Floquet dynamics in the quantum measurement of mechanical motion

Laser Cooling of a Nanomechanical Oscillator to Its Zero-Point Energy

“…Laser cooling of mechanical systems occurs via coupling of mechanical and electromagnetic degrees of freedom (optomechanical coupling) and has been demonstrated with a wide range of structures [12,[16][17][18][19][20][21][22][23][24][25]. It has led to the observation of radiation pressure shot noise [26], ponderomotive squeezing of light [27,28], and motional sideband asymmetry [16,[29][30][31][32].Many optomechanical protocols, including mechanical squeezing [33][34][35][36], entanglement [37], state swaps [38], generation of non-classical states [39][40][41][42], and back-action evading (BAE) measurements below the standard quantum limit (SQL) [43][44][45], require ground state preparation of a wellsideband-resolved system, where Stokes and anti-Stokes motional transitions can be driven selectively. In this case, driving of anti-Stokes transitions can be efficiently applied to damp the motion and sideband cool the system.…”

“…Yet despite these promising features, ground-state preparation of silicon OMCs has only been possible via passive cooling to milli-Kelvin temperatures in dilution refrigerators [54,55]. Significant heating due to optical absorption-a consequence of the extremely small optical mode volume and inefficient thermalization [56]has limited experiments to use of weak laser pulses [39][40][41]48] and precluded continuous measurements [32,45,54].In this work, we demonstrate laser cooling of a strongly sideband-resolved silicon OMC to the zero-point energy, with residual mean phonon occupancy of 0.09 +0.02 −0.01 (i.e. −7.4 dB of the zero-point energy).…”

“…−7.4 dB of the zero-point energy). The measurement is self-calibrated using motional sideband asymmetry [16,30,32,57,58]. Our experimental system, shown in Fig.…”

“…1(a,b), consists of a quasione-dimensional silicon optomechanical crystal [32,45,47]. The OMC is mounted in a 3 He cryostat (Oxford Instruments HelioxTL) operated at ∼ 2.0 K and a buffer-gas pressure of ∼ 40 mbar, which ensures efficient thermalization of the device [32,45]. A tapered optical fiber is used to couple light evanescently into the coupling waveguide (40% efficiency in this work).…”

“…The local oscillator (LO) is used for detection and is not sent to the cavity.vacuum optomechanical coupling rate is g 0 /2π 1080 kHz.The buffer-gas causes additional damping, increasing the mechanical linewidth to Γ m = Γ int + Γ gas 2π × 115 kHz [59]. Motional sideband asymmetry, a signature of the quantum nature of the optomechanical interaction, was recently observed in various optomechanical systems [29][30][31] and used to perform self-calibrated thermometry of the mechanical oscillator close to its ground state [32,57,58]. In our experiments, we adopt a two-tone pumping scheme [ Fig.…”