Original Paper Ann. Phys. (Berlin) 527, No. 1–2, 89–99 (2015) / DOI 10.1002/andp.201400093 Dynamical back-action efects in low loss optomechanical oscillators Antonio Pontin 1,2 , Michele Bonaldi 1,3 , Antonio Borrielli 1,3 , Francesco Marino 4,5 , Lorenzo Marconi 6 , Alvise Bagolini 7 , Gregory Pandraud 8 , Enrico Serra 1,8,9 , Giovanni A. Prodi 1,2 , and Francesco Marin 4,6,10,∗ Received 2 May 2014, revised 23 July 2014, accepted 15 July 2014 Published online 13 August 2014 The problem of the stability of a cavity optomechanical sys- tem based on an oscillator having at the same time low op- tical and mechanical losses is addressed. As it is the aim to extend the use of optical squeezing as a tool for improving quantum limited displacement sensing at low frequency, a family of opto-mechanical devices designed to work at frequencies of about 100 kHz was developed . The devices actually meet the initial design goals, but new require- ments have emerged from the analysis of their behavior in optical cavities, due to the interaction between the cav- ity locking system and the low order normal modes of the devices. The optomechanics field of research has been gather- ing a lot of momentum during the last couple of years, driven by the achievement of long-awaited experimen- tal results. For example, micro- and nano-oscillators can now be cooled down to an occupation number below unity, or very close to it, opening up the possibility to ob- serve quantum phenomena [1–6]. We are particularly interested in optical squeezing as a tool for improving quantum limited displacement sensing [7] in the audio-band, in particular for improv- ing the sensitivity of gravitational wave interferome- ters [8]. Experiments have recently achieved squeezing around the mechanical resonance in the MHz range, us- ing a silicon nanomechanical resonator [9], and a thin semi-transparent membrane within a Fabry-P´ erot cav- ity [10]. At lower frequencies however, various sources of technical noise, such as thermal noise, phase/frequency noise associated with the input field and/or the slow cavity fluctuations, have detrimental effects on the manifestation of quantum phenomena, making low- frequency ponderomotive squeezing much more diffi- cult to achieve. As a first step, we are addressing these problems by developing a family of opto-mechanical devices specifically designed to ease the detection of pondero-motive squeezing (or, more generally, to pro- duce a cavity quantum optomechanical system) at fre- quencies of about 100 kHz. Our approach is focused on relatively thick silicon os- cillators with high reflectivity coating [11]. The relatively high mass (about 100 μg) of our devices is compensated by the capability to manage high power at low tempera- tures (down to 1 K), owing to a favorable geometric factor (thick connectors) and the excellent thermal conductiv- ity of silicon crystals at cryogenic temperature. We point out that most of the schemes designed to detect quan- tum properties of light cannot take advantage from laser cooling of the mechanical oscillator involved in the mea- surement. Therefore, a low thermal noise background is required (i.e., low temperature), together with a weak in- teraction between the oscillator and its thermal bath (i.e., high mechanical quality factors Q). In such devices, the mirror coatings must provide high reflectivity and low losses, as radiation-pressure ∗ Corresponding author E-mail: marin@f.infn.it 1 INFN, Trento Institute for Fundamental Physics and Application, I- 38123, Povo, (TN), Italy 2 Dipartimento di Fisica, Universit` a di Trento, I-38123, Povo, Italy 3 Institute of Materials for Electronics and Magnetism, Nanoscience-Trento-FBK Division, 38123, Povo, (TN), Italy 4 INFN, Sezione di Firenze, 50019, Sesto Fiorentino, (FI), Italy 5 CNR-INO, L.go Enrico Fermi 6, I-50125, Firenze, Italy 6 LENS, Via Carrara 1, I-50019, Sesto Fiorentino, (FI), Italy 7 Microtechnology Laboratory FBK-CMM, 38123, Povo, (TN), Italy 8 DIMES Technology Center-TU Delf, Feldmannweg 17, 2628, CT Delf, The Netherlands 9 Interdisciplinary Laboratory for Computational Science (LISC), FBK- University of Trento, I-38123, Povo, (TN), Italy 10 Dipartimento di Fisica e Astronomia, Universit` a di Firenze, Via Sansone 1, I-50019, Sesto Fiorentino, (FI), Italy C  2014 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 89