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(Color online) (a) Schematic of a silicon cantilever resonator. (b) Schematic of a double-clamped graphene-based nanoresonator.
(Color online) (a) Δx zp versus silicon beam size with h si = 0.1 μm. (b) Δx zp versus graphene film size. The zero-displacement of graphene caused by quantum noise can easily reach nanometer level, two orders of magnitude larger than that of silicon with comparable geometry sizes.
(Color online) (a) log(R) versus silicon beam length with h si = 0.1 μm at T = 5 K. (b) log(R) versus graphene film length at T = 5 K. The quantum and thermomechanical noise squeezing of graphene nanoresonators can be implemented with coarse condition of T = 5 K and V = 2 V, while silicon nanoresonators cannot achieve squeezed states without increasing the applied pumping voltage and reducing the temperature.
(Color online) Phase dependence of ΔX 1 and ΔX 2 which are expressed in unit of Δx zp with T = 5 K and V = 2 V. The dashed reference line is ΔX = Δx zp. The Si nanoresonator has the same structural size as the graphene resonator in Ref. 16 (except for h si = 0.1 μm). (a) Silicon at t = 0.2 t c(si). (b) Monolayer graphene at t = 0.2 t c(graphene). (c) Silicon at t = 1.2 t c(si). (d) Monolayer graphene at t = 1.2 t c(graphene). The minimum value of R is 0.2945. The inset shows that the precise phase control is required to obtain R < 1. Compared with traditional Si nanoresonators, graphene nanoresonators provide larger room to meet squeezing conditions.
(Color online) Time dependence of ΔX 1 and ΔX 2 which are expressed in units of Δx zp. Time is in unit of t c. Here, T = 5 K, V = 2 V, and θ = 0. The dashed reference line is ΔX = Δx zp. The Si nanoresonator (a) has the same structural size as the graphene resonator (b) in Ref. 16 (except for h si = 0.1 μm).
(Color online) Temperature dependence of ΔX1. The top line shows the original upshift of the oscillator deviation without parametric pumping and the bottom line shows the relation between ΔX1 and temperature by applying the previous experimental resonator quality factors and structural parameters in Ref. 16. Circles are obtained by directly submitting the experimental data of Q-T relation into the latter equation and triangles are theoretical values of the former equation drawn at same temperatures for comparison.
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