A correlated electromechanical system

Abstract

A correlation with phonons sustained by a pair of electromechanical resonators that differ both in size and frequency is demonstrated. In spite of the electromechanical resonators being spatially distinct, they can still be strongly dynamically coupled via a classical analogue of the beam splitter interaction with a cooperativity exceeding five, and parametric down-conversion which results in both resonators self-oscillating. This latter regime yields a classical variant of a two-mode squeezed state which is identified as perfectly correlated phase-locked vibrations between the two resonators. The creation of a correlation between two separate mechanical resonators suggests that extending this interaction to vacuum phonon states could enable a macroscopic two-mode squeezed state to be generated. Conversely, the ability to resolve the correlated state via the self-oscillations could be harnessed to build a new class of detector where an external stimulus neutralises the phase-locked vibrations.

Strong phonon-cavity coupling and parametric interaction in a single microcantilever under ambient conditions

“…, thereby compensating the energy dissipation and leading to mechanical parametric amplification in both modes simultaneously. 9,26,31 Similar results can be obtained when mode 2 is weakly probed by a mechanical drive at the frequency ωd near the ω2, and the frequency responses of the mode 2 (detected at ωd) and mode 1 (detected at ωpd) are shown in Figure 3e and 3f, respectively. Note that the amplification demonstrated here belongs to non-degenerate parametric amplification, which can be achieved in both modes simultaneously with evasion of the phase influence.…”

“…At the maximum pump amplitude before entering parametric instability, the measured coupling rate reaches up to ~2π × 7290 Hz, corresponding to a cooperativity (C) of ~398 which is much higher than that of many counterparts operated in vacuum, such as the graphene drum resonator (C = 60) 26 and GaAs-based mechanical resonators (C = 5 ~ 18). 20,21,23,25,31 When mode 1 is on blue pump, S11(ω) shows an increasing enhancement of resonance with improving pump strength (Figure 4g). The effective Q of mode 1 (Qeff-1) fitted from S11(ω) via eq S18 (Supporting Information S3) is displayed in Figure 4j.…”

“…6 Fortunately, the mechanical pump offers great capabilities to produce parametric cooling and thermomechanical squeezing state in the resonator, which can break the thermal noise limitation thus further improve the force sensitivity. 6,27,29,31 The thermal noise displacement from both modes of the microcantilever can be decomposed into slowly varying inphase xn and quadrature yn components within a narrow bandwidth via cos( ) sin( ) 6,29 When parametric cooling is implemented, the fluctuations of xn and yn will be uniformly cooled down leading to attenuation of the thermal noise in both two quadratures, 52 this can be observed from Figure 5c where mode 1 is parametrically cooled by applying red pump (ωp = ω − , 0.2 Vpp). In comparison to uniform cooling, the thermomechanical squeezing allows noise in one quadrature to be reduced with a possibility of infinite reduction at the expense of increasing noise in the orthogonal quadrature.…”

“…Figures 3(a It is clear that both modes one and two show evident parametric amplification under the blue pump, and the vibrations of modes one and two are synchronously enhanced. This result can be understood using process '3' shown in figure 1(d), in which the pump phonons are converted to phonons in both modes one and two via the down-conversion process, i.e., ℏω p → ℏω 1 + ℏω 2 , thereby compensating for the energy dissipation and simultaneously leading to mechanical parametric amplification in both modes [9,26,34]. Similar results can be obtained when mode two is weakly probed by a mechanical drive at a frequency ω d near ω 2 ; the frequency responses of mode two (detected at ω d ) and mode one (detected at ω p−d ) are shown in figures 3(e) and (f), respectively.…”

“…Up to now, a large number of fundamental studies have demonstrated the applications of the mechanical pump on many specially fabricated strong coupling systems, such as MEMS or NEMS, in which are usually operated in the low dissipative environments, i.e., vacuum or even low temperature. 9,[19][20][21][22][23][25][26][27][28][29][30][31][32][33][34] Whereas the investigations about the phonon-cavity coupling and mechanical pump as well as their practical applications for measurements in the high dissipative environments, such as ambient atmosphere, have rarely been reported for both the specially designed and commercially available resonator systems. This is because low dissipation conditions can significantly minimize the energy dissipated per vibration cycle of the resonator, 9 which largely promotes the generation of strong coupling thus mechanical pump can be effectively applied.…”