Introduction to Nanomechanics (Spring 2012)


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: Wednesdays, 13.00-15.00, Seminarzimmer 1.09
Exercise Sessions: Tuesdays, 13.00-14.00, 1.09
Date Lecture Content
21.02.2012 Preliminary Logistics & Introduction
Course outline and expectations; What is nanomechanics? Why study nanomechanics? Cantilever basics (static case).

Exercise Session: None.

Downloads: Lecture slides, Lecture notes.
07.03.2012 Cantilevers and Mechanical Sensors
Cantilever basics (dynamic case). Cantilevers as harmonic oscillators.

Exercise Session (Jonathan Prechtel): Discuss the following papers: M. L. Roukes, Physics World 14, 8 (2001); K. C. Schwab and M. L. Roukes, Phys. Today 58, 36 (2005); A. N. Cleland, Phys. Today 62, 68 (2009).

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

Downloads: Lecture slides, Lecture notes.
14.03.2012 Dissipation and Noise in Mechanical Systems I
Equipartition theorem; thermal noise; fluctuation-dissipation theorem.

Exercise Session (Jonathan Prechtel): Hand in and discuss Problem Set 1: Statics and Dynamics of Beams.

Reading: Fundamentals of Statistical and Thermal Physics: p. 248-254, 560-577.

Downloads: Lecture slides, Lecture notes.
21.03.2012 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 (Gunter Wüst): Hand in and discuss Problem Set 2: Classical Harmonic Oscillator.

Reading: Foundations of Nanomechanics: p. 277-301.

Downloads: Lecture notes.
28.03.2012 Dissipation and Noise in Mechanical Systems III
End of our discussion on dissipation and noise in nanomechanical systems.

Exercise Session (Michele Montinaro): Hand in and discuss Problem Set 3: Quantum Harmonic Oscillator.

Downloads: Exercise Sheet 3, Lecture slides.
04.04.2012 Nanomechanical Measurements
Measurement of displacement, frequency, and dissipation; types of transducers for nanomechanics; focus on optical interferometry.

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

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.
11.04.2012 Cooling Mechanical Resonators I
Thermal motion; cryogenic cooling; recent experimental efforts; theoretical questions: ground state cooling.

Exercise Session (Gunter Wüst): Hand in and discuss Problem Set 4.

Reading: F. Marquardt and S. M. Girvin, Physics 2, 40 (2009).

Downloads: Lecture slides, Lecture notes.
18.04.2012 NO LECTURE
There will be no lecture this week, however, there will be an exercise session.

Exercise Session (Michele Montinaro): Discuss the following paper: J. Chaste et al., Nature Nanotech., online publication (2012).

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

Downloads:
25.04.2012 Cooling Mechanical Resonators II
Cooling individual mechanical modes; optical cooling; feedback cooling; practical motivations: measurement bandwidth and dynamic range.

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

Reading: Foundations of Nanomechanics, chp. 9.

Downloads: Lecture slides, Lecture Notes.
02.05.2012 The Standard Quantum Limit
Back-action; standard quantum limit (SQL); approaching the SQL.

Exercise Session: "Tag der Arbeit".

Reading: J. D. Teufel, C. A. Regal, and K. W. Lehnert, New J. Phys. 10, 095002 (2008); B. Abbott et al., New J. Phys. 11, 073032 (2009).

Downloads: Lecture slides, Lecture Notes.
09.05.2012 Overview of Significant Experiments
Quantum of thermal conductance; Overview of top-down and bottom-up nanomechanical oscillators and related experiments.

Exercise Session (Michele Montinaro): Hand in and discuss Problem Set 5.

Reading: A. A. Clerk et al., Rev. Mod. Phys. 82, 1155 (2010) and Appendix.

Downloads: Exercise Sheet 5, Lecture slides, Lecture notes.
16.05.2012 NO LECTURE
There will be no lecture this week ("Auffahrt"), however, there will be an exercise session.

Exercise Session (Fei Xue): The session will include a short lecture entitled, "Nano-resonator fabrication: top-down & bottom-up".

Reading: M. Poot and H. S. J. van der Zant, Phys. Rep. 511, 273 (2012).
23.05.2012 Recent Developements in Ground State Cooling
We will discuss 2 experiments carried out in the last 2 years which have succeeded in demonstrating the prepartation of a nano-mechanical oscillator in its ground state.

Exercise Session: none.

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, Publication list.
30.05.2012 Focus: Mechanically Detected nano-MRI (Fei Xue)
Review of recent developments in ultrasensitive magnetic resonance force microscopy (MRFM) and it's application to nanometer-scale magnetic resonance imaging (nano-MRI).

Exercise Session (Paper Presentations): Each student will present a 5-minute abstract of his/her final paper to the class. The final paper is due on 29.06.2012.

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

Downloads:



References

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

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