Near-field cavity optomechanics with nanomechanical oscillators

Abstract

Cavity-enhanced radiation pressure coupling between optical and mechanical degrees of freedom allows quantum-limited position measurements and gives rise to dynamical backaction enabling amplification and cooling of mechanical motion. Here we demonstrate purely dispersive coupling of high Q nanomechanical oscillators to an ultra-high finesse optical microresonator via its evanescent field, extending cavity optomechanics to nanomechanical oscillators. Dynamical backaction mediated by the optical dipole force is observed, leading to laser-like coherent nanomechanical oscillations solely due to radiation pressure. Moreover, sub-fm/Hz 1/2 displacement sensitivity is achieved, with a measurement imprecision equal to the standard quantum limit (SQL), which coincides with the nanomechanical oscillator's zero-point fluctuations. The achievement of an imprecision at the SQL and radiation-pressure dynamical backaction for nanomechanical oscillators may have implications not only for detecting quantum phenomena in mechanical systems, but also for a variety of other precision experiments. Owing to the flexibility of the near-field coupling approach, it can be readily extended to a diverse set of nanomechanical oscillators and particularly provides a route to experiments where radiation pressure quantum backaction dominates at room temperature, enabling ponderomotive squeezing or QND measurements.Nanomechanical oscillators [1, 2] possess wide-ranging applications in both fundamental and applied sciences. Due to their small mass they are ideal candidates for probing quantum limits of mechanical motion in an experimental setting. Moreover, they are the basis of various precision measurements [3, 4] and integral part of atomic and magnetic force microscopy [5] that are pivotal tools for solid state physics and material science. Significant attention has been devoted to developing sensitive readout techniques for nanomechanical motion over the past decade. A natural scale for comparing the performance achieved with systems of different size and mass is given by the variance of the mechanical oscillators' zero-point motion x (t) 2 zp = /(2mΩm) ( : reduced Planck constant; m, Ωm/2π, Q: mass, resonance frequency, quality factor of the oscillator). In Fourier space the zero-point motion can be described by the single-sided (double-sided) spectral density Sxx [Ω], which at the mechanical oscillator's resonance evaluates to Sxx [Ωm] = 2 Q/mΩ 2 m (Sxx [Ωm] = Q/mΩ 2 m ) and coincides with the standard quantum limit [6, 7, 8, 9] (SQL) of continuous position measurement. So far, the most sensitive transducers for nanomechanical motion have been based on electron flow using a single electron transistor [10] (SET) or atomic point contact [11] (APC) coupled to a nanomechanical string in cryogenic environment and have achieved a position imprecision of order 10 −15 m/Hz 1/2 . An imprecision at the level of the SQL, however, has not been achieved yet. In contrast, parametric motion transducers based on photons in a cavity-which are the b...

Multichannel cavity optomechanics for all-optical amplification of radio frequency signals

“…In it, a small gap (50 nm) is created and a 22-µm long cantilevered waveguide is suspended from the substrate. The evanescent optical field of the micro-disk's resonance mode applies a gradient optical force on the signal waveguide and, inversely, the signal waveguide's motion also dispersively perturbs the cavity's resonance 20,22 . In contrast to the conventional phase sensitive detection method, which relies on the cavity resonance, the optomechanical motion of the signal waveguide is detected directly by monitoring the intensity of transmission.…”

“…The evanescent field of the circulating light in the micro-disk generates a gradient optical force on the signal waveguide 20,22 . This force is attractive toward the micro-disk and can be expressed as 22 :…”

“…γ = γ 1 + γ 2 + γ i = ω c /2Q is the total damping rate of the cavity including the coupling rate with the control and the signal waveguides γ 1 and γ 2 , respectively, and the cavity's intrinsic damping rate γ i . g(x) is the important optomechanical coupling coefficient, which under the perturbation approximation 20 , depends exponentially on the signal waveguide's displacement δx = x − x 0 and can be expressed as g(x) = ∂ω c /∂x = g 0 exp( − 2α δx), where α is the evanescent field decay constant of the cavity resonance mode. In our device, the static value of g 0 for the TE mode (4,89) is experimentally determined to be 2π × 11.3 MHz nm − 1 (see Supplementary Methods) 25 .…”

“…Optomechanical devices also provide unique attributes that are unattainable with conventional optical devices, such as the all-optical signal amplification demonstrated here and the ability to be reconfigured and re-programmed 6,20,43 . The broad optical bandwidth enabled by the new multichannel configuration offers great flexibility for cavity optomechanics to be integrated at a higher level, allowing their remarkable properties to be applied in cohorts with conventional photonic systems for optical and RF communications.…”

“…For example, in systems based on micro-and nanoscale cavities, optical coupling with the cavity is through either a single optical fiber 5,20,21 or an integrated waveguide 6,22 . Furthermore, in these systems, because the mechanical element is embedded inside the high finesse cavity, optomechanical effects can only be interrogated within extremely narrow bandwidths at the discrete resonance frequencies.…”