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 solidstate 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 twolevel 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 nonMarkovian effects which affect how work and heat are defined. We quantify the degree of nonMarkovianity induced by this measurement protocol, when applied to a qubit, based on a previously developed theoretical model. Importantly, we show that nonMarkovianity 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 welldefined 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 observerindependent 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.
Translated title of the contribution  Work and energy fluctuations in open quantum systems 

Original language  English 
Qualification  Doctor's degree 
Awarding Institution 

Supervisors/Advisors 

Publisher  
Print ISBNs  9789526084145 
Electronic ISBNs  9789526084152 
Publication status  Published  2019 
MoE publication type  G5 Doctoral dissertation (article) 
Keywords
 open quantum systems
 singleshot energy fluctuations
 calorimetric measurements
 bohmian mechanics
 conditional wave function
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Sampaio, R. (2019). Work and energy fluctuations in open quantum systems. Aalto University. http://urn.fi/URN:ISBN:9789526084152