Open quantum systems, optimal stochastic control, stochastic methods

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Physics

Synopsis:

The course aims at providing basic mathematical and theoretical concepts needed in concrete quantum technology applications. The applications in view are those related to concrete experiments performed or ongoing in Aalto laboratories.

This is course TCM315 provided by the University of Helsinki to CTU students in the framework of the QTEdu Quantum Technology Open Master pilot project. To complete the course, students are expected to attend the on-line lectures and exercises (in real time or the recorded version) by the lecturers Paolo Muratore-Ginanneschi (PMG, UH), Jukka Pekola (JP, Aalto) and teaching assistant Tuomas Pyhäranta (Aalto).

Requirements:

Syllabus of lectures:

Classical open system: system in a harmonic bath

Classical master equations

Work and heat in stochastic thermodynamics

State operator and geometry

Elements of Quantum Probability

Boson and fermion oscillators

Fock space dynamics

Open dynamics of a central oscillator

Qualitative analysis of unitary time evolution

Jaynes-Cummings-Gaudin model

The Nakajima--Zwanzig projection operator technique

Quantum Master equations

Derivation of the completely positive master equation

Unravelling of master equations by Poisson processes

General stochastic Schrödinger equation with jumps

Quantum trajectories driven by white noise

Syllabus of tutorials:

During the exercises we will be reviewing the homework assigned by the remote lecturer.

Study Objective:

Assessment based on fulfilment of assignments handed out during exercises.

Study materials:

Key references:

[1] Lecture notes at: https://wiki.helsinki.fi/display/mathphys/TCM315+Fall+2022:+Open+Quantum+Systems

Recommended references:

[2] Wiseman, H. M. & Milburn, G. J.: Quantum Measurement and Control, Cambridge University Press, 2009.

[3] Breuer, H.-P., Petruccione, F.: The Theory of Open Quantum Systems, Oxford University Press, 2002.

[4] Jacobs, K.: Quantum Measurement Theory and its Applications Cambridge University Press, 2014.

[5] Barchielli, A. & Gregoratti, M.: Quantum Trajectories and Measurements in Continuous Time, Springer, 2009

[6] Peliti, L. & Pigolotti, S. Stochastic Thermodynamics: a gentle introduction, Princeton University Press 2021.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: