Signatures of Hong-Ou-Mandel Interference at Microwave Frequencies

Two-photon quantum interference at a beam splitter, commonly known as Hong-Ou-Mandel interference, was recently demonstrated with \emph{microwave-frequency} photons by Lang \emph{et al.}\,\cite{lang:microwaveHOM}. This experiment employed circuit QED systems as sources of microwave photons, and was based on the measurement of second-order cross-correlation and auto-correlation functions of the microwave fields at the outputs of the beam splitter. Here we present the calculation of these correlation functions for the cases of inputs corresponding to: (i) trains of \emph{pulsed} Gaussian or Lorentzian single microwave photons, and (ii) resonant fluorescent microwave fields from \emph{continuously-driven} circuit QED systems. The calculations include the effects of the finite bandwidth of the detection scheme. In both cases, the signature of two-photon quantum interference is a suppression of the second-order cross-correlation function for small delays. The experiment described in Ref. \onlinecite{lang:microwaveHOM} was performed with trains of \emph{Lorentzian} single photons, and very good agreement between the calculations and the experimental data was obtained.Comment: 11 pages, 3 figure

Propagation of sound through a sheared flow

Sound generated in a moving fluid must propagate through a shear layer in order to be measured by a fixed instrument. These propagation effects were evaluated for noise sources typically associated with single and co-flowing subsonic jets and for subcritical flow over airfoils in such jets. The techniques for describing acoustic propagation fall into two categories: geometric acoustics and wave acoustics. Geometric acoustics is most convenient and accurate for high frequency sound. In the frequency range of interest to the present study (greater than 150 Hz), the geometric acoustics approach was determined to be most useful and practical

Continuous quantum non-demolition measurement of Fock states of a nanoresonator using feedback-controlled circuit QED

We propose a scheme for the quantum non-demolition (QND) measurement of Fock states of a nanomechanical resonator via feedback control of a coupled circuit QED system. A Cooper pair box (CPB) is coupled to both the nanoresonator and microwave cavity. The CPB is read-out via homodyne detection on the cavity and feedback control is used to effect a non-dissipative measurement of the CPB. This realizes an indirect QND measurement of the nanoresonator via a second-order coupling of the CPB to the nanoresonator number operator. The phonon number of the Fock state may be determined by integrating the stochastic master equation derived, or by processing of the measurement signal.Comment: 5 pages, 3 figure

Nonlinear metrology with a quantum interface

We describe nonlinear quantum atom-light interfaces and nonlinear quantum metrology in the collective continuous variable formalism. We develop a nonlinear effective Hamiltonian in terms of spin and polarization collective variables and show that model Hamiltonians of interest for nonlinear quantum metrology can be produced in $^{87}$Rb ensembles. With these Hamiltonians, metrologically relevant atomic properties, e.g. the collective spin, can be measured better than the "Heisenberg limit" $\propto 1/N$. In contrast to other proposed nonlinear metrology systems, the atom-light interface allows both linear and non-linear estimation of the same atomic quantities.Comment: 8 pages, 1 figure

Evaluation of the 50km/h default urban speed limit in South Australia

On the 1st March 2003 the Default Urban Speed Limit (DUSL) in South Australia was lowered from 60 km/h to 50 km/h. Since this date, all urban roads have a speed limit of 50 km/h unless otherwise signed. This paper reports the results of an evaluation of the effectiveness of the reduced DUSL and is based on speed surveys and crash data analysis. Vehicles speeds were measured at 52 randomly chosen sites across the State. Crash data was analysed by examining the crash history of all roads with a 50 km/h or 60 km/h speed limit, a year before and after the new DUSL was introduced. The study found that, on average, mean speeds have fallen by approximately 2.2 km/h on streets where the speed limit was reduced and by 0.7 km/h on arterial roads where 60 km/h speed limit signs were erected. There was a 19.8% reduction in casualty crashes on 50 km/h roads and a corresponding 4.6% reduction on 60 km/h arterial roads when compared with the previous year.C. Kloeden, J. Woolley and J. McLea

Modelling biological invasions: individual to population scales at interfaces

Extracting the population level behaviour of biological systems from that of the individual is critical in understanding dynamics across multiple scales and thus has been the subject of numerous investigations. Here, the influence of spatial heterogeneity in such contexts is explored for interfaces with a separation of the length scales characterising the individual and the interface, a situation that can arise in applications involving cellular modelling. As an illustrative example, we consider cell movement between white and grey matter in the brain which may be relevant in considering the invasive dynamics of glioma. We show that while one can safely neglect intrinsic noise, at least when considering glioma cell invasion, profound differences in population behaviours emerge in the presence of interfaces with only subtle alterations in the dynamics at the individual level. Transport driven by local cell sensing generates predictions of cell accumulations along interfaces where cell motility changes. This behaviour is not predicted with the commonly used Fickian diffusion transport model, but can be extracted from preliminary observations of specific cell lines in recent, novel, cryo-imaging. Consequently, these findings suggest a need to consider the impact of individual behaviour, spatial heterogeneity and especially interfaces in experimental and modelling frameworks of cellular dynamics, for instance in the characterisation of glioma cell motility