Introduction to Nanomechanics (Fall 2009)


Overview

This course (not surprisingly) focuses on the mechanics of very small objects. In particular, we will discuss the regime of nanometer-scale objects where classical theory begins to break down and quantum mechanical behavior emerges. After covering the fundamentals of the field, we will study its most important results up to and including contemporary work. We will emphasize the experimental side of the field. We will highlight current applications of nanomechanical devices in addition to speculating on possible future applications. In particular, we will investigate the use of micro- and nanomechanical resonators as ultrasensitive sensors of force, mass, and displacement. The course will focus the experimental rather than theoretical aspects of the field.

The main topics to be covered include: mechanical sensors, cantilever mechanics (statics and dynamics), dissipation and noise in mechanical systems, nanomechanical transducers, cooling mechanical resonators, the standard quantum limit on displacement measurement, nanomechanical mass sensing, nanomechanical magnetometry, fabrication of nanomechanical devices.


Format and Requirements

The course consists of one 2-hour lecture per week and one 1-hour exercise session per week. Exercise sessions will be a forum for in depth discussion of relevant papers, assigned exercises, and general questions. A final report on an important experimental paper is required (4-5 pages or 3000-5000 words). The course will be conducted in English. The grading is pass/fail.

This course will be aimed at 3rd-year bachelor and master students in physics and nanoscience. Physics III is a prerequisite. Previous course-work in solid-state physics and statistical mechanics is expected.

Most of the source material and reading in this class will be drawn from original papers in scientific journals and will be provided in class. Some reading will be based on short sections of Foundations of Nanomechanics, A. N. Cleland (Springer, 2003) and Fundamentals of Statistical and Thermal Physics, F. Reif (McGraw-Hill, 1965). Copies of these readings will be distributed in class.


Schedule


Lectures: Tuesdays, 12.00-14.00, Seminarzimmer 1.09
Exercise Sessions: Thursdays, 13.00-14.00, 3.12
Date Lecture Content
15.09.2009 Preliminary Logistics & Introduction
Course outline and expectations; What is nanomechanics? Why study nanomechanics? Cantilever basics (static case).

Exercise Session: M. L. Roukes, Physics World 14, 8 (2001); K. C. Schwab and M. L. Roukes, Phys. Today 58, 36 (2005).

Optional Reading: A. N. Cleland, Phys. Today 62, 68 (2009).

Downloads: Lecture slides, Lecture notes, Exercise sheet 1.
22.09.2009 Cantilevers and Mechanical Sensors
Cantilever basics (dynamic case). Cantilevers as harmonic oscillators.

Exercise Session: Foundations of Nanomechanics: p. 199-211, 233-237.

Downloads: Lecture slides, Lecture notes, Exercise sheet 2.
29.09.2009 Dissipation and Noise in Mechanical Systems I
Equipartition theorem; thermal noise; fluctuation-dissipation theorem.

Exercise Session: Fundamentals of Statistical and Thermal Physics: p. 248-253, 560-567; Foundations of Nanomechanics: p. 277-301.

Optional Reading: Fundamentals of Statistical and Thermal Physics: p. 567-577.

Downloads: Lecture slides, Lecture notes, Exercise sheet 3.
06.10.2009 Dissipation and Noise in Mechanical Systems II
Common sources of dissipation and noise in nanomechanical systems; measuring in the presence of mechanical dissipation and noise.

Exercise Session: A. C. Bleszynski-Jayich et al., Appl. Phys. Lett. 92, 013123 (2008).

Optional Reading: K. Y. Yasumura et al., J. Microelectromech. Sys. 9, 117 (2000); A. N. Cleland and M. L. Roukes, J. Appl. Phys. 92, 2758 (2002); J. G. E. Harris et al., Appl. Phys. Lett. 82, 3532 (2003).

Downloads: Lecture slides, Lecture notes, Exercise sheet 4.
13.10.2009 Nanomechanical Measurements
Measurement of displacement, frequency, and dissipation; types of transducers for nanomechanics; focus on optical interferometry.

Exercise Session: D. Rugar et al., Rev. Sci. Inst. 59, 2337 (1988); D. Rugar H. J. Mamin, and P. Guethner, Appl. Phys. Lett. 55, 2588 (1989).

Optional Reading: R. G. Knobel and A. N. Cleland, Nature 424, 291 (2003); M. Poggio et al., Nature Phys. 4, 635 (2008); C. A. Regal, J. D. Teufel, and K. W. Lehnert, Nature Phys. 4, 555 (2008).

Downloads: Lecture slides, Lecture notes, Exercise sheet 5.
20.10.2009 Cooling Mechanical Resonators I
Thermal motion; cryogenic cooling; recent experimental efforts; theoretical questions: ground state cooling (?).

Exercise Session: M. D. LaHaye et al., Science 304, 74 (2004).

Optional Reading: J. D. Teufel, C. A. Regal, and K. W. Lehnert, New J. Phys. 10, 095002 (2008).

Downloads: Lecture slides, Lecture notes, Exercise sheet 5 (no new excercises this week).
27.10.2009 Cooling Mechanical Resonators II
Cooling individual mechanical modes; optical cooling; feedback cooling; practical motivations: measurement bandwidth and dynamic range.

Exercise Session: S. Gröblacher et al., Nature Phys. 5, 485 (2009); M. Poggio et al., Phys. Rev. Lett. 99, 017201 (2007).

Optional Reading: J. D. Teufel, C. A. Regal, and K. W. Lehnert, New J. Phys. 10, 095002 (2008); F. Marquardt and S. M. Girvin, Physics 2, 40 (2009); B. Abbott et al., New J. Phys. 11, 073032 (2009).

Downloads: Lecture slides, Lecture notes, Review paper to read: F. Marquardt and S. M. Girvin, Physics 2, 40 (2009).
03.11.2009 LECTURE CANCELLED
There will be no lecture this week; there will, however, be an exercise session.

Exercise Session: Nanomechanical mass sensing.
10.11.2009 The Standard Quantum Limit
Back-action; standard quantum limit (SQL); approaching the SQL. See A. A. Clerk et al., arXiv:0810.4729 (2008) for a detailed review.

Exercise Session: K. Jensen, K. Kim, and A. Zettl, Nature Nanotech. 3, 533 (2008).

Downloads: Lecture slides, Lecture notes.
17.11.2009 Nano-resonator Fabrication: Top-down & Bottom-up
Standard top-down techniques: a typical process; Singly clamped beams; doubly clamped beams; bottom-up resonators: nanotubes, nanowires, graphene, etc.

Exercise Session: CANCELLED. Attendance at the following seminar is suggested: Nanomechanical Measurements of a Superconducting Qubit, Prof. Matt LaHaye, Syracuse University, 19.11.2009, 15:00, Room 1.09.

Optional Reading: Foundations of Nanomechanics: chp. 11-12; J. M. Nichol et al., Appl. Phys. Lett. 93, 193110 (2008); J. S. Bunch et al., Science 315, 490 (2007).

Downloads: Lecture slides, Publication list for final report.
24.11.2009 Overview of Significant Experiments
RF resonator; parametric and nonlinear resonators; mechanical electrometer; quantum of thermal conductance; electron transport and mechanical motion.

Exercise Session: CANCELLED.

Optional Reading: Foundations of Nanomechanics, chp. 9.

Downloads: Lecture slides, Lecture notes.
01.12.2009 Focus: Nanomechanical Magnetometry
Magnetic resonance force microscopy.

Exercise Session: CANCELLED.

Optional Reading: C. L. Degen et al., Proc. Nat. Acad. Sci. U.S.A. 106, 1313 (2009).

Downloads: Lecture slides.
08.12.2009 Focus: Nanomechanical Magnetometry
Torsional magnetometry: recent experiments on persistent currents in metallic rings.

Exercise Session: CANCELLED.

Optional Reading: A. C. Bleszynski-Jayich et al., J. Vac. Sci. Technol. B 26, 1412 (2008); A. C. Bleszynski-Jayich et al., Science 326, 272 (2009).

Downloads: Lecture slides, Lecture notes.
15.12.2009 Paper Presentations
Each student will present a 5-minute abstract of his/her final paper to the class.



References

  • Foundations of Nanomechanics, A. N. Cleland (Springer, 2003).

  • Fundamentals of Statistical and Thermal Physics, F. Reif (McGraw-Hill, 1965).