We investigate the transverse mode structure of the down-converted beams generated by a type-II optical parametric oscillator (OPO) driven by a structured pump. Our analysis focus on the selection rules imposed by the spatial overlap between the transverse modes of the three fields involved in the non-linear interaction. These rules imply a hierarchy of oscillation thresholds that determine the possible transverse modes generated by the OPO, as remarkably confirmed with experimental results.

No abstract

Controlling the evolution of photonic quantum states is crucial for most quantum information processing and metrology tasks. Due to its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood; however, the fundamental phase anomaly of evolving waves, called the Gouy phase, has had a limited number of studies in the context of elementary quantum states of light, especially in the case of photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception attributing the increased phase sensitivity of multi-photon quantum states solely to an effective de Broglie wavelength.

No abstract

No abstract

This paper compares the interpolation abilities of nonparametric and parametric term structure models which are widely used by the main Central Banks of the world. Seeking the combination of smoothness and flexibility, a new Nelson-Siegel class model is introduced. It emerges as an extension of the Svensson (1994) and the five factor model proposed by De Rezende & Ferreira (2008) and Christensen et al. (2008). It is shown the superiority of the smoothing spline model in interpolating the spot and forward rates as well as the advantage of the proposed model over the other Nelson-Siegel models. The superiority of the smoothing spline, however, comes with a cost: its instability in fitting the initial vertices of the term structure. The proposed model, on the other hand, exhibits the desirable properties of smoothness and flexibility, especially for the forward rates and the spot rates of medium and long terms.

We investigate the dynamical properties of a type-II optical parametric oscillator pumped by a structured light beam carrying orbital angular momentum. Different dynamical regimes are theoretically derived and experimentally demonstrated, depending on the anisotropy effects imposed by the nonlinear medium. In a weakly anisotropic regime, fine-tuning of the orbital angular momentum transfer is obtained by adjusting the crystal parameters. Under strong anisotropy, orbital angular momentum transfer is not possible and a sharp dynamical behavior is observed, with abrupt switching between different transverse modes.

Controlling the evolution of a photonic quantum states is crucial for most quantum information processing and metrology tasks. Because of its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood. However, the fundamental phase anomaly of evolving waves called the Gouy phase has not been studied in the context of elementary quantum states of light such as photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception related to the nature of the increased phase sensitivity of multi-photon quantum states.