Bounds and optimisation of orbital angular momentum bandwidths within parametric down-conversion systems

The measurement of high-dimensional entangled states of orbital angular momentum prepared by spontaneous parametric down-conversion can be considered in two separate stages: a generation stage and a detection stage. Given a certain number of generated modes, the number of measured modes is determined by the measurement apparatus. We derive a simple relationship between the generation and detection parameters and the number of measured entangled modes.Comment: 6 pages, 4 figure

Quantum spiral bandwidth of entangled two-photon states

We put forward the concept of quantum spiral bandwidth of the spatial mode function of the two-photon entangled state in spontaneous parametric downconversion. We obtain the bandwidth using the eigenstates of the orbital angular momentum of the biphoton states, and reveal its dependence with the length of the down converting crystal and waist of the pump beam. The connection between the quantum spiral bandwidth and the entropy of entanglement of the quantum state is discussed.Comment: 10 pages, 3 figure

Schmidt modes generated in parametric downconversion

This paper presents the general Schmidt decomposition of two-photon fields generated in spontaneous parametric down-conversion (SPDC). It discusses in particular the separation of the radial and azimuthal degrees of freedom, the role of projection in modal analysis, and the benefits of collinear phase mismatch. The paper is written in a review style and presents a wealth of numerical results. It aims at emphasising the physics beyond the mathematics, through discussions and graphical representations of key results.Comment: 11 pages, 13 figure

b-physics signals of the lightest CP-odd Higgs in the NMSSM at large tan beta

We investigate the low energy phenomenology of the lighter pseudoscalar $A_1^0$ in the NMSSM. The $A_1^0$ mass can naturally be small due to a global $U(1)_R$ symmetry of the Higgs potential, which is only broken by trilinear soft terms. The $A_1^0$ mass is further protected from renormalization group effects in the large $\tan \beta$ limit. We calculate the $b \to s A_1^0$ amplitude at leading order in $\tan \beta$ and work out the contributions to rare $K$, $B$ and radiative $\Upsilon$-decays and $B -\bar B$ mixing. We obtain constraints on the $A_1^0$ mass and couplings and show that masses down to ${\cal{O}}(10)$ MeV are allowed. The $b$-physics phenomenology of the NMSSM differs from the MSSM in the appearance of sizeable renormalization effects from neutral Higgses to the photon and gluon dipole operators and the breakdown of the MSSM correlation between the $B_s \to \mu^+ \mu^-$ branching ratio and $B_s - \bar B_s$ mixing. For $A_1^0$ masses above the tau threshold the $A_1^0$ can be searched for in $b \to s \tau^+ \tau^-$ processes with branching ratios \lsim 10^{-3}.Comment: 18 pages, 3 figures; references adde