Related papers: Optimal Monitoring of Position in Nonlinear Quantu…
Application of the path-integral approach to continuous measurements leads to effective Lagrangians or Hamiltonians in which the effect of the measurement is taken into account through an imaginary term. We apply these considerations to…
We consider a particle in harmonic oscillator potential, whose position is periodically measured with an instrument of finite precision. We show that the distribution of the measured positions tends to a limiting distribution when the…
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
The measurability by means of continuous measurements, of an observable $\A(t_0)$, at an instant, and of a time averaged observable, $\bar \A=1/T\int \A(t')dt'$, is examined for linear and in particular for non-linear quantum mechanical…
We present a general framework for sensitivity optimization in quantum parameter estimation schemes based on continuous (indirect) observation of a dynamical system. As an illustrative example, we analyze the canonical scenario of…
We consider a single copy of a quantum particle moving in a potential and show that it is possible to monitor its complete wave function by only continuously measuring its position. While we assume that the potential is known, no…
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first con- tribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i)…
We extend the optimal filtering equation known from the Stratonovich filtering theory on the quantum process case. The used observation model is based on an indirect measurement method, where the measurement is performed on an ancilla…
As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and…
We introduce a method of quantum tomography for a continuous variable system in position and momentum space. We consider a single two-level probe interacting with a quantum harmonic oscillator by means of a class of Hamiltonians, linear in…
We study the fundamental bounds on precision measurements of parameters contained in a time-dependent nonlinear optomechanical Hamiltonian, which includes the nonlinear light-matter coupling, a mechanical displacement term, and a…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
It is shown that having degenerate ground states over the domain of the wavefunction of a system is a sufficient condition for a quantum system to act as a measuring apparatus for the system. Measurements are then instances of spontaneous…
We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We…
We consider the problem of a state determination for a two-level quantum system which can be in one of two nonorthogonal mixed states. It is proved that for the two independent identical systems the optimal combined measurement (which…
Several optomechanics experiments are now entering the highly sought nonlinear regime where optomechanical interactions are large even for low light levels. Within this regime, new quantum phenomena and improved performance may be achieved,…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
We introduce a resource monotone, the completeness stability, to quantify the quality of quantum measurements within a resource-theoretic framework. By viewing a quantum measurement as a frame, the minimum eigenvalue of a frame operator…
We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asympotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved…