Quantum-State Purity of Heralded Single Photons Produced from Frequency-Anti-Correlated Biphotons

We analyze the quantum-state purity of heralded single photons produced from frequency-anti-correlated biphotons. We find that the quantum-state purity in time-frequency domain depends strongly on the response time uncertainty of the trigger-photon detector that heralds the generation of its paired photon. If the trigger response time is much shorter than the two-photon coherence time, the time-frequency quantum-state purity of heralded single photons approaches unity and the heralded single photon is in a nearly pure state. If the trigger response time is much longer than the two-photon coherence time, the heralded photon is then projected onto a mixed state. Making use of the time-frequency entanglement, heralded single photons with a well-defined temporal wave function or a frequency superposition state can be produced and engineered. This time-frequency entanglement allows for shaping heralded single photons through nonlocal spectral modulation

On solvability of an indefinite Riccati equation

This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is derived, based on a monotonicity property of a newly defined set. Such a set is used to describe a family of solvable equations.Comment: 11 page

Effect of CSLM imaging rate on biofilms of P. aeruginosa and S. aureus

Biofilms are sessile communities of bacteria that can be found in an wide range of environments. Their inhabitants are phenotypically distinct from plank- tonic bacteria and are capable of forming complex, three-dimensional structures. Biofilms are studied using confocal scanning laser microscopy, or CSLM. This technique uses lasers and Novel Fluorescent Proteins (NFPs) to measure growth and structure formation of single- and multi-species biofilms in situ in three dimensions. We investigate the effects of slow and fast rates of image acquisition on mono- and co-cultures of biofilm forming bacteria: Pseudomonas aeruginosa and Staphylococcus aureus. After calculating growth rates and lag times, we find that fast scanning rates reduce the growth rate of P. aeruginosa in co-culture. Additionally, co-culture speeds up P. aeruginosa growth relative to monoculture when imaged at a slow rate, and fast scanning reverts co-culture growth to monoculture-like behavior. Additionally, a significant lag time is observed for P. aeruginosa grown in co-culture. The observed influence of confocal imaging rate on population dynamics should be considered in future studies to ensure accurate measurement of bacterial phenomena.Physic