogating beams traverse a loop, but with their velocities detuned by a small amount $2u$, with $v_{R/L}=v_F\pm u$. In this paper we perform a perturbative non-equilibrium calculation of Sagnac interference in single channel wires as well as armchair nanotube loops. We study the dependence of the Sagnac conductance oscillations on temperature and interactions. We find that the Sagnac interference is not destroyed by strong interactions, but becomes weakly dependent on the velocity detuning $u$. In armchairs nanotubes with typical interaction strength, $0.25 \leq g \leq 0.5$, we find that the necessary temperature for observing the interference effect, $T_{SAG}$ is also only weakly dependent on the interaction, and is enhanced by a factor of 8 relative to the temperature necessary for observing Fabry-Perot interference in the same system, $T_{FP}$.Comment: 12 pages, 8 figure

Lensfree on-chip microscopy over a wide field-of-view using pixel super-resolution.

We demonstrate lensfree holographic microscopy on a chip to achieve approximately 0.6 microm spatial resolution corresponding to a numerical aperture of approximately 0.5 over a large field-of-view of approximately 24 mm2. By using partially coherent illumination from a large aperture (approximately 50 microm), we acquire lower resolution lensfree in-line holograms of the objects with unit fringe magnification. For each lensfree hologram, the pixel size at the sensor chip limits the spatial resolution of the reconstructed image. To circumvent this limitation, we implement a sub-pixel shifting based super-resolution algorithm to effectively recover much higher resolution digital holograms of the objects, permitting sub-micron spatial resolution to be achieved across the entire sensor chip active area, which is also equivalent to the imaging field-of-view (24 mm2) due to unit magnification. We demonstrate the success of this pixel super-resolution approach by imaging patterned transparent substrates, blood smear samples, as well as Caenoharbditis Elegans