Back-action-evading measurements of nanomechanical motion

Abstract

When performing continuous measurements of position with sensitivity approaching quantum mechanical limits, one must confront the fundamental effects of detector back-action. Back-action forces are responsible for the ultimate limit on continuous position detection, can also be harnessed to cool the observed structure [1,2,3,4], and are expected to generate quantum entanglement [5]. Back-action can also be evaded[6,7,11], allowing measurements with sensitivities that exceed the standard quantum limit, and potentially allowing for the generation of quantum squeezed states. We realize a device based on the parametric coupling between an ultra-low dissipation nanomechanical resonator (Q~10 6 ) and a microwave resonator.[20] Here we demonstrate back-action evading (BAE) detection of a single quadrature of motion with sensitivity 4 times the quantum zero-point motion,, back-action cooling of the mechanical resonator to 12  NR n quanta, and a parametric mechanical pre-amplification effect which is harnessed to achieve position resolution a factor 1.3 times ZP x  .When attempting to obtain complete knowledge of the dynamics of a simple harmonic oscillator, x(t), back-action effects combined with the quantum zero-point motion of the oscillator limit the ultimate resolution to the standard quantum limit (SQL) [8,9]. The origin of this limit is the primitive fact that position and momentum are non-commuting, and are then linked through the equations of motion, , but are not linked dynamically and are constants of the motion:Furthermore, it was realized how to couple 1 X to a detector in a way which does not * Correspondence should be sent to schwab@caltech.edu perturb the dynamics of 1, where int H is the interaction Hamiltonian.[12,13] Thus, while a measurement of 1 X necessarily disturbs 2 X , this disturbance has no effect on the subsequent dynamics or measurements of X1. One can thus increase the coupling strength arbitrarily without fear of back-action, meaning that the sensitivity of such an ideal single quadrature probe is not fundamentally limited The expected quantum Hamiltonian of our parametrically coupled system is given by:

Detection of weak stochastic forces in a parametrically stabilized micro-optomechanical system

“…Detecting a weak stochastic signal on a stronger background is an important task in the research field of quantum mechanics with macroscopic oscillators, in particular when exploring the properties of oscillators with low occupation number, or, e.g., in a squeezed state [16,[24][25][26] or other peculiarly quantum states. In this situation, the measurement back-action can destroy the interesting features.…”

“…In this situation, the measurement back-action can destroy the interesting features. Particular measurement schemes can be conceived and applied [24,25,27,28], but the use of a weak measurement, where the signature of the oscillator is intrinsically weaker than the measurement noise (see, e.g., Ref. [29]), can be a useful affordable solution.…”

Quantum dynamics of simultaneously measured non-commuting observables

“…We accomplish this with what we call a single quadrature measurement (SQM), motivated by the backaction evading techniques recently conceived for optomechanical systems 19,20 . The central idea is to drive Rabi oscillations Ω R /2π = 40 MHz on the qubit so that its Hamiltonian becomes that of an effective low frequency qubit.…”

Cavity optoelectromechanical system combining strong electrical actuation with ultrasensitive transduction

“…Two key requirements to enter this quantum regime are the capacities to efficiently quantum control the oscillator and to achieve zeropoint-motion-limited transduction sensitivity. Strong electrical actuation of mechanical oscillators, an enabling step for quantum control, has been achieved in nanoelectromechanical systems (NEMS) [10][11][12][13][14][15][16]. Furthermore, transduction sensitivities near the quantum limit have been reached with cavity optomechanical systems (COMS) [17,18].…”

“…In a purely electrical setting the combination of strong mechanical actuation with precise mechanical transduction has been achieved with NEMS, where the mechanical resonator plays the role of a fluctuating capacitor in an electrical circuit [11,12,14,15]. Incorporating gigahertz frequency electrical resonances in these devices has enabled the integration of micromechanical resonators with ultracold superconducting circuits and circuit quantum electrodynamics and the achievement of the long-standing goal of quantum control of a mechanical resonator in its ground state [6].…”