Overwhelming Thermomechanical Motion with Microwave Radiation Pressure Shot Noise

Abstract

We measure the fundamental noise processes associated with a continuous linear position measurement of a micromechanical membrane incorporated in a microwave cavity optomechanical circuit. We observe the trade-off between the two fundamental sources of noises that enforce the standard quantum limit: the measurement imprecision and radiation-pressure backaction from photon shot noise. We demonstrate that the quantum backaction of the measurement can overwhelm the intrinsic thermal motion by 24 dB, entering a new regime for cavity optomechanical systems.Quantum mechanics places limits on the precision with which one can simultaneously measure canonically conjugate variables, such as the position and momentum of an object. For example, if one scatters light off an object to determine its position, the momentum kicks from individual photons will necessarily apply forces back on that object. In the limit of a continuous measurement in which a coherent state of light is used to infer the state of the mechanical degree of freedom, it is the quantum statistics of the photons that will place simultaneous limits on the information gained and the backaction imparted. So while a stronger measurement reduces the imprecision, this comes at the cost of increasing radiation pressure shot noise forces. The minimum noise added by the measurement process is bounded by the standard quantum limit (SQL) and occurs when the imprecision noise and backaction noise are perfectly balanced [1,2]. Experimentally observing this fundamental trade-off requires a system that interacts strongly with the measurement yet weakly with its thermal environment.One successful strategy for the measurement of mechanical systems has been that of cavity optomechanics [3], in which the displacement of a mechanical oscillator of frequency Ω m tunes the resonance frequency ω c of a high-frequency electromagnetic cavity. When the cavity is excited with a coherent drive of power P at ω c , the mechanical motion becomes encoded as phase fluctuations of the reflected light. As the measurement power is increased this mechanical signal rises above the measurement noise floor, ideally limited by the vacuum fluctuations in the phase quadrature of the drive. This improvement in the measurement imprecision comes at the expense of an increasing backaction force, ideally solely from the vacuum fluctuations in the amplitude quadrature of the drive.The measured total displacement spectral density S x at the mechanical resonance frequency is a combination of the zero-point motion S zp x , the thermal motion S th x , the measurement imprecision S imp x and measurement backaction S ba x . The SQL can be stated by the inequalityFor an ideal homodyne detection of the phase quadrature of the light, the added noise of the The power required to reach the SQL for an ideal, lossless cavity optomechanical system is P SQL = arXiv:1508.05320v1 [quant-ph]

Near-Field Integration of a SiN Nanobeam and aSiO2Microcavity for Heisenberg-Limited Displacement Sensing

“…The first challenge has been met by several cryogenic optomechanical [13,14] and electromechanical systems [15] (via resolved-sideband cooling [16]). The latter, corresponding to a measurement at the standard quantum limit (SQL) [17], remains outstanding; however, readout noise far below the zero-point displacement has been reported [18,19], as well as RPSN dominating the thermal force [20,21]. Reaching the SQL ultimately requires a 'Heisenberg-limited' displacement sensor for which the product of the read out noise and the total force noise is the minimum allowed by the uncertainty principle.…”

Measuring and imaging nanomechanical motion with laser light

“…This sensitivity is rivaled only by techniques based on superconducting microwave electromechanical systems, which operate at ultra-low (T ≪ 1 K ) cryogenic temperatures [39,40]. Interest in this quantum domain has originally been motivated by observatories such as LIGO and can now, for the first time, be explored with optical and microwave experiments [3,9,15,41,42]. In addition, laser-based techniques can provide spatial imaging of mechanical displacement patterns.…”

Quantum Limits on Measurement and Control of a Mechanical Oscillator

“…On the feedback front, the question of how to optimally treat the measurement record before feeding back, is of prime importance. Section 5.1.1 addresses this problem; the simple filter used in chapters 3 and 4 can in fact be bettered using an optimal filter, at the expense of 5.1 This regime has now been accessed in at least one other experiment [295], where a Ω m = 2π · 9.3 MHz mechanical oscillator is measured using a microwave cavity interferometer operated at ≈ 100 mK. Red is the intrinsic mechanical susceptibility χ x , while blue is the susceptibility of the cold-damping filter χ −1 fb,cold ∝ −ig fb ΩΓ m , and green is the susceptibility of the optimal feedback filter χ fb,opt .…”

“…For large measurement strengths, quantum measurement back-action [294,295] should in principle exceed the ambient thermal force. As shown in fig.…”