Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum

Two path interferometry with coherent states and squeezed vacuum can achieve phase sensitivities close to the Heisenberg limit when the average photon number of the squeezed vacuum is close to the average photon number of the coherent light. Here, we investigate the phase sensitivity of such states in the presence of photon losses. It is shown that the Cramer-Rao bound of phase sensitivity can be achieved experimentally by using a weak local oscillator and photon counting in the output. The phase sensitivity is then given by the Fisher information F of the state. In the limit of high squeezing, the ratio (F-N)/N^2 of Fisher information above shot noise to the square of the average photon number N depends only on the average number of photons lost, n_loss, and the fraction of squeezed vacuum photons mu. For mu=1/2, the effect of losses is given by (F-N)/N^2=1/(1+2 n_loss). The possibility of increasing the robustness against losses by lowering the squeezing fraction mu is considered and an optimized result is derived. However, the improvements are rather small, with a maximal improvement by a factor of two at high losses.Comment: 7 pages, including 6 figure

Nucleon Flow and Fragment Flow in Heavy Ion Reactions

The collective flow of nucleons and that of fragments in the 12C + 12C reaction below 150 MeV/nucleon are calculated with the antisymmetrized version of molecular dynamics combined with the statistical decay calculation. Density dependent Gogny force is used as the effective interaction. The calculated balance energy is about 100 MeV/nucleon, which is close to the observed value. Below the balance energy, the absolute value of the fragment flow is larger than that of nucleon flow, which is also in accordance with data. The dependence of the flow on the stochastic collision cross section and its origin are discussed. All the results are naturally understood by introducing the concept of two components of flow: the flow of dynamically emitted nucleons and the flow of the nuclear matter which contributes to both the flow of fragments and the flow of nucleons due to the statistical decay.Comment: 20 pages, PostScript figures, LaTeX with REVTeX and EPSF, KUNS 121

Antisymmetrized molecular dynamics with quantum branching processes for collisions of heavy nuclei

Antisymmetrized molecular dynamics (AMD) with quantum branching processes is reformulated so that it can be applicable to the collisions of heavy nuclei such as Au + Au multifragmentation reactions. The quantum branching process due to the wave packet diffusion effect is treated as a random term in a Langevin-type equation of motion, whose numerical treatment is much easier than the method of the previous papers. Furthermore a new approximation formula, called the triple-loop approximation, is introduced in order to evaluate the Hamiltonian in the equation of motion with much less computation time than the exact calculation. A calculation is performed for the Au + Au central collisions at 150 MeV/nucleon. The result shows that AMD almost reproduces the copious fragment formation in this reaction.Comment: 24 pages, 5 figures embedde

Antisymmetrized molecular dynamics of wave packets with stochastic incorporation of Vlasov equation

On the basis of the antisymmetrized molecular dynamics (AMD) of wave packets for the quantum system, a novel model (called AMD-V) is constructed by the stochastic incorporation of the diffusion and the deformation of wave packets which is calculated by Vlasov equation without any restriction on the one-body distribution. In other words, the stochastic branching process in molecular dynamics is formulated so that the instantaneous time evolution of the averaged one-body distribution is essentially equivalent to the solution of Vlasov equation. Furthermore, as usual molecular dynamics, AMD-V keeps the many-body correlation and can naturally describe the fluctuation among many channels of the reaction. It is demonstrated that the newly introduced process of AMD-V has drastic effects in heavy ion collisions of 40Ca + 40Ca at 35 MeV/nucleon, especially on the fragmentation mechanism, and AMD-V reproduces the fragmentation data very well. Discussions are given on the interrelation among the frameworks of AMD, AMD-V and other microscopic models developed for the nuclear dynamics.Comment: 26 pages, LaTeX with revtex and epsf, embedded postscript figure

Non-existence of Ramanujan congruences in modular forms of level four

Ramanujan famously found congruences for the partition function like p(5n+4) = 0 modulo 5. We provide a method to find all simple congruences of this type in the coefficients of the inverse of a modular form on Gamma_{1}(4) which is non-vanishing on the upper half plane. This is applied to answer open questions about the (non)-existence of congruences in the generating functions for overpartitions, crank differences, and 2-colored F-partitions.Comment: 19 page

High photon number path entanglement in the interference of spontaneously downconverted photon pairs with coherent laser light

We show that the quantum interference between downconverted photon pairs and photons from coherent laser light can produce a maximally path entangled N-photon output component with a fidelity greater than 90% for arbitrarily high photon numbers. A simple beam splitter operation can thus transform the 2-photon coherence of down-converted light into an almost optimal N-photon coherence.Comment: 5 pages, including 2 figures and 1 table, final version for publication as rapid communication in Phys. Rev.

Proof of the Umbral Moonshine Conjecture

The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case involving the largest sporadic simple Mathieu group. Here we establish the existence of the umbral moonshine modules in the remaining 22 cases.Comment: 56 pages, to appear in Research in the Mathematical Science

Pariah moonshine

Finite simple groups are the building blocks of finite symmetry. The effort to classify them precipitated the discovery of new examples, including the monster, and six pariah groups which do not belong to any of the natural families, and are not involved in the monster. It also precipitated monstrous moonshine, which is an appearance of monster symmetry in number theory that catalysed developments in mathematics and physics. Forty years ago the pioneers of moonshine asked if there is anything similar for pariahs. Here we report on a solution to this problem that reveals the O'Nan pariah group as a source of hidden symmetry in quadratic forms and elliptic curves. Using this we prove congruences for class numbers, and Selmer groups and Tate--Shafarevich groups of elliptic curves. This demonstrates that pariah groups play a role in some of the deepest problems in mathematics, and represents an appearance of pariah groups in nature.Comment: 20 page

High-performance nn-type organic field-effect transistors with ionic liquid gates

High-performance $n$-type organic field-effect transistors were developed with ionic-liquid gates and N,N$^"$-bis(n-alkyl)-(1,7 and 1,6)-dicyanoperylene-3,4:9,10-bis(dicarboximide)s single-crystals. Transport measurements show that these devices reproducibly operate in ambient atmosphere with negligible gate threshold voltage and mobility values as high as 5.0 cm$^2$/Vs. These mobility values are essentially identical to those measured in the same devices without the ionic liquid, using vacuum or air as the gate dielectric. Our results indicate that the ionic-liquid and $n$-type organic semiconductor interfaces are suitable to realize high-quality $n$-type organic transistors operating at small gate voltage, without sacrificing electron mobility