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-...

Abstract. Considering some important classes of generalized coherent states known in literature, we demonstrated that all of them can be created via conventional fashion, i.e. the "lowering operator eigen-state" and the "displacement operator" techniques using the "nonlinear coherent states" approach. As a result we obtained a "unified method" to construct a large class of coherent states which already have been introduced by different prescriptions.

Using the analytic representation of the so-called Gazeau-Klauder coherent states(CSs), we shall demonstrate that how a new class of generalized CSs namely the family of dual states associated with theses states can be constructed through viewing these states as temporally stable nonlinear CSs. Also we find that the ladder operators, as well as the displacement type operator corresponding to these two pairs of generalized CSs, may be easily obtained using our formalism, without employing the supersymmetric quantum mechanics(SUSYQM) techniques. Then, we have applied this method to some physical systems with known spectrum, such as Pöschl-Teller, infinite well, Morse potential and Hydrogen-like spectrum as some quantum mechanical systems. Finally, we propose the generalized form of Gazeau-Klauder CS and the corresponding dual family.

Abstract. Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in each dual pair of families of nonlinear coherent states, at least one family is related to a (generally) non-unitary projective representation of the Weyl-Heisenberg group, which can then be thought of as characterizing the dual pair.

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.