Mechanical Squeezing via Parametric Amplification and Weak Measurement

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 PACS numbers: 42.50.Dv, 85.85.+j Recent experiments have demonstrated impressive progress in cooling towards the ground state and measuring the zero-point motion of mechanical oscillators. This brings within reach the observation of nonclassical phonon states, with applications in quantum information and tests of quantum mechanics [1] The most successful systems to date involve cryogenically cooled high frequency oscillators strongly coupled to optical or microwave fields [2,3]. However, techniques to manipulate quantum states and investigate nonclassical behavior of phonons, apart from creating single phonon states [4], are less well developed.A squeezed state, in which the variance of one quadrature of motion is below the zero-point motion, is the most accessible of quantum resources in optomechanical systems. This can be achieved, for example, by resolved sideband cooling using squeezed or modulated input light [5,6]. Also promising is squeezing via backaction evading measurement (BAE) [7], which is close to being realized [8]. These schemes would allow for ultrasensitive force detection [9] and normal mode entanglement [10] but are constrained by the requirement of strong coupling to the optical mode. Additional downsides are the requirement of ultralow temperatures and the side-effect of parametric instability due to strong radiation pressure [8].Electrostatic forces, on the other hand, are strong enough to create nonclassical states in an oscillator by driving it into the nonlinear regime [1]. It has been predicted that micro-and nanoelectromechanical systems (MEMS/NEMS) can be engineered in this way to excite arbitrary Fock states [11] and induce macroscopic quantum tunnelling [12]. In a similar fashion, mechanical squeezing can be achieved via mechanical parametric amplification (MPA) [13]. MPA exploits nonlinearities in the electrostatic driving field [14], the resonator's intrinsic motion [15] or a coupled charge qubit [16]. A periodic modulation in the oscillator's spring constant at twice its resonance frequency gives rise to an in-phase amplified quadrature and an out-of-phase damped quadrature. The amplified gain approaches infinity at threshold, whereas the squeezing due to damping is limited to a factor of 1 half. This is a long-standing problem that also limits the intracavity variance of an optical ...

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“…This method has the great advantage of being able to create unconditional squeezing in the steady state. This is in contrast with many other plausible methods of squeezing generation [14][15][16][17][18][19][20]. Our approach is closely related to the quantum nondemolition measurements [21][22][23] which, however, are not able to generate true squeezing without feedback.…”

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