arXiv subjects

P. Staszewski

Publications and source records attributed to P. Staszewski.

5 recordsLinked to original sources

arXiv2012

Squeezed coherent state undergoing a continuous nondemolition observation

The time evolution of a squeezed coherent state conditioned by the results of a single and double heterodyne measurement is discussed. The mean values of quadratures as well as the dynamics of quadrature uncertainties have been obtained within the framework of the theory of continuous measurements based on filtration equations. It has been found that while the mean values depend on the measured noise, the uncertainties in the optical quadratures are deterministic. Explicit solutions for the latter have been provided. Finally, a time development of the squeeze parameter for the posterior squeezed coherent state has been found.

quant-ph↗

arXiv2012

Filtering equation for a measurement of a coherent channel

A stochastic model for a continuous photon counting and heterodyne measurement of a coherent source is proposed. A nonlinear filtering equation for the posterior state of a single-mode field in a cavity is derived by using the methods of quantum stochastic calculus. The posterior dynamics is found for the observation of a Bose field being initially in a coherent state. The filtering equations for counting and diffusion processes are given.

quant-ph↗

arXiv2005

Quantum Stochastic Differential Equation

A semi-classical non-Hamiltonian model of a spontaneous collapse of unstable quantum system is given. The time evolution of the system becomes non-Hamiltonian at random instants of transition of pure states to reduced ones, given by a contraction C. The counting trajectories are assumed to satisfy the Poisson law. A unitary dilation of the concractive stochastic dynamics is found. In particular, in the limit of frequent detection corresponding to the large number limit we obtain the Ito-Schroedinger stochastic unitary evolution for the pure state of unstable quantum system providing a new stochastic version of the quantum Zeno effect.

math-ph↗

arXiv2005

A Quantum Particle Undergoing Continuous Observation

A stochastic model for the continuous nondemolition ohservation of the position of a quantum particle in a potential field and a boson reservoir is given. lt is shown that any Gaussian wave function evolving according to the posterior wave equation with a quadratic potential collapses to a Gaussian wave packet given by the stationary solution of this equation.

quant-ph↗

arXiv2005

Nondemolition observation of a free quantum particle

A stochastic model of a continuous nondemolition observation of a free quantum Brownian motion is presented. The nonlinear stochastic wave equation describing the posterior dynamics of the observed quantum system is solved in a Gaussian case for a free particle of mass m. It is shown that the dispersion of the wave packet does not increase to infinity like for the free unobserved particle but tends to the finite limit.

quant-ph↗