Related papers: From point processes to quantum optics and back
The theory of quantum optomechanics is reconstructed from first principles by finding a Lagrangian from light's equation of motion and then proceeding to the Hamiltonian. The nonlinear terms, including the quadratic and higher-order…
High-dimensional self-exciting point processes have been widely used in many application areas to model discrete event data in which past and current events affect the likelihood of future events. In this paper, we are concerned with…
Stochastic models of point patterns in space and time are widely used to issue forecasts or assess risk, and often they affect societally relevant decisions. We adapt the concept of consistent scoring functions and proper scoring rules,…
Universal quantum computers promise a dramatic speed-up over classical computers but a full-size realization remains challenging. However, intermediate quantum computational models have been proposed that are not universal, but can solve…
Point processes offer a versatile framework for sequential event modeling. However, the computational challenges and constrained representational power of the existing point process models have impeded their potential for wider…
We propose a general quantum theory of optical phase and instantaneous frequency in the time domain for slowly varying optical signals. Guided by classical estimation theory, we design homodyne phase-locked loops that enable quantum-limited…
The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…
The quantum dynamics of optomechanical systems was mostly studied for their fluctuations around classical steady states. We present a theoretical approach to determining the system observables of optomechanical systems as genuine quantum…
In this paper we describe in detail and generalize a method for quantum process tomography that was presented in [A. Bendersky, F. Pastawski, J. P. Paz, Physical Review Letters 100, 190403 (2008)]. The method enables the efficient…
Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…
In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only…
An experimental comparison of several operational phase concepts is presented. In particular, it is shown that statistically motivated evaluation of experimental data may lead to a significant improvement in phase fitting upon the…
For a locally finite point set $\Lambda \subset \mathbb{R}$, consider the collection of exponential functions given by $\mathcal{E}_{\Lambda}:= \{e^{i \lambda x} : \lambda \in L \}$. We examine the question whether $\mathcal{E}_{\Lambda}$…
This Habilitation manuscript describes the work done at JQI-NIST and LKB-ENS-Sorbonne University since 2010. After a brief introduction of the needed concepts for non-linear and quantum optics in optically dense atomic medium, I review…
A central concept in the theory of phase transitions beyond the Landau-Ginzburg-Wilson paradigm is fractionalization: the formation of new quasiparticles that interact via emergent gauge fields. This concept has been extensively explored in…
In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two spatially separated and noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements…
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…
In this paper, we propose a new paradigm for atom interferometry and demonstrate that there exists a universal set of atom optic components for inertial sensing. These components constitute gates with which we carry out quantum operations…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
The analogy between determinantal point processes (DPPs) and free fermionic calculi is well-known. We point out that, from the perspective of free fermionic algebras, Pfaffian point processes (PfPPs) naturally emerge, and show that a…