There are numerous physical phenomena that rely on time-dependent Hamiltonians (or parametric driving) to amplify, cool, squeeze or couple resonating systems. In this course, we shall introduce parametric phenomena in different fields of physics, ranging from classical engineering ideas to devices proposed for quantum neural networks.
Learning objective
In this course, the students will grasp the ubiquitous nature of parametric phenomena and apply it to both classical and quantum systems. The students will understand both the theoretical foundations leading to the parametric drive as well as the experimental aspect related to the realizations of the effect. Each student will analyze an independent system using the tools acquired in the course and will present his/her insights to the class.
Content
This course will provide a general framework for understanding and linking various phenomena, ranging from the child-on-a-swing problem to quantum limited amplifiers, to optical frequency combs, and to optomechanical sensors used in the LIGO experiment. The course will combine theoretical lectures and the study of important experiments through literature.
The students will receive an extended lecture summary as well as numerous MATHEMATICA and Python scripts, including QuTiP notebooks. These tools will enable them to apply analytical and numerical methods to a wide range of systems beyond the duration of the course.
Prerequisites / Notice
The students should be familiar with wave mechanics as well as second quantization. Following the course requires a laptop with Python and MATHEMATICA installed.
