Nil-potent vacuum in homodyne noise

In the absence of a signal field, vacuum entering through the empty beam splitter port is considered to be the sole contributor to the output noise of conventional two-port homodyne detection. We study a modified configuration that alters the input coefficient of vacuum, predicting an output noise less than that of the conventional configuration. Measurements, however, reveal identical output noise profiles for both the configurations. We explain the observations in terms of the incident field noise alone, and suggest that vacuum does not contribute to homodyne noise or shot-noise. We extend our results to the measurement of squeezed light, with non-ideal detectors.

Point process simulation of generalised inverse Gaussian processes and estimation of the Jaeger integral

In this paper novel simulation methods are provided for the generalised inverse Gaussian (GIG) Lévy process. Such processes are intractable for simulation except in certain special edge cases, since the Lévy density associated with the GIG process is expressed as an integral involving certain Bessel functions, known as the Jaeger integral in diffusive transport applications. We here show for the first time how to solve the problem indirectly, using generalised shot-noise methods to simulate the underlying point processes and constructing an auxiliary variables approach that avoids any direct calculation of the integrals involved. The resulting augmented bivariate process is still intractable and so we propose a novel thinning method based on upper bounds on the intractable integrand. Moreover, our approach leads to lower and upper bounds on the Jaeger integral itself, which may be compared with other approximation methods. The shot noise method involves a truncated infinite series of decreasing random variables, and as such is approximate, although the series are found to be rapidly convergent in most cases. We note that the GIG process is the required Brownian motion subordinator for the generalised hyperbolic (GH) Lévy process and so our simulation approach will straightforwardly extend also to the simulation of these intractable processes. Our new methods will find application in forward simulation of processes of GIG and GH type, in financial and engineering data, for example, as well as inference for states and parameters of stochastic processes driven by GIG and GH Lévy processes.

High-Speed Low-Light In Vivo Two-Photon Voltage Imaging of Large Neuronal Populations

Monitoring spiking activity across large neuronal populations at behaviorally relevant timescales is critical for understanding neural circuit function. Unlike calcium imaging, voltage imaging requires kilohertz sampling rates which reduces fluorescence detection to near shot noise levels. High-photon flux excitation can overcome photon-limited shot noise but photo-bleaching and photo-damage restricts the number and duration of simultaneously imaged neurons. We investigated an alternative approach aimed at low two-photon flux, voltage imaging below the shot noise limit. This framework involved developing: a positive-going voltage indicator with improved spike detection (SpikeyGi); an ultra-fast two-photon microscope for kilohertz frame-rate imaging across a 0.4x0.4mm2 field of view, and; a self-supervised denoising algorithm (DeepVID) for inferring fluorescence from shot-noise limited signals. Through these combined advances, we achieved simultaneous high-speed, deep-tissue imaging of more than one hundred densely-labeled neurons over one hour in awake behaving mice. This demonstrates a scalable approach for voltage imaging across increasing neuronal populations.

A Model of Spectral Line Broadening in Signal Forecasts for Line-intensity Mapping Experiments

Line-intensity mapping observations will find fluctuations of integrated line emission are attenuated by varying degrees at small scales due to the width of the line emission profiles. This attenuation may significantly impact estimates of astrophysical or cosmological quantities derived from measurements. We consider a theoretical treatment of the effect of line broadening on both the clustering and shot-noise components of the power spectrum of a generic line-intensity power spectrum using a halo model. We then consider possible simplifications to allow easier application in analysis, particularly in the context of inferences that require numerous, repeated, fast computations of model line-intensity signals across a large parameter space. For the CO Mapping Array Project and the CO(1–0) line-intensity field at z ∼ 3 serving as our primary case study, we expect a ∼10% attenuation of the spherically averaged power spectrum on average at relevant scales of k ≈ 0.2–0.3 Mpc−1 compared to ∼25% for the interferometric Millimetre-wave Intensity Mapping Experiment targeting shot noise from CO lines at z ∼ 1–5 at scales of k ≳ 1 Mpc−1. We also consider the nature and amplitude of errors introduced by simplified treatments of line broadening and find that while an approximation using a single effective velocity scale is sufficient for spherically averaged power spectra, a more careful treatment is necessary when considering other statistics such as higher multipoles of the anisotropic power spectrum or the voxel intensity distribution.

Shot noise processes with randomly delayed cluster arrivals and dependent noises in the large-intensity regime

We study shot noise processes with cluster arrivals, in which entities in each cluster may experience random delays (possibly correlated), and noises within each cluster may be correlated. We prove functional limit theorems for the process in the large-intensity asymptotic regime, where the arrival rate gets large while the shot shape function, cluster sizes, delays, and noises are unscaled. In the functional central limit theorem, the limit process is a continuous Gaussian process (assuming the arrival process satisfies a functional central limit theorem with a Brownian motion limit). We discuss the impact of the dependence among the random delays and among the noises within each cluster using several examples of dependent structures. We also study infinite-server queues with cluster/batch arrivals where customers in each batch may experience random delays before receiving service, with similar dependence structures.

An evaluation of resonant scanning as a high-speed imaging technique for two-photon imaging of cortical vasculature

We demonstrate a simple, low-cost two-photon microscope design with both galvo-galvo and resonant-galvo scanning capabilities. We quantify and compare the signal-to-noise ratios and imaging speeds of the galvo-galvo and resonant-galvo scanning modes when used for murine neurovascular imaging. The two scanning modes perform as expected under shot-noise limited detection and are found to achieve comparable signal-to-noise ratios. Resonant-galvo scanning is capable of reaching desired signal-to-noise ratios using less acquisition time when higher excitation power can be used. Given equal excitation power and total pixel dwell time between the two methods, galvo-galvo scanning outperforms resonant-galvo scanning in image quality when detection deviates from being shot-noise limited.