|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
|Rene Reimann www.nano-optics.org 2015-11-27 4
Equations of Motion
Cavity:
Oscillator:
|Rene Reimann www.nano-optics.org 2015-11-27 5
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
|Rene Reimann www.nano-optics.org 2015-11-27 10
Sideband Cooling
|Rene Reimann www.nano-optics.org 2015-11-27 11
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