A Quantum Thermal Machine

A quantum thermal machine G. J. Milburn and M. S. Kim (Imperial College London)

There have been investigations on quantum-mechanical machinery. A quantum Szilard engine was considered to show how information plays in the operations to generate work [1]. An experimental realisation of Maxwell’s demon was demonstrated for photonic systems [2]. A recent theoretical work shows the implications of the second law of thermodynamics in quantum coherences which do not increase by a thermal operation. In this project, we are interested in investigating a quantum thermal machine. Frenzel et al [3] have proposed a general scheme for a quantum thermal machine that makes explicit the role of a clock and the measurement of energy. Consider two quantum systems, a two-level system labelled S and a machine labelled M. The key point is that the energy difference between the two states of the system can be periodically modulated by the coupling to the machine M. We can think of the time dependent Hamiltonian for the system as describing the system upon which the machine does work, periodically raising and lowering the energy difference between the two states. If the system starts in state |0> it remains there unless the thermal reservoir induces a transition to the state |1>. The task is to extract that small amount of thermal energy by making measurements on the machine M. Clearly the ability to extract energy from the reservoir in this way will be subject to fluctuations. In order to regard the machine as not only controlling the system energy but also capable of making measurements upon the system energy we need to move beyond the semiclassical description to include possible entanglement between the system and the machine. The detail of the project is as follows:

Six-month project: The work will be on how to realise the quantum machine using superconductor qubits. We will then compare it with the machine proposed by Frenzel et al. After a short literature survey on the quantum machine and superconductor qubit interactions, the student will be able to set up a theoretical framework for the quantum machine using the superconductor qubits. This will be followed by their consideration on real experimental conditions. PhD project: Based on what is learned in the first six months, the students will work further on developing machine that works on quantum-mechanical principles. In this, we can test some of the principles and laws of thermodynamics in the quantum-mechanical regime. We also expect to generalise some of the thermodynamical terms to work in quantum mechanics.

The calculation will require both analytic and numerical work on quantum trajectories. The necessary background can be found in the cited references and in Wiseman and Milburn, Quantum measurement and Control, as well as Milburn’s lecture notes for the CDT course.

[1] S.W. Kim et al., Phys. Rev. Lett 106, 070401 (2011). [2] M. D. Vidrighin et al., Phys. Rev. Lett. 116, 050401 (2016). [3] M. F. Frenzel, D. Jennings and T. Rudolph, New J. Phys. 18 023037 (2016).