Snir Gazit

Super-resolution and reconstruction of sparse sub-wavelength images.

We show that, in contrast to popular belief, sub-wavelength information can be recovered from the far-field of an optical image, thereby overcoming the loss of information embedded in decaying evanescent waves. The only requirement is that the image is known to be sparse, a specific but very general and wide-spread property of signals which occur almost everywhere in nature. The reconstruction method relies on newly-developed compressed sensing techniques, which we adapt to optical super-resolution and sub-wavelength imaging. Our approach exhibits robustness to noise and imperfections. We provide an experimental proof-of-principle by demonstrating image recovery at a spatial resolution 5-times higher than the finest resolution defined by a spatial filter. The technique is general, and can be extended beyond optical microscopy, for example, to atomic force microscopes, scanning-tunneling microscopes, and other imaging systems.

Super-resolution and reconstruction of sparse images carried by incoherent light

We demonstrate theoretically and experimentally the reconstruction of images borne on incoherent light at a resolution greatly exceeding the finest resolution defined by the NA of the system. Our method relies on compressed sensing techniques, which assume that the object is sparse in a known basis, and only that. The approach is robust against noise and can be used for reconstructing subwavelength images through measurements taken in the optical far field.

Fate of the Higgs mode near quantum criticality.

We study a relativistic O(N) model near the quantum critical point in 2 + 1 dimensions for N = 2 and N = 3. The scalar susceptibility is evaluated by Monte Carlo simulation. We show that the spectrum contains a well-defined peak associated with the Higgs mode arbitrarily close to the critical point. The peak fidelity and the amplitude ratio between the critical energy scales on both sides of the transition are determined.

Spin transport of weakly disordered Heisenberg chain at infinite temperature

We study the disordered Heisenberg spin chain, which exhibits many body localization at strong disorder, in the weak to moderate disorder regime. A continued fraction calculation of dynamical correlations is devised, using a variational extrapolation of recurrents. Good convergence for the infinite chain limit is shown. We find that the local spin correlations decay at long times as

Critical capacitance and charge-vortex duality near the superfluid-to-insulator transition.

C \sim t^{-\beta}

Emergent Dirac fermions and broken symmetries in confined and deconfined phases of Z2 gauge theories

, while the conductivity exhibits a low frequency power law

Confinement transition of ℤ2 gauge theories coupled to massless fermions: Emergent quantum chromodynamics and SO(5) symmetry

\sigma \sim \omega^{\alpha}

Super-resolution and reconstruction of sparse sub-wavelength images: erratum

. The exponents depict sub-diffusive behavior

Bosonic topological phase in a paired superfluid

\beta 0

Critical Conductivity and Charge Vortex Duality Near Quantum Criticality

at all finite disorders, and convergence to the scaling result,