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 module 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 module consists of a lecture and exercises and will be given in English.

This semester the Nano- and Optomechanics course will be given in a hybrid format: in-presence and remote learning via pre-recorded videos. Lecture notes are available on Moodle.

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.

This Module consists of a lecture and integrated exercises. During the lectures, the teaching and learning content is presented and explained in a didactical, structured, and comprehensive form. This includes basic background knowledge and an overview of current topics from the very broad research field. The former consists of theoretical tools, as well as an analysis of common experimental methods. Universal concepts are emphasized between different topics. Crucial facts are conveyed by involving the students in scientific discussions to develop their intellectual power and to stimulate their analytic thinking on physics problems.

In the exercises, which will be integrated in the lectures, the concepts learned in the lectures are practiced and deepened. Problems will either be solved individually under supervision, in small groups, or plenary with input from all participants. The results are discussed during the exercise class. Additional problems for self study are available and in one of the classes, we will learn to use a finite-element program to simulate the mechanics of nanomechanical devices.

Although recordings of previous editions of the lectures will be made available, regular attendance of the lectures and exercise classes is highly recommended.

Lectures with blackboard work and beamer presentation, presentation files of the lecture, problem sheets. Hands-on exercise classes for finite-element-modeling using COMSOL. Recordings of previous editions of the lectures will be available.

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 an oral exam of 20 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
• Name different designs of mechanical resonators
• Recall the optomechanical Hamiltonian and the derivation of its limiting cases
• Illustrate the difference between bottom-up and top-down devices