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arXiv:1107.1294 · Physical Review Letters

Mechanical Squeezing via Parametric Amplification and Weak Measurement

Alex Szorkovszky, Andrew C. Doherty, Glen I. Harris, Warwick P. Bowen

Published Nov 15, 2011• 170 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.107.213603

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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 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.
Recently it has been demonstrated that the combination of continuous position detection with detuned parametric driving can lead to significant steady-state mechanical squeezing, far beyond the 3 dB limit normally associated with parametric driving. In this work, we show the close connection between this detuned scheme and quantum non-demolition (QND) measurement of a single mechanical quadrature. In particular, we show that applying an experimentally realistic detuned parametric drive to a cavity optomechanical system allows one to effectively realize a QND measurement despite being in the bad-cavity limit. In the limit of strong squeezing, we show that this scheme offers significant advantages over standard backaction evasion, not only by allowing operation in the weak measurement and low efficiency regimes, but also in terms of the purity of the mechanical state.
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.
A scheme to achieve strong quantum squeezing of a mechanical resonator in a membrane-in-the-middle optomechanical system is developed. To this end, simultaneous linear and nonlinear coupling between the mechanical resonator and the cavity modes is applied. A two-tone driving light field, comprising unequal red-detuned and blue-detuned sidebands, helps in generating a coherent feedback force through the linear coupling with the membrane resonator. Another driving light field with its amplitude modulated at twice the mechanical frequency drives the mechanical parametric amplification through a second-order coupling with the resonator. The combined effect produces strong quantum squeezing of the mechanical state. The proposed scheme is quite robust to excess second-order coupling observed in coherent feedback operations and can suppress the fluctuations in the mechanical quadrature to far below the zero point and achieve strong squeezing (greater than 10 dB) for realistic parameters.
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.