Nano- and Optomechanics

Nano- and optomechanics is a rapidly developing field where mechanical resonators - ranging from the nanoscale to km-sized gravitational-wave detectors - are studied with extremely sensitive methods. In this course we will study some of the most intriguing aspects of this topic, including mechanics at the nanoscale, NEMS sensors, synchronization, and quantum-limited measurements. The course consists of a lecture and exercises and will be given in English.

After successful participation in the module, the student is able to:

• Name different designs of mechanical resonators, and of NEMS and optomechanical detectors. Tell what their main pros and cons are.
• Illustrate the difference between bottom-up and top-down devices.
• Recall the optomechanical Hamiltonian and the derivation of its limiting cases. Evaluate the outcome with different quantum mechanical states.
• Classify different damping mechanism in mechanical devices and relate this to force noise and temperature.
• Select the right material(s) for a resonator+detector design, based on an understanding of the fabrication techniques and material properties
• Explain the working principle of different detector schemes. Distinguish its detection- and back action mechanisms
• Model the interaction between a detector and the resonator. Discover how this leads to the standard quantum limit (SQL), quantum non-demolition (QND) measurements, and optomechanically-induced transparency (OMIT).
• Outline different cooling mechanism and evaluate the final temperature of a cooling experiment.
• Analyze the properties of simple (e.g. string, beam) and more complex (e.g. H) mechanical structures.
• Assess the feasibility of a given design of an optomechanical sensor for small and large motion amplitudes.
• Plan an experiment to measure one of the effects discussed in the module.

No preconditions in addition to the requirements for the Master’s program in Physics.

• Lectures with a beamer (copies will be made available),
• Lectures with blackboard
• Discussion
• Excercise classes

Presentation files of the lectures, problem sheets

The lecture is based on the contents of two review articles:

• M. Poot and H. van der Zant, "Mechanical systems in the quantum regime", Physics Reports 511 (2012) 273–335
• M. Aspelmeyer et. al, "Cavity optomechanics", Rev. Mod. Phys. 86 (2014) 1391-1452

There will be a written exam of 120 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using calculation problems and comprehension questions.

For example an assignment in the exam might be:

• Explain in your own words the Haus-Caves limit
• Calculate the temperature of a resonator with properties XY coupled to a dc SQUID with properties Z

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.