|Rene Reimann www.nano-optics.org

Cavity Optomechanics

- Interaction of Light with Mechanical StructuresNano-Optics Lecture

2015-11-27 1

Image: PhD thesis of Albert Schließer, LMU München

|Rene Reimann www.nano-optics.org 2015-11-27 2

Cavity Optomechanics

Properties

High mechanical quality factors

Often small sizes (on-chip design)

Versatile: Couple to different

systems

Why optomechanics?

Test of fundamental physics

Quantum to classical transition

Gravitational wave detection

Thermodynamics

Chemistry

…

Measurement and amplification of

tiny forces and displacements

Possible use in hybrid systems as

storage devices or universal

transducers in quantum information

From M. Aspelmeyer et al., Physics Today 65, 29-35 (2012)

|Rene Reimann www.nano-optics.org 2015-11-27 3

Radiation Pressure Force

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Equations of Motion

Cavity:

Oscillator:

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Coupled Equations of Motion

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Effective Equation of Motion + Solutions

Detailed treatment: PhD thesis of Albert Schließer, LMU München

|Rene Reimann www.nano-optics.org 2015-11-27 7

Effective Temperature

With Wiener Khintchine theorem:

With Equipartition theorem:

|Rene Reimann www.nano-optics.org 2015-11-27 8

Sidebands

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Sideband Cooling

ω

Ωmech Ωmech

𝜔𝐿 𝜔cav

𝑚𝑚 − 1

𝑚 + 1

Ground-state cooling

works in the resolved

sideband regime:

2𝛾0 ≪ Ω0

2𝛾0

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Sideband Cooling

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References

Recent Review: Aspelmeyer, M., Kippenberg, T. J., & Marquardt, F. (2014). Cavity

optomechanics. Reviews of Modern Physics, 86(4), 1391–1452.

http://doi.org/10.1103/RevModPhys.86.1391

In the language of the course: Chapter 11.4: Novotny, L., & Hecht, B. (2006). Principles of Nano-

Optics. Cambridge University Press.

Reflection from vibrating mirror: Van Bladel, J., & De Zutter, D. (1981). Reflections from linearly

vibrating objects: Plane mirror at normal incidence. IEEE Transactions on Antennas and

Propagation, 29(4), 629–637. http://doi.org/10.1109/TAP.1981.1142645

𝛿𝑇 and 𝛿Γ equations: Schließer, A. (2009). Cavity optomechanics and optical frequency comb

generation with silica whispering-gallery-mode microresonators. Thesis LMU München.

http://edoc.ub.uni-muenchen.de/10940/1/Schliesser_Albert.pdf

For fluctuating force: Kubo, R. (1966). The fluctuation-dissipation theorem. Reports on Progress

in Physics, 29(1), 306. http://doi.org/10.1088/0034-4885/29/1/306

Very nice lectures (lectures 18 to 21) by Florian Marquardt alvailable as videos on

http://theorie2.physik.uni-erlangen.de/index.php/Lecture_Quantum-

optical_phenomena_in_nanophysics#Videos