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arXiv:1210.1657 · Physical Review Letters

Strong Thermomechanical Squeezing via Weak Measurement

Alex Szorkovszky, George A. Brawley, Andrew C. Doherty, Warwick P. Bowen

Published May 2, 2013• 116 citations
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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

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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.
Nonlinear forces allow motion of a mechanical oscillator to be squeezed below the zero-point motion. Of existing methods, mechanical parametric amplification is relatively accessible, but previously thought to be limited to 3 dB of squeezing in the steady state. We consider the effect of applying continuous weak measurement and feedback to this system. If the parametric drive is optimally detuned from resonance, correlations between the quadratures of motion allow unlimited steady-state squeezing. Compared to backaction evasion, we demonstrate that the measurement strength, temperature and efficiency requirements for quantum squeezing are significantly relaxed.
We present a single-quadrature feedback scheme able to overcome the conventional 3 dB limit on parametric squeezing. The method is experimentally demonstrated in a micromechanical system based on a cantilever with a magnetic tip. The cantilever is detected at low temperature by a SQUID susceptometer, while parametric pumping is obtained by modulating the magnetic field gradient at twice the cantilever frequency. A maximum squeezing of 11.5 dB and 11.3 dB is observed, respectively, in the response to a sinusoidal test signal and in the thermomechanical noise. So far, the maximum squeezing factor is limited only by the maximum achievable parametric modulation. The proposed technique might be used to squeeze one quadrature of a mechanical resonator below the quantum noise level, even without the need for a quantum limited detector.
Squeezing the quadrature noise of a harmonic oscillator enhances its sensitivity. Stabilization of the antisqueezed quadrature can overcome the 3 dB squeezing limit by parametric modulation. Here, we apply this method to soft-clamped membrane resonators, which hold promise for both classical and quantum sensing applications. We compare piezoelectric and capacitive parametric modulation and observe thermomechanical squeezing by up to 17 and 21 dB, respectively. Finally, we provide a full quantum theory of combining this approach with quantum-limited motion measurement. We conclude that quantum squeezing is feasible at moderate cryogenic temperatures and realistic device parameters.
Unlike classical systems, the very act of observing quantum systems perturbs their behaviour. This introduces noise, which imposes limits on the knowledge that can be obtained through measurement. Certain measurement techniques, known generally as quantum non-demolition (QND) measurements, exist to circumvent this noise. An alternative method to evade backaction noise is to amplify the observable of interest above the noise. However, this generally leaves the system in a different state, and is therefore not considered a QND measurement. In this thesis, I examine the benefits of amplification for various kinds of measurement of mechanical harmonic oscillators which, at the micrometre and nanometre scale, comprise an emerging quantum technology. For this prototypical case, modulation of the spring constant, also known as parametric amplification, is a well-studied noiseless amplification technique. Using the theory of trajectories developed in the field of quantum optics, I show that a weak measurement combined with a detuned parametric drive achieves the same ends as strong QND measurement. Namely, it allows backaction-free observation of one quadrature of mechanical motion, and through this, quantum squeezing below the quantum zero-point motion. This equivalence is experimentally confirmed in the classical limit using an optically detected, electrically modulated cantilever. In addition, I analyse similar amplification enhanced techniques for quantum entanglement and quantum tomography. These results are applicable to research in quantum optomechanics and electromechanics, and can be translated to other kinds of quantum harmonic oscillators, such as microwave cavities.
Abstract Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic quantum simulations. However, these applications require the engineering of squeezing and nonlinearities in the quantum regime. Here we demonstrate squeezing below the zero-point fluctuations of a gigahertz-frequency mechanical resonator coupled to a superconducting qubit. This is achieved by parametrically driving the qubit, which results in an effective two-phonon drive. In addition, we show that the resonator mode inherits a nonlinearity from the off-resonant coupling with the qubit, which can be tuned by controlling the detuning. We, thus, realize a mechanical squeezed Kerr oscillator, in which we demonstrate the preparation of non-Gaussian quantum states of motion with Wigner function negativities and high quantum Fisher information. This shows that our results can also have applications in quantum metrology and sensing.
We use a reservoir engineering technique based on two-tone driving to generate and stabilize a quantum squeezed state of a micron-scale mechanical oscillator in a microwave optomechanical system. Using an independent backaction-evading measurement to directly quantify the squeezing, we observe 4.7±0.9 dB of squeezing below the zero-point level surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of squeezing obtained in the experiment.