We propose and analyse a feasible experimental scheme for a quantum force sensor based on the elimination of backaction noise through coherent quantum noise cancellation (CQNC) in a hybrid atom-cavity optomechanical setup assisted with squeezed vacuum injection. The force detector, which allows for a continuous, broadband detection of weak forces well below the standard quantum limit (SQL), is formed by a single optical cavity simultaneously coupled to a mechanical oscillator and to an ensemble of ultracold atoms. The latter acts as a negative-mass oscillator so that atomic noise exactly cancels the backaction noise from the mechanical oscillator due to destructive quantum interference. Squeezed vacuum injection enforces this cancellation and allows sub-SQL sensitivity to be reached in a very wide frequency band, and at much lower input laser powers.A different approach for sub-SQL measurements has recently been introduced [2, 3], based on the CQNC of backaction noise via quantum interference. The idea is based on introducing an 'anti-noise' path in the dynamics of the optomechanical system via the addition of an ancillary oscillator which manifests an equal and opposite response to the light field, i.e, an oscillator with an effective negative mass. In the context of atomic spin measurements an analogous idea for coherent backaction cancellation was proposed independently [31,32], and has been applied for magnetometry below the SQL [33], demonstrating that Einstein-Podolski-Rosen (EPR)-like entanglement of atoms generated by a measurement enhances the sensitivity to pulsed magnetic fields. The original proposal [2] focused on the use of an ancillary cavity that is red-detuned from the optomechanical cavity. A quantum non-demolition coupling of the electromagnetic fields within the two cavities yields the necessary anti-noise path, so that the backaction noise is coherently cancelled.[34] considered in more detail the all-optical realization of the CQNC proposal put forwarded in [2,3], and found that the requirements for its experimental implementation appear to be very challenging, especially for the experimentally relevant case of low mechanical frequencies and high-quality mechanical oscillators (MO) such as gravitational wave detectors. Other setups, which provide effective negative masses of ancillary systems for CQNC, have been suggested based on employing Bose-Einstein condensates [35], or the combination of a twotone drive technique and positive-negative mass oscillators [36].In recent years, hybrid optomechanical systems assisted by the additional coupling of the cavity mode with an atomic gas have attracted considerable attention. It has been found that the additional atomic ensemble may lead to the improvement of optomechanical cooling [37-41], thereby providing the possibility of ground state cooling outside the resolved sideband regime [42,43]. Moreover, the coupling of the mechanical oscillator to an atomic ensemble can be used to generate a squeezed state of the mechanical mode [44], or robust EPR-...

In this paper, the scheme of a force sensor is proposed which has been composed of a hybrid optomechanical cavity containing an interacting cigar-shaped Bose-Einstein condensate (BEC) where the s-wave scattering frequency of the BEC atoms as well as the spring coefficient of the cavity moving end-mirror (the mechanical oscillator) are parametrically modulated. It is shown that in the red-detuned regime and under the so-called impedance-matching condition, the mechanical response of the system to the input signal is enhanced substantially which leads to the amplification of the weak input signal while the added noises of measurement (backaction noises) can be suppressed and lowered much below the standard quantum limit (SQL). Furthermore, because of its large mechanical gain, such a modulated hybrid system is a much better amplifier in comparison to the (modulated) bare optomechanical system which can generate a stronger output signal while keeping the sensitivity nearly the same as that of the (modulated) bare one. The other advantages of the presented nonlinear hybrid system accompanied with the mechanical and atomic modulations in comparison to the bare optomechanical cavities are its controllability as well as the extension of amplification bandwidth.

Spontaneous synchronization is a significant collective behavior of weakly coupled systems. Due to their inherent nonlinear nature, optomechanical systems can exhibit self-sustained oscillations which can be exploited for synchronizing different mechanical resonators. In this paper, we explore the synchronization dynamics of two membranes coupled to a common optical field within a cavity, and pumped with a strong blue-detuned laser drive. We focus on the system quantum dynamics in the parameter regime corresponding to synchronization of the classical motion of the two membranes. With an appropriate definition of the phase difference operator for the resonators, we study synchronization in the quantum case through the covariance matrix formalism. We find that for sufficiently large driving, quantum synchronization is robust with respect to quantum fluctuations and to thermal noise up to not too large temperatures. Under synchronization, the two membranes are never entangled, while quantum discord behaves similarly to quantum synchronization, that is, it is larger when the variance of the phase difference is smaller.

The field of optomechanics provides us with several examples of quantum photon-phonon interface. In this paper, we theoretically investigate the generation and manipulation of quantum correlations in a microfabricated optomechanical array. We consider a system consisting of localized photonic and phononic modes interacting locally via radiation pressure at each lattice site with the possibility of hopping of photons and phonons between neighboring sites. We show that such an interaction can correlate various modes of a driven coupled optomechanical array with well-chosen system parameters. Moreover, in the linearized regime of Gaussian fluctuations, the quantum correlations not only survive in the presence of thermal noise, but may also be generated thermally. We find that these optomechanical arrays provide a suitable platform for quantum simulation of various many-body systems. I. INTRODUCTIONThe impressive experimental progress in fabricating micromechanical and nanomechanical devices have opened a route towards the exhibition of quantum behavior at macroscopic scales. The interaction between micro-or nanomechanical oscillators and the optical field via the radiation pressure force is the basis of a wide variety of optomechanical phenomena. Despite their variety in the system sizes, parameters, and configurations, optomechanical systems (OMSs) share common features. Almost all OMSs are described by the same physics. OMSs offer further insights into the issues concerning the development of quantum memory for quantum computers [1], high precision position, mass or force sensing [2-6], quantum transducers [7], classical and quantum communication [8], ground state cooling of mechanical oscillators [9,10], nonclassical correlations between single photons and phonons [11], generation of nonclassical states [12] and testing of the foundations of quantum mechanics [13][14][15][16]. For a recent review and current areas of focus of quantum optomechanics see Refs. [17,18].The extension to multimode systems is an attractive route for quantum optomechanics. A group of mechanical oscillators interacting via the radiation pressure with a common optical mode [19][20][21][22][23][24][25][26], or a group of mechanical oscillators locally interacting with a single optical mode involving the tunneling of photons and phonons between neighboring sites [27][28][29][30][31][32][33][34][35][36][37][38] are the two realizations of multimode optomechanics. The former is realized in a single optical cavity containing multiple membranes while the latter is realized experimentally in the so-called optomechanical crystals (OMCs) in one and two *

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