Two-Way Exchange of Quantum Information and Thermodynamic Work with a Nanomechanical Platform

The aim of this project is to develop the theoretical understanding of work exchanged by a quantum system when energetic coherence are involved, and translate this theory into concrete protocols for new experimental platforms on which these predictions can be tested. The overall fundamental goal is to answer if and when thermodynamic processes could benefit from making use of coherences.

The particular experimental platform that we will focus on is a new nanomechanics experiment that is being built by the Ares group at the University of Oxford. The platform consists of a semiconducting carbon nanotube suspended between two metal pillars, whose conduction electrons act simultaneously as source and drain for the nanotube, and as thermal reservoirs with well-defined temperature. Gate electrodes tune the potential barrier for electrons tunneling into and out of the nanotube, and have been shown to control current to the level of single electrons. The group is currently investigating how to encode coherent states into the electrons' spin-valley degree of freedom. Mechanical oscillations of the tube when driven by an alternating field have been shown to be strongly coupled to the state. Work done by the electron on the nanotube's motion is anticipated to be detectable via its effect on the capacitance of a resonant LC circuit.

During this project, the student will build theoretical models and predictions to quantify the thermodynamic work needed to perform certain quantum information processing tasks, such as Landauer erasure and work extraction from coherences.
This will involve assessing key issues such as "where did the work go" and "what entropy should one use" to assess information changes and energetic exchanges in the quantum regime. The student will also clarify if processing of two or more non-commuting quantum states has the same work balance as when processing the commuting quantum states.
The student will work closely with the experimental group in Oxford to discuss progress and measurement results, as well as the philosophical implications of our findings. It is expected that these first experimental tests of work associated with quantum states/coherences can bring up entirely new perspectives on the thermodynamic cost of quantum information processing, which we hope to explore.
Regular visits of the Exeter theory PhD student to the experimental group in Oxford, as well as visits to the other team members in Grenoble/Madrid, will be part of the PhD project.