Strong Thermomechanical Squeezing via Weak Measurement

Abstract

We experimentally surpass the 3 dB limit to steady-state parametric squeezing of a mechanical oscillator. The localization of an atomic force microscope cantilever, achieved by optimal estimation, is enhanced by up to 6.2 dB in one position quadrature when a detuned parametric drive is used. This squeezing is, in principle, limited only by the oscillator Q factor. Used on low temperature, high frequency oscillators, this technique provides a pathway to achieve robust quantum squeezing below the zero-point motion. Broadly, our results demonstrate that control systems engineering can overcome well established limits in applications of nonlinear processes. Conversely, by localizing the mechanical position to better than the measurement precision of our apparatus, they demonstrate the usefulness of mechanical nonlinearities in control applications. DOI: 10.1103/PhysRevLett.110.184301 PACS numbers: 45.80.+r, 05.40.Àa High-quality mechanical oscillators are widely used for weak force detection [1,2], nanoscale manipulation [3,4], and quantum state engineering [5,6]. Such applications often utilize optimal estimation to localize the oscillator, followed by feedback control to confine its position. In a classical context, this type of control is commonly used to linearize the response of sensors driven into their nonlinear regime, resulting in increased dynamic range and suppression of resonance frequency fluctuations [7]. Furthermore, spurred by the growing prospect of accessing new quantum physics [8], similar techniques are now being applied to state-of-the art mechanical oscillators to cool them close to the quantum limit set by mechanical zero-point motion [9,10], and ultimately surpass it via quantum control techniques such as backaction evasion [11][12][13]. However, the level of achievable oscillator localization has always previously been limited to at best the measurement precision, presenting a significant barrier to applications in both quantum and classical regimes.Applications of mechanical oscillators can also benefit from nonlinearities without requiring any measurement. An example of particular relevance to this Letter is mechanical parametric amplification, where direct modulation of the spring constant induces amplification of in-phase motion [14]. This technique is often used in microelectromechanical (MEMS) and nanoelectromechanical systems to boost mechanical signals from in-phase forces above the measurement noise floor [15,16]. Conversely, out-of-phase motion is deamplified and thereby more strongly confined or ''squeezed.'' In principle, squeezing below the zero-point motion variance V g is possible. Such ''quantum squeezing'' has applications in quantum metrology and tests of macroscale entanglement and quantum gravity [8]. However, the emergence of mechanical instability limits the improvement in confinement to at most 50% (or À3 dB) in the steady state [17]. Since a mean thermal occupancy of just half a phonon increases the oscillator's motional variance to twice the zero-point motion var...

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.…”

Quantum squeezing of motion in a mechanical resonator

“…While sideband cooling has led to occupations of less than one phonon in recent years [56,10], nonlinearities and heating tend to prevent the phonon occupation from dropping far below 1, making quantum squeezing via parametric techniques difficult. There are many theoretical proposals for surpassing the 3 dB limit to produce quantum squeezing [44,48,14,68,27,34,54,57,23,5,33], and improvement over the 3 dB limit has been realized experimentally with modified parametric techniques [53,58,42]. Squeezing below the zero-point fluctuations, however, has yet to be achieved.…”

Quantum Nondemolition Measurement of a Quantum Squeezed State Beyond the 3 dB Limit

“…Therefore, it is, in principle, impossible to have a steady state where the mechanical motion is squeezed below one half of the zero-point level using only parametric driving. These limitations may be overcome by combining continuous quantum measurement and feedback [9][10][11][12], but it would substantially increase the experimental complexity.Another method to generate a robust quantum state is quantum reservoir engineering [13], which has been used to generate quantum squeezed states and entanglement with trapped ions [14,15] and superconducting qubits [16]. It can also be applied to an optomechanical system to generate strong steady-state squeezing without quantumlimited measurement and feedback [17].…”

“…Therefore, it is, in principle, impossible to have a steady state where the mechanical motion is squeezed below one half of the zero-point level using only parametric driving. These limitations may be overcome by combining continuous quantum measurement and feedback [9][10][11][12], but it would substantially increase the experimental complexity.…”