Monitoring the states of single quantum systems.
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Date
2012
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Abstract
Continuous weak measurement provide a convenient way to gather information about a quantum
system without the need to prepare huge ensembles of identical systems as required by standard
quantum measurement theory. Even though weak measurement alter the dynamics of the wave
function slightly, they nevertheless are a good tool to monitor the dynamics of the wave function
in real time in the presence of certain perturbations, for example, sudden momentum kicks due to
collisions with particles of a surrounding gas. With weak measurement it is possible to monitor
the dynamics of the wave function without knowing it initially. The continuous monitoring can
be employed to influence the dynamics by means of feedback. This thesis focuses on the numeric
simulation of the continuous monitoring of the position of a free massive particle as well as a particle
bound in the following one-dimensional potentials: harmonic and double well. The monitoring
scheme involves estimating the wave function of the hydrogen atom initially and then applying the
results of the weak measurement its position to update the estimate through a numerically simulated
stochastic evolution. We also simulate evolution of the true wave function. The key highlights of
this thesis include: discussion of an alternative way to derive the stochastic differential equations
that govern the evolution of the true and estimated wave functions of the system, as well as the
explanation of the second order numerical scheme.
Description
Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2012.
Keywords
Quantum theory., Quantum measure theory., Wave functions., Theses--Physics.