Starting in Fall 2018, a PhD fellowship in Mathematical Physics will open in the framework of the European ITN project QUSCo.
Title: Adiabatic Control of Open Quantum Systems
Host institution: Inria team CAGE, Laboratoire Jacques-Louis Lions, UPMC Paris 6, France
Duration: 3 years
Net salary: [Gross salary: around 2000 euro/month (around 1600 euro/month net)]
Facilities: funding for traveling to conferences and for the attendance of graduate schools, laptop, etc...
Supervisors: Ugo Boscain, Pierre Rouchon and Mario Sigalotti. The PhD program includes several research stays at Universitaet Kassel, in the group of Christiane Koch
Adiabatic methods are very powerful techniques to prove controllability for closed quantum systems both in finite and infinite dimension, in particular when coupled with a deep knowledge of the structure of the eigenvalue intersection in the space of controls. In the finite-dimensional case these techniques permit to give easily verifiable conditions for exact controllability while in the infinite dimensional case they permit to characterize approximate controllability properties (that is the strongest controllability condition that one can expect). One of the most interesting features of adiabatic methods is that they provide, together with the controllability property, the explicit expression of the control necessary to realize the transition. Moreover they are robust in the sense that they permit to drive, with the same control, a continuum of systems with slightly different parameters. This last property is known as simultaneous controllability and it is very often crucial in Nuclear Magnetic Resonance. Typical adiabatic pulses achieving simultaneous controllability are the chirped pulses, which work by slowly modulating the frequency of the controls.
The purpose of this PhD project is to extend these techniques to open systems, which are fundamental models in most applications. There are very few theoretical contributions in this direction so far and our aim is to bridge this gap by using the geometric control language to translate and extend the adiabatic formalism.
The techniques necessary for achieving the goals of this thesis cover a large scientific spectrum. The candidate should have a good knowledge of quantum physics, operator theory, differential geometry, Lie groups, and dynamical systems.
The candidate must obtain his M2 within October 2018. The recruitment must fulfil the mobility rule: the candidate must not have resided or carried out his main activity (work, studies, etc.) in France for more than 12 months in the 3 years immediately before the recruitment date.