Work and energy fluctuations in open quantum systems
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School of Science |
Doctoral thesis (article-based)
| Defence date: 2019-02-15
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Author
Date
2019
Major/Subject
Mcode
Degree programme
Language
en
Pages
69 + app. 49
Series
Aalto University publication series DOCTORAL DISSERTATIONS, 25/2019
Abstract
Technological advances over the past few decades have made it possible to address quantum systems down to individual quanta of energy. Artificial atoms are now routinely fabricated and manipulated using solid-state technology. Exciting new applications are now within grasp, such as quantum heat engines, which have been theorised to achieve energy efficiencies not possible for their classical counterparts. Energy fluctuations are an inherent part of these devices and a detailed understanding of them is required. However, the proper theoretical framework under which such fluctuations are to be understood is still debated. In this thesis, we study energy fluctuations in open quantum systems at the level of individual runs of an experimental protocol. This work has been carried out in two parts. In the first part, we focus on calorimetric measurements – a promising new experimental protocol to continuously measure energy fluctuations of a qubit interacting with a thermal environment. Applying the protocol to more complex systems is not straightforward. Using a simple two-level approximation, we show that for some experimental parameters this protocol can be extended to a driven harmonic oscillator. Another aspect of the calorimetric protocol is that it can induce non-Markovian effects which affect how work and heat are defined. We quantify the degree of non-Markovianity induced by this measurement protocol, when applied to a qubit, based on a previously developed theoretical model. Importantly, we show that non-Markovianity does not necessarily decrease monotonically with the environment size. The attempt to extend the calorimetric protocol to general systems has led to the second part of this thesis. The calorimetric detection is a particular case of a continuously monitored system. However, other schemes exist that lead to different definitions of work and heat. Reconciling these approaches is not straightforward, as evidenced by the many work definitions present in the literature. The difficulty is centred at the fact that, in the orthodox interpretation of quantum mechanics, energy is not always a well-defined quantity. Here, based on the Bohmian interpretation of quantum mechanics, we put forward a general framework to remove this problem in a clear conceptual manner. In particular, we show that the classical definition of work for closed systems can be straightforwardly generalised to the quantum case. For an open system, we used the Bohmian conditional wave function which provides a stochastic state evolution for the open system. We show that this approach can lead to new insights regarding the role of entanglement in energy fluctuations and has the potential to provide a general and observer-independent framework of energy fluctuations in open quantum systems. The results presented in this thesis give a small contribution to the developing field of quantum thermodynamics.Description
Supervising professor
Ala-Nissilä, Tapio, Prof., Aalto University, Department of Applied Physics, FinlandThesis advisor
Ala-Nissilä, Tapio, Prof., Aalto University, Department of Applied Physics, FinlandKeywords
open quantum systems, single-shot energy fluctuations, calorimetric measurements, bohmian mechanics, conditional wave function
Other note
Parts
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[Publication 1]: Rui Sampaio, Samu Suomela, Tapio Ala-Nissila. Calorimetric measurement of work for a driven harmonic oscillator. Physical Review E, 2016, Volume 94, Issue 6, 062122. Full Text in Acris/Aaltodoc: http://urn.fi/URN:NBN:fi:aalto-201701191211.
DOI: 10.1103/PhysRevE.94.062122 View at publisher
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[Publication 2]: Rui Sampaio, Samu Suomela, Rebecca Schmidt, Tapio Ala-Nissila. Quantifying non-Markovianity due to driving and a finite-size environment in an open quantum system. Physical Review A, 2017, Volume 95, Issue 2, 022120,
DOI: 10.1103/PhysRevA.95.022120 View at publisher
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[Publication 3]: R. Sampaio, S. Suomela, T. Ala-Nissila, J. Anders, T.G. Philbin. Quantum work in the Bohmian framework. Physical Review A, 2018, Volume 97, Issue 1, 012131. Full Text in Acris/Aaltodoc: http://urn.fi/URN:NBN:fi:aalto-201803161712.
DOI: 10.1103/PhysRevA.97.012131 View at publisher
- [Publication 4]: R. Sampaio, S. Suomela, T. Ala-Nissila, J. Anders, T.G. Philbin. Contributions to single-shot energy exchanges in open quantum systems. Submitted to Physical Review E, September 2018.
