Control of recoil losses in nanomechanical SiN membrane resonators

Abstract

In the context of a recoil damping analysis, we have designed and produced a membrane resonator equipped with a specific on-chip structure working as a "loss shield" for a circular membrane. In this device the vibrations of the membrane, with a quality factor of 10 7 , reach the limit set by the intrinsic dissipation in silicon nitride, for all the modes and regardless of the modal shape, also at low frequency. Guided by our theoretical model of the loss shield, we describe the design rationale of the device, which can be used as effective replacement of commercial membrane resonators in advanced optomechanical setups, also at cryogenic temperatures. DOI: 10.1103/PhysRevB.94.121403 Since the first demonstrations of use in an optical cavity [1,2], membrane resonators have widely spread in optomechanical experiments, both as isolated mechanical oscillators and as components of hybrid systems. Their striking optical and mechanical properties allowed the observation of quantum effects induced by optomechanical interaction in the behavior of nano-oscillators [3] and in the properties of radiation itself [4].Currently, membrane-based resonators represent a flexible tool for a wide range of scientific and technological goals: interfacing radiation at very different wavelengths [5,6], implementing hybrid mechanical-atomic systems [7], fixing significant constraints on quantum gravity theories [8], and studying multimode optomechanical systems in the quantum regime [9]. These developments motivate a strong commitment to improving the performance of membrane-based oscillators. We address here the issue of mechanical losses in high stress silicon nitride (SiN) membranes, proposing a perspective which allows us to realize a "loss shield" for the membrane resonator.SiN membrane-based devices have many mechanical resonances with frequencies starting from 0.1 MHz, with intrinsic losses well described by a model [10] where the elastic constant K includes an imaginary part, K = k(1 + iφ), with φ = 1/Q the loss angle and Q the quality factor. Though the intrinsic quality factor is in the range 10 6 -10 8 , depending on dimensions and temperature, the loss through the supporting substrate can reduce this figure by several orders of magnitude. This phenomenon is more pronounced for the lower frequency resonances, which would be the most suitable for the experimental optomechanics as higher order resonances are surrounded by numerous neighboring resonances [11]. An additional problem is the poor reproducibility of the loss * bonaldi@science.unitn.it contributed by the support, which depends on the mounting details [12], and by the loss in the sample holder [13], and it is known that these losses can sometimes be reduced by minimizing the contact of the chip frame with the sample mount [2].The loss through the supporting substrate is usually evaluated from the energy transfer rate mediated by phonons tunneling from the membrane resonator into the substrate [14,15], an approach that motivated the development of isolation systems ba...

Calibrated quantum thermometry in cavity optomechanics

“…This frame is suspended on four points with alternating flexural and torsional springs, forming an on-chip "loss shield" structure [20]. More information about the design, fabrication and the characteristic of the device can be found in Borrielli et al [21] and Serra et al [22,23]. The theoretical resonance frequencies of the drum modes in a circular membrane are given by the expression f mn = f 0 α mn where α mn is the n-th root of the Bessel polynomial J m of order m, and f 0 = 1 π T ρ 1 Φ (T is the stress, ρ the density, Φ the diameter of the membrane).…”

Imaging Correlations in Heterodyne Spectra for Quantum Displacement Sensing

“…The data time series required for our analysis were obtained by operating a cavity optomechanics setup based on the membrane in the middle configuration. The circular, high-stress SiN x membrane (shown as photographic inset Fig.1(a)) is integrated in an on-chip "loss shield" structure [16] and placed in a Fabry-Perot cavity of length 4.38 mm and cavity Finesse of F ≈ 13000 (half-linewidth κ = 1.3 MHz × 2π). The membrane was placed at a fixed position, 2 mm, from the cavity output mirror.…”

Silicon Nitride MOMS Oscillator for Room Temperature Quantum Optomechanics

“…In this frequency range, the silicon die cannot be considered as a rigid body but its full modal response must be considered in evaluating its admittance, because a support resonating at the same frequency of the membrane can be very effective in absorbing mechanical energy. For this reason we have developed a theoretical model [19] where we evaluate the loss when the membrane and support are fully-coupled, i.e. allowing for the transfer of energy in both ways.…”

“…Indeed, this figure of merit determines the number of coherent oscillations in the presence of thermal fluctuations, and the minimum requirement for room-temperature quantum optomechanics is Q × f > 6.2 THz [2]. We have recently proposed a novel coupled oscillators model for the mechanical losses in a membrane oscillator [19], considering the mutual interaction between the membrane and the frame in a recoil losses analysis. We were able to design an effective shield for the losses for all mechanical modes also in the low frequency range.…”