Effects of laser linewidth on the back-action cooling of optomechanical resonators. Gregory A. Phelps This work is sponsored by: UA NASA Space Grant, NSF, ARO, ONR

1000 times smaller than a proton! Introduction Gravitational Wave Detection (LIGO) 4 kilometer interferometer (Hartle, 339-342) 1000 times smaller than a proton! LIGO at Hanford [1] Quantum Mechanical ground state of a macroscopic object. [1] http://www.jb.man.ac.uk/research/pulsar/images/Ligo_hanford.jpg

Optomechanical System From T. Kippenberg and K. Vahala Science 321, 1172 (2008)

Under-damped driven harmonic oscillator. Equations of Motion Under-damped driven harmonic oscillator. Forcing terms are due to thermal motion of the mirror and the interaction with the intra-cavity light field. Equations are derived from Quantum Mechanical Hamiltonian for the mirror and light field.

Thermal and Laser Noise Thermal Noise: Laser Noise (Frequency):

Monte Carlo Methods/Simulations

Temperature vs. Linewidth

Laser noise places a limit on the temperatures attainable. Conclusions The opto-mechanical system can be modeled as a damped, driven harmonic oscillator. The final temperature of the mirror is linearly dependent on the linewidth of the laser, for small linewidth. Laser noise places a limit on the temperatures attainable. Constructing the system to have certain parameters can help to overcome laser noise. Feedback systems in the laser can reduce the laser noise. These sources of noise place a limitation on the sensitivity of the interferometer at LIGO.

Acknowledgments I would like to thank my advisor Pierre Meystre, Dan Goldbaum, Swati Singh, Ewan Wright for our lengthy discussions and their helpful insights. This work is supported by the University of Arizona/NASA Space Grant, NSF, ARO, and ONR.

References Hartle, James. GRAVITY, An Introduction to Einstein's General Relativity. 1st ed. 1. San Francisco: Addison Wesley, 2003. 339-342. Print.