Weak Measurement of Quantum Harmonic Oscillators
(2025) FYSK04 20242Mathematical Physics
Department of Physics
- Abstract
- In this thesis we investigate the effect that weak measurement has on a quantum harmonic oscillator. By implementing a measurement process described by density matrices and positive operator valued-measures, we establish a model where the position eigenstates of a quantum harmonic oscillator in an initially pure state, are measured with a specific measurement strength. The results show that by increasing measuring strength, the uncertainty of our measurement result decreases, while the post-measurement state is increasingly disturbed. By representing the post-measurement state in phase-space with a Wigner quasi-probability distribution, we further analyze the dynamics of the quantum harmonic oscillator during measurement and find that the... (More)
- In this thesis we investigate the effect that weak measurement has on a quantum harmonic oscillator. By implementing a measurement process described by density matrices and positive operator valued-measures, we establish a model where the position eigenstates of a quantum harmonic oscillator in an initially pure state, are measured with a specific measurement strength. The results show that by increasing measuring strength, the uncertainty of our measurement result decreases, while the post-measurement state is increasingly disturbed. By representing the post-measurement state in phase-space with a Wigner quasi-probability distribution, we further analyze the dynamics of the quantum harmonic oscillator during measurement and find that the resulting decrease in uncertainty of the position eigenstates will increase the uncertainty in momentum, as is consistent with the uncertainty principle. (Less)
- Popular Abstract
- Measurement in quantum mechanics has always been a fascinating and weird concept. Many of the quirks in quantum mechanics stem from the problem of measurement, including Schrödinger’s cat, and the many world's theory, where a measurement has the effect of essentially splitting the universe in half. And for the longest time quantum measurement was interpreted as “we measure, then some magic happens, and our quantum state is gone”.
This all changed with advancements in technology, such as particle traps, which made it possible for us to study quantum particles more closely and for longer durations. We started to realize that there is a need to, and could, develop more intricate models to gain a deeper understanding of measurement. It is... (More) - Measurement in quantum mechanics has always been a fascinating and weird concept. Many of the quirks in quantum mechanics stem from the problem of measurement, including Schrödinger’s cat, and the many world's theory, where a measurement has the effect of essentially splitting the universe in half. And for the longest time quantum measurement was interpreted as “we measure, then some magic happens, and our quantum state is gone”.
This all changed with advancements in technology, such as particle traps, which made it possible for us to study quantum particles more closely and for longer durations. We started to realize that there is a need to, and could, develop more intricate models to gain a deeper understanding of measurement. It is possible to imagine a more generalized measurement process which extracts some information but does not destroy the quantum state, and that we might even be able to influence the quantum nature of our system through this measurement process.
In this thesis we consider a model of weak measurement, where we only try to extract partial information from our system in order to maintain its quantum nature. We will then apply this model on a quantum harmonic oscillator, which is a common object found in physics. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9185605
- author
- Verhaard Karlsson, Emil LU
- supervisor
- organization
- course
- FYSK04 20242
- year
- 2025
- type
- M2 - Bachelor Degree
- subject
- language
- English
- id
- 9185605
- date added to LUP
- 2025-03-03 08:51:16
- date last changed
- 2025-03-03 08:51:16
@misc{9185605,
abstract = {{In this thesis we investigate the effect that weak measurement has on a quantum harmonic oscillator. By implementing a measurement process described by density matrices and positive operator valued-measures, we establish a model where the position eigenstates of a quantum harmonic oscillator in an initially pure state, are measured with a specific measurement strength. The results show that by increasing measuring strength, the uncertainty of our measurement result decreases, while the post-measurement state is increasingly disturbed. By representing the post-measurement state in phase-space with a Wigner quasi-probability distribution, we further analyze the dynamics of the quantum harmonic oscillator during measurement and find that the resulting decrease in uncertainty of the position eigenstates will increase the uncertainty in momentum, as is consistent with the uncertainty principle.}},
author = {{Verhaard Karlsson, Emil}},
language = {{eng}},
note = {{Student Paper}},
title = {{Weak Measurement of Quantum Harmonic Oscillators}},
year = {{2025}},
}