Towards Rapid Parameter Estimation on Gravitational Waves from Compact Binaries using Interpolated Waveforms

Accurate parameter estimation of gravitational waves from coalescing compact binary sources is a key requirement for gravitational-wave astronomy. Evaluating the posterior probability density function of the binary's parameters (component masses, sky location, distance, etc.) requires computing millions of waveforms. The computational expense of parameter estimation is dominated by waveform generation and scales linearly with the waveform computational cost. Previous work showed that gravitational waveforms from non-spinning compact binary sources are amenable to a truncated singular value decomposition, which allows them to be reconstructed via interpolation at fixed computational cost. However, the accuracy requirement for parameter estimation is typically higher than for searches, so it is crucial to ascertain that interpolation does not lead to significant errors. Here we provide a proof of principle to show that interpolated waveforms can be used to recover posterior probability density functions with negligible loss in accuracy with respect to non-interpolated waveforms. This technique has the potential to significantly increase the efficiency of parameter estimation.Comment: 7 pages, 2 figure

Intensity fluctuations in steady state superradiance

Alkaline-earth like atoms with ultra-narrow optical transitions enable superradiance in steady state. The emitted light promises to have an unprecedented stability with a linewidth as narrow as a few millihertz. In order to evaluate the potential usefulness of this light source as an ultrastable oscillator in clock and precision metrology applications it is crucial to understand the noise properties of this device. In this paper we present a detailed analysis of the intensity fluctuations by means of Monte-Carlo simulations and semi-classical approximations. We find that the light exhibits bunching below threshold, is to a good approximation coherent in the superradiant regime, and is chaotic above the second threshold.Comment: 8 pages, 5 figure

On the influence of resonance photon scattering on atom interference

Here, the influence of resonance photon-atom scattering on the atom interference pattern at the exit of a three-grating Mach-Zehnder interferometer is studied. It is assumed that the scattering process does not destroy the atomic wave function describing the state of the atom before the scattering process takes place, but only induces a certain shift and change of its phase. We find that the visibility of the interference strongly depends on the statistical distribution of transferred momenta to the atom during the photon-atom scattering event. This also explains the experimentally observed (Chapman et al 1995 Phys. Rev. Lett. 75 2783) dependence of the visibility on the ratio d_p/\lambda_i = y'_{12} (2\pi/kd\lambda_i), where y'_{12} is distance between the place where the scattering event occurs and the first grating, k is the wave number of the atomic center-of-mass motion, $d$ is the grating constant and \lambda_i is the photon wavelength. Furthermore, it is remarkable that photon-atom scattering events happen experimentally within the Fresnel region, i.e. the near field region, associated with the first grating, which should be taken into account when drawing conclusions about the relevance of "which-way" information for the interference visibility.Comment: 9 pages, 1 figur

Topological phase for entangled two-qubit states and the representation of the SO(3)group

We discuss the representation of the $SO(3)$ group by two-qubit maximally entangled states (MES). We analyze the correspondence between $SO(3)$ and the set of two-qubit MES which are experimentally realizable. As a result, we offer a new interpretation of some recently proposed experiments based on MES. Employing the tools of quantum optics we treat in terms of two-qubit MES some classical experiments in neutron interferometry, which showed the $\pi$-phase accrued by a spin-$1/2$ particle precessing in a magnetic field. By so doing, we can analyze the extent to which the recently proposed experiments - and future ones of the same sort - would involve essentially new physical aspects as compared with those performed in the past. We argue that the proposed experiments do extend the possibilities for displaying the double connectedness of $SO(3)$, although for that to be the case it results necessary to map elements of $SU(2)$ onto physical operations acting on two-level systems.Comment: 25 pages, 9 figure

Further evidence of antibunching of two coherent beams of fermions

We describe an experiment confirming the evidence of the antibunching effect on a beam of non interacting thermal neutrons. The comparison between the results recorded with a high energy-resolution source of neutrons and those recorded with a broad energy-resolution source enables us to clarify the role played by the beam coherence in the occurrence of the antibunching effect.Comment: 4 pages, 3 figure

Effect of an atom on a quantum guided field in a weakly driven fiber-Bragg-grating cavity

We study the interaction of an atom with a quantum guided field in a weakly driven fiber-Bragg-grating (FBG) cavity. We present an effective Hamiltonian and derive the density-matrix equations for the combined atom-cavity system. We calculate the mean photon number, the second-order photon correlation function, and the atomic excited-state population. We show that, due to the confinement of the guided cavity field in the fiber cross-section plane and in the space between the FBG mirrors, the presence of the atom in the FBG cavity can significantly affect the mean photon number and the photon statistics even though the cavity finesse is moderate, the cavity is long, and the probe field is weak.Comment: Accepted for Phys. Rev.

Steady-state Ab Initio Laser Theory: Generalizations and Analytic Results

We improve the steady-state ab initio laser theory (SALT) of Tureci et al. by expressing its fundamental self-consistent equation in a basis set of threshold constant flux states that contains the exact threshold lasing mode. For cavities with non-uniform index and/or non-uniform gain, the new basis set allows the steady-state lasing properties to be computed with much greater efficiency. This formulation of the SALT can be solved in the single-pole approximation, which gives the intensities and thresholds, including the effects of nonlinear hole-burning interactions to all orders, with negligible computational effort. The approximation yields a number of analytic predictions, including a "gain-clamping" transition at which strong modal interactions suppress all higher modes. We show that the single-pole approximation agrees well with exact SALT calculations, particularly for high-Q cavities. Within this range of validity, it provides an extraordinarily efficient technique for modeling realistic and complex lasers.Comment: 17 pages, 11 figure

Biased tomography schemes: an objective approach

We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal. A quantum analogy of the transfer function determines the space where the reconstruction should be done without the need for any ad hoc truncations of the Hilbert space. An illustration of this method is provided by a simple yet practically important tomography of an optical signal registered by realistic binary detectors.Comment: 4 pages, 3 figures, accepted in PR

Coherence loss and revivals in atomic interferometry: A quantum-recoil analysis

The coherence effects induced by external photons coupled to matter waves inside a Mach-Zehnder three-grating interferometer are analyzed. Alternatively to atom-photon entanglement scenarios, the model considered here only relies on the atomic wave function and the momentum shift induced in it by the photon scattering events. A functional dependence is thus found between the observables, namely the fringe visibility and the phase shift, and the transversal momentum transfer distribution. A good quantitative agreement is found when comparing the results obtained from our model with the experimental data.Comment: 18 pages, 4 figure