Measurement & Feedback Control of a Two Level System

Abstract

In this bachelor project, the main objective is to investigate how a two-level quantum system can be controlled using weak continuous measurements and feedback control. The Monte-Carlo method was used to simulate the system dynamics under measurement and feedback to investigate how the system state can be controlled. This thesis concludes on how the feedback function impacts the purity of the state, represented by the Bloch vector on a Bloch sphere. The applications of this project extend to quantum information.

Popular Abstract

How may one measure a highly sensitive system without disturbing it? This bachelor's project will investigate the possible techniques of measuring and controlling a quantum two-level system.

A two-level quantum system may be likened to a nightclub, where there are people that like all genres of music. Essentially, if a certain jam is being played, the people who enjoy that song will go on the dancefloor and start throwing shapes. Analogously, the particles in a quantized system will be excited by an external stimulus, which allows the particles to move from a calm state to an excited state. To be able to observe the particles moving around, one needs to introduce a measurement technique, which must be sensitive enough to be able to extract little information but not strong enough to affect the system. A quantum system reacts to any external impulse much like climate and weather can be affected by the concentration of greenhouse gases in the atmosphere. Therefore, it is incredibly important that one understands how the quantum system may be affected through the measurement process. In this project, the focus will lie on implementing an existing measurement technique which can be applied to continuously evolving systems through “poking” at the system repeatedly. Unfortunately, theory suggests that repeated poking of the system may still lead to an undesirable effect onto the quantum system. This undesirable quantum effect is known as the Quantum Zeno effect and is often referred to as a measurement paradox. The mining of information from a quantum system may result in mixed results, in other words, one may obtain a mixture of two states, which leads to complications with respect to the interpretations.

Why are quantum technologies, specifically measurement instruments, so crucial in the upcoming future? Many technological gadgets are using so-called lithium-ion technology to store and provide electrical power. Unfortunately, the abundance of lithium salts is diminishing much like it has for oil for the past decades. Considering the latest news on the shortage of semiconductor technology, inventions and innovations are indispensable to curb the carbon emissions due to anthropological processes in an energy hungry society. The complexity revolved around the energy network in modern society provides major incentives for technological developments and societal adaptations. It should not appear as a surprise that many countries have invested a considerable amount of money on developing quantum technologies to minimize the energy consumption. On a political level, discussions have been held about carbon dioxide emissions such as the Paris Climate Accords COP 2015. As an example the history of automobiles, where a vast majority of the technology has shifted from analogue to digital based systems has shown an increase propulsion efficiency inducing a reduction in carbon emissions.

The results of the simulation will enlighten us on better understanding how to apply quantum mechanics in modern technology for more efficient energy usage. As a secondary consequence, one may gain a better understanding of how quantum mechanical systems behave under a nano-scope.

• author: Ali Khan, Sayan
• supervisor: Peter Samuelsson; Björn Annby Andersson
• organization: Mathematical Physics; Department of Physics
• course: FYSK02 20221
• year: 2022
• type: M2 - Bachelor Degree
• subject: Physics and Astronomy
• keywords: Quantum Measurement, Generalized Measurements, POVM (Positive Operator Valued Measure), Feedback Control, Two-Level System
• language: English
• id: 9095445
• date added to LUP: 2022-08-25 13:29:29
• date last changed: 2022-08-25 13:29:29