Thermodynamics of continuously measured superconducting qubits: heat flow and control

Lead Research Organisation: Lancaster University
Department Name: Physics

Abstract

The transformation of energy in the forms of heat and work pertains to everyday life and is a crucial aspect in the efficiency of machines. In fact, the laws of thermodynamics, which govern these energy transformations, are so fundamental that have their say in almost all branches of physics. The first law acknowledges that heat is energy to be accounted for in energy conservation. The second law of thermodynamics qualitatively distinguishes heat from other forms of energy by associating it to entropy, a measurement of the "lack of information" about a system, and by stating that entropy grows in macroscopic systems.
The generality of these statements stems from general statistical properties of macroscopic objects with a large number of degrees of freedoms. However, the technological advances in engineering and operating nanoscale objects like molecular machines, forces us to rethink the implications of thermodynamics for microscopic few-particle systems, where thermal fluctuations are significant. Here the laws of thermodynamics can be reformulated in terms of probabilistic equations, known as fluctuation theorems, which account for rare microscopic events, like those where entropy decreases, which are instead washed away by statistics in the macroscopic word.
The formulation and experimental verification of these theorems have been a success of stochastic thermodynamics in the past decade. The nanoscale world, however, challenges us further with quantum mechanical processes emerging at this scale, and devices built upon them. How do we include quantum fluctuations into the laws of thermodynamics? Current research is advancing on this front with some success by analyzing quantum machines operating between classical thermal sources, to identify genuine quantum effects and generalize the definitions of heat and work for quantum processes. The main problem is that in quantum mechanics even measuring the energy of an isolated system is a deterministic process, and that measuring a specified variable, e.g. work along quantum evolution, comes with unavoidable back-action that needs to be taken into account.
In this project, we set aside the usual thermodynamic setup where a system is coupled to a thermal bath and focus instead on the measurement process, where a detector monitoring the system is the reservoir with which the system exchanges energy. This kind of configuration allows us to focus on the role of quantum measurement, and it brings new aspects into play, like the fact of dealing with an out-of-equilibrium environment, and the thermodynamic role of the information gained during the measurement. It also comes with the possibility of short-term experimental realizations, since quantum detector's readout is experimentally available, as opposed to thermal baths' readout.
The project will set-up the tools to deal with the thermodynamics of quantum measurement and use them to engineer heat flow detectors and possibly heat flow engineering at the nanoscale.

Planned Impact

The goal of the project is the development of fundamental science, and its impact will be primarily academic. Nonetheless, the results and the development of the project will have a societal as well as a long-term economic and technological impact.

Academic impact

The objectives of the project are timed to have an immediate impact on the community working on quantum thermodynamics, where studies on the role of quantum measurement are growing fast. The objectives also have the potential to influence other branches of physics, like quantum computation and quantum optics, and other disciplines like chemistry. In this way, the project can contribute to maintaining the leading position of UK research in the area of quantum thermodynamics, and more broadly in the field of quantum technologies. Moreover, the theme of energy and its manipulation the project is about is of strategic growing importance in plans for UK research developments.

Economic and Technological impact

The possibility of controlling heat flow by elementary quantum processes has a potential technological impact: It might help in optimizing the design of nanoscale machines and circuitry, or even in optimizing operations and running protocols for nanodevices. However, the specific output of the project is at the level of proof-of-principle of elementary protocols, and, though early contact with industrial enterprises might be possible, a foreseeable technological impact is beyond the project time-scales.

People and skills

The project will provide a comprehensive training of a PDRA in an active topic of current research in condensed matter theory. The PDRA will acquire high-level scientific competences in analytical modeling, numerical simulations, Besides the specific scientific competences, the PDRA will gain expertise in scientific communication via written publications and talk delivery as well as in team working skills. These benefits will extend to MPhys and Ph.D. students who will be working on projects spin-offed and related to the proposed research.

Societal impact

The projects bring about new ideas which, besides their scientific value, pertain to concepts like heat, work, and energy of interest for everybody in everyday life. How these common-sense concepts have to be modified at microscopic quantum level is of general interest. The development of the project is accompanied by a related outreach activity. This consist in the production of high-quality, informative material, dedicated websites, public lectures, and contributes to public-facing websites. Particular care is given to the outreach impact on the local community by participation in outreach programs in schools including schools visits and popular talks and taking part in LU activities like STEM Taster Days.

Publications

10 25 50
 
Description For quantum systems exchanging energy with an external driving and an external thermal bath, it is hard to detect heat and work separately, hence controlling the thermodynamic properties of the system. By replacing the thermal bath with a quantum-limited detector, we showed it is possible to come up with consistent definitions of heat and work which are applicable to single-shot quantum evolutions (quantum trajectories). In collaboration with our experimental partners, we showed that (i) our proposed definitions of heat and work are consistent with the first and second law of thermodynamics, and that (ii) heat and work contributions to a quantum evolution can be tracked along single quantum trajectories. By incorporating quantum feedback into the process, we are able to experimentally verify the second law of thermodynamics taking into account the information-exchange between system and detector. We showed that, as a result of quantum coherence and back-action, the average information exchange can cross from positive (information gain) to negative (information loss) upon changing the entropy of the initial state of the system.
Exploitation Route These findings put forward weakly measured quantum system as a promising architecture to explore thermodynamics of quantum systems. Such an architecture can be used to explore quantum fluctuations of thermal machines or information engines and characterize the statistics of their efficiency at the quantum level.
Sectors Digital/Communication/Information Technologies (including Software),Electronics

 
Description The main impact of the project findings is divulgation beyond academia. The results have been used in popular talks in schools (see engagement section) and popular video posted on youtube (https://www.youtube.com/watch?v=pvtnkdZPNak) by co-authors of the publications of the project.
Impact Types Cultural

 
Description Experimental verification of thermodynamics of weakly measured superconducting qubits 
Organisation Friedrich-Alexander University Erlangen-Nuremberg
Country Germany 
Sector Academic/University 
PI Contribution Theoretical study of thermodynamics of quantum systems along single quantum evolutions. Simulations of the results for architectures based on superconducting systems used in experiments by our partner
Collaborator Contribution - Realisation of experiments to verify the theoretical predictions for thermodynamics along single quantum trajectories of superconducting qubits.
Impact 2 submitted manuscripts: https://arxiv.org/abs/1703.05885, https://arxiv.org/abs/1802.07205
Start Year 2017
 
Description Experimental verification of thermodynamics of weakly measured superconducting qubits 
Organisation Washington University in St Louis
Country United States 
Sector Academic/University 
PI Contribution Theoretical study of thermodynamics of quantum systems along single quantum evolutions. Simulations of the results for architectures based on superconducting systems used in experiments by our partner
Collaborator Contribution - Realisation of experiments to verify the theoretical predictions for thermodynamics along single quantum trajectories of superconducting qubits.
Impact 2 submitted manuscripts: https://arxiv.org/abs/1703.05885, https://arxiv.org/abs/1802.07205
Start Year 2017
 
Description Conference talk 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The talk was delivered at an international workshop on frontiers of quantum physics and spread the impact of the project results within the community.
Year(s) Of Engagement Activity 2018
 
Description Conference talk (Lancaster) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Talk given at the UK Meeting on Superconducting Quantum Devices. The talk aimed at divulgating our results actoss the community working on superconductivity in UK
Year(s) Of Engagement Activity 2017
URL https://www.iopconferences.org/iop/frontend/reg/thome.csp?pageID=643249&ef_sel_menu=6399&eventID=110...
 
Description Programme/workhop 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact The talk was delivered at a 2-month programme specifically put together on quantum thermodynamics and spread the impact of the project results within the community.
Year(s) Of Engagement Activity 2018
 
Description School visit (our Lady Catholic College, Lancaster) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Schools
Results and Impact Talk on quantum computing and thermodynamics
Year(s) Of Engagement Activity 2018
 
Description Talk at University (Belfast) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Talk given at Belfast University. The aim was to divulgate the project results across the UK community
Year(s) Of Engagement Activity 2018