Figure 1

(a) Representative scanning electron micrograph of the nanomechanical system consisting of a doubly clamped beam suspended above a GaAs substrate and a triangular electrode fused to the beam center; the APC is formed at the junction between the electrode and the beam. (b) Simplified schematic consisting of a displacement measurement shown to the right of the APC and a drive mechanism (using a Lorentz force created by passing a current through the beam in the presence of a 9 T magnetic field) shown to the left. (c) $V_{\mathrm{ref}}$ (thick line) and APC resistance (thin line) versus applied force.Reuse & Permissions

Figure 2

(a) Measured response amplitude (solid) and phase (dashed) as a function of drive frequency for three of the five observed resonant modes measured with the APC amplifier. (b) Corresponding finite-element simulation of beam mode shapes (dot corresponds to position of spring used to model the interatomic potential at the APC; color indicates displacement from equilibrium position with minimum displacement at the ends of the beam).Reuse & Permissions

Figure 3

(Main) APC amplifier noise spectrum $\delta V_{\mathrm{ref}}$ (right axis) versus frequency and corresponding displacement fluctuations of the beam $\delta x$ (left axis) at 5 K (squares, right peak) and 10 K (circles, left peak) for $G=290\mathrm{nA}/\mathrm{nm}$ and square root of Lorentzian fits (lines). (Inset) Integrated strength $\Delta x_T^2$ as a function of $T_{\mathrm{cryo}}$ (dot, $G=290\mathrm{nA}/\mathrm{nm}$) with a fit (line) to the model for $\Delta x_T^2$. For low temperatures we observe deviations from the model due to local heating by the bias current of the dissipative environment coupled to the mechanical system.Reuse & Permissions

Figure 4

(a) Backaction temperature $T_{\mathrm{BA}}$ versus the temperature of the cryogenic system, $T_{\mathrm{cryo}}$, with gains $G=290\mathrm{nA}/\mathrm{nm}$ (circle), $G=130\mathrm{nA}/\mathrm{nm}$ (square), $G=60\mathrm{nA}/\mathrm{nm}$ (triangle), and $G=30\mathrm{nA}/\mathrm{nm}$ (cross). Error bars are extracted from one sigma uncertainties in fits to Lorentzian noise peaks [Fig. 3]; hollow symbols are excluded from the fit (lines) to the model. (b) Measurement imprecision quanta $N_x=k_s{S}_x\gamma /4\hslash {\omega }_0$ (solid dots) and momentum backaction quanta $N_p=S_F/4m\gamma \hslash {\omega }_0$ (hollow squares) at 5 K as a function of $G$ (which is proportional to the average current $⟨I⟩$). The uncertainty in the imprecision (error bars are the size of the solid dots) and backaction are dominated by the uncertainty in the beam temperature. The measurement imprecision $N_x=N_{\mathrm{SN}}+N_A$ (solid line) is the sum of the intrinsic APC amplifier noise $N_{\mathrm{SN}}=k_s{S}_I^{\mathrm{SN}}\gamma /4G^2\hslash {\omega }_0$ (dashed line) and the HEMT amplifier noise $N_A=k_s{S}_I^A\gamma /4G^2\hslash {\omega }_0$ (dot-dashed line), [Fig. 1c].Reuse & Permissions