Filtering out photonic Fock states

Unprecedented optical nonlinearities can be generated probabilistically in simple linear-optical networks conditioned on specific measurement outcomes. We describe a highly controllable quantum filter for photon number states, which takes advantage of such a measurement-induced amplitude nonlinearity. The basis for this filter is multiphoton nonclassical interference which we demonstrate for one- and two-photon states over a wide range of beam splitter reflectivities. Specifically, we show that the transmission probability, conditional on a specific measurement outcome, can be larger for a two-photon state than a one-photon state; this is not possible with linear optics alone.     

Reversible electromigration of thallium adatoms on the Si(1 1 1) surface

By means of low-energy electron diffraction (LEED), we found a reversible structural change of on thallium (Tl) adsorbed Si(1 1 1) surfaces by switching the polarity of applied DC voltage for heating the sample. It was shown in the literature that Tl adatoms are located on the T₄ sites of the bulk-terminated surface both in the (1 × 1) and . It is clarified that the structural change is caused by the electromigration of the Tl adatoms. Tl atoms migrate towards the cathode, being induced by the electric field (10-20 V/cm). We discussed an atomic process of the electromigration.     

Observation of new states decaying into Lambda(c)(+)Kappa(-)pi(+) and Lambda(c)(+)Kappa(0)/(s)pi(-)

We report the first observation of two charmed strange baryons that decay into Lambda(c)(+)Kappa(-)pi(+). The broader of the two states is measured to have a mass of 2978.5+/-2.1+/-2.0 MeV/c2 and a width of 43.5+/-7.5+/-7.0 MeV/c2. The mass and width of the narrow state are measured to be 3076.7+/-0.9+/-0.5 MeV/c;{2} and 6.2+/-1.2+/-0.8 MeV/c2, respectively. We also perform a search for the isospin partner states that decay into Lambda(c)(+)Kappa(0)/(s)pi(-) and observe a significant signal at the mass of 3082.8+/-1.8+/-1.5 MeV/c2. The data used for this analysis were accumulated at or near the Upsilon(4S) resonance, using the Belle detector at the e+ e- asymmetric-energy collider KEKB. The integrated luminosity of the data sample used is 461.5 fb(-1).     

Distillation of squeezing from non-Gaussian quantum states

We show that single copy distillation of squeezing from continuous variable non-Gaussian states is possible using linear optics and conditional homodyne detection. A specific non-Gaussian noise source, corresponding to a random linear displacement, is investigated experimentally. Conditioning the signal on a tap measurement, we observe probabilistic recovery of squeezing.     

Pressure-induced metal-insulator transition in LaMnO3 is not of Mott-Hubbard type

Calculations employing the local density approximation combined with static and dynamical mean field theories (LDA+U and LDA+DMFT) indicate that the metal-insulator transition observed at 32 GPa in paramagnetic LaMnO3 at room temperature is not a Mott-Hubbard transition, but is caused by orbital splitting of the majority-spin eg bands. For LaMnO3 to be insulating at pressures below 32 GPa, both on-site Coulomb repulsion and Jahn-Teller distortion are needed.     

Stochastic differential equations with coefficients in Sobolev spaces

We consider the Itô stochastic differential equation on Rd. The diffusion coefficients A₁,…,Am are supposed to be in the Sobolev space with p>d, and to have linear growth. For the drift coefficient A₀, we distinguish two cases: (i) A₀ is a continuous vector field whose distributional divergence δ(A₀) with respect to the Gaussian measure γd exists, (ii) A₀ has Sobolev regularity for some p^′>1. Assume for some λ₀>0. In case (i), if the pathwise uniqueness of solutions holds, then the push-forward #(Xt)γd admits a density with respect to γd. In particular, if the coefficients are bounded Lipschitz continuous, then Xt leaves the Lebesgue measure Lebd quasi-invariant. In case (ii), we develop a method used by G. Crippa and C. De Lellis for ODE and implemented by X. Zhang for SDE, to establish existence and uniqueness of stochastic flow of maps.     

New canonical forms of self-adjoint boundary conditions for regular differential operators of order four

In this paper, we find new canonical forms of self-adjoint boundary conditions for regular differential operators of order two and four. In the second order case the new canonical form unifies the coupled and separated canonical forms which were known before. Our fourth order forms are similar to the new second order ones and also unify the coupled and separated forms. Canonical forms of self-adjoint boundary conditions are instrumental in the study of the dependence of eigenvalues on the boundary conditions and for their numerical computation. In the second order case this dependence is now well understood due to some surprisingly recent results given the long history and voluminous literature of Sturm-Liouville problems. And there is a robust code for their computation: SLEIGN2.     

On isomorphism problem for von Neumann flows with one discontinuity

A von Neumann flow is a special flow over an irrational rotation of the circle and under a piecewise C¹ roof function with a non-zero sum of jumps. We prove that the absolute value of the jump is a (measure theoretic) invariant in the class of von Neumann special flows with one discontinuity, i.e., two ergodic von Neumann flows with one discontinuity are not isomorphic if the jumps of the roof functions have different absolute values, regardless of the irrational rotation in the base.     

Summability properties of Gabor expansions

We show that there exist complete and minimal systems of time-frequency shifts of Gaussians in $L^2(\mathbb{R})$ which are not strong Markushevich basis (do not admit the spectral synthesis). In particular, it implies that there is no linear summation method for general Gaussian Gabor expansions. On the other hand we prove that the spectral synthesis for such Gabor systems holds up to one dimensional defect.