Multi-Point Virtual Structure Constants and Mirror Computation of CP^2-model

In this paper, we propose a geometrical approach to mirror computation of genus 0 Gromov-Witten invariants of CP^2. We use multi-point virtual structure constants, which are defined as intersection numbers of a compact moduli space of quasi maps from CP^1 to CP^2 with 2+n marked points. We conjecture that some generating functions of them produce mirror map and the others are translated into generating functions of Gromov-Witten invariants via the mirror map. We generalize this formalism to open string case. In this case, we have to introduce infinite number of deformation parameters to obtain results that agree with some known results of open Gromov-Witten invariants of CP^2. We also apply multi-point virtual structure constants to compute closed and open Gromov-Witten invariants of a non-nef hypersurface in projective space. This application simplifies the computational process of generalized mirror transformation.Comment: 26 pages, Late

Open Virtual Structure Constants and Mirror Computation of Open Gromov-Witten Invariants of Projective Hypersurfaces

In this paper, we generalize Walcher's computation of the open Gromov-Witten invariants of the quintic hypersurface to Fano and Calabi-Yau projective hypersurfaces. Our main tool is the open virtual structure constants. We also propose the generalized mirror transformation for the open Gromov-Witten invariants, some parts of which are proven explicitly. We also discuss possible modification of the multiple covering formula for the case of higher dimensional Calabi-Yau manifolds. The generalized disk invariants for some Calabi-Yau and Fano manifolds are shown and they are certainly integers after re-summation by the modified multiple covering formula. This paper also contains the direct integration method of the period integrals for higher dimensional Calabi-Yau hypersurfaces in the appendix.Comment: 24pages, 5figure

Detection-dependent six-photon NOON state interference

NOON state interference (NOON-SI) is a powerful tool to improve the phase sensing precision, and can play an important role in quantum sensing and quantum imaging. However, most of the previous NOON-SI experiments only investigated the center part of the interference pattern, while the full range of the NOON-SI pattern has not yet been well explored.In this Letter, we experimentally and theoretically demonstrate up to six-photon NOON-SI and study the properties of the interference patterns over the full range.The multi-photons were generated at a wavelength of 1584 nm from a PPKTP crystal in a parametric down conversion process.It was found that the shape, the coherence time and the visibility of the interference patterns were strongly dependent on the detection schemes.This experiment can be used for applications which are based on the envelope of the NOON-SI pattern, such as quantum spectroscopy and quantum metrology.Comment: 5 pages, 3 figure