New Haven, CT 06511 USA'
- '$^\dagger$These authors contributed equally to this work.'
author:
- 'A. M. Jayich$^{1\dagger}$, J. C. Sankey$^{2\dagger}$, K. B[ø]{}rkje$^{1\dagger}$, D. Lee$^1$, C. Yang$^1$, M. Underwood$^1$, L. Childress$^1$, A. Petrenko$^1$, S. M. Girvin$^{1,3}$, J. G. E. Harris$^{1,3}$'
bibliography:
- 'JackSankey.bib'
title: 'Cryogenic Optomechanics with a [Si$_3$N$_4$]{} Membrane and Classical Laser Noise'
---

Introduction
============

Cavity optomechanical systems offer a new arena for studying nonlinear optics, the quantum behavior of massive objects, and possible connections between quantum optics and condensed matter systems [@2007_OpticsExpress_Kippenberg_Vahala; @Marquardt2009Optomechanics; @Heinrich2011Collective; @Pikovski2012Probing; @Isart2011Large; @Chang2009Cavity]. Many of the scientific goals for this field share two prerequisites: cooling a mechanical mode close to its ground state, and detecting its zero-point motion with an adequate signal-to-noise ratio.

The first experiment to satisfy these prerequisites used a conventional dilution refrigerator to cool a piezoelectric mechanical element coupled to a superconducting qubit [@OConnell2010Quantum]. The base temperature of the refrigerator ensured that one of the higher-order vibrational modes (a dilatational mode with resonance frequency $\sim$ 6 GHz) was in its quantum mechanical ground state. At the same time, the mechanical element was strongly coupled to a superconducting qubit via its piezoelectric charge, ensuring that the presence of a single phonon 