We propose an efficient optomechanical mass sensor operating at exceptional points (EPs), nonhermitian degeneracies where eigenvalues of a system and their corresponding eigenvectors simultaneously coalesce. The benchmark system consists of two optomechanical cavities (OMCs) that are mechanically coupled, where we engineer mechanical gain (loss) by driving the cavity with a blue (red) detuned laser. The system features EP at the gain and loss balance, where any perturbation induces a frequency splitting that scales as the square-root of the perturbation strength, resulting in a giant sensitivity factor enhancement compared to the conventional optomechanical sensors. For non-degenerated mechanical resonators, quadratic optomechanical coupling is used to tune the mismatch frequency in order to get closer to the EP, extending the efficiency of our sensing scheme to mismatched resonators. This work paves the way towards new levels of sensitivity for optomechanical sensors, which could find applications in many other fields including nanoparticles detection, precision measurement, and quantum metrology. arXiv:1903.02542v2 [cond-mat.mes-hall]

We engineer mechanical gain (loss) in system formed by two optomechanical cavities (OMCs), that are mechanically coupled. The gain (loss) is controlled by driving the resonator with laser that is blue (red) detuned. We predict analytically the existence of multiple exceptional points (EPs), a form of degeneracy where the eigenvalues of the system coalesce. At each EP, phase transition occurs, and the system switches from weak to strong coupling regimes and vice versa. In the weak coupling regime, the system locks on an intermediate frequency, resulting from coalescence at the EP. In strong coupling regime, however, two or several mechanical modes are excited depending on system parameters. The mechanical resonators exhibit Rabi-oscillations when two mechanical modes are involved, otherwise the interaction triggers chaos in strong coupling regime. This chaos is bounded by EPs, making it easily controllable by tuning these degeneracies. Moreover, this chaotic attractor shows up for low driving power, compared to what happens when the coupled OMCs are both drived in blue sidebands. This works opens up promising avenues to use EPs as a new tool to study collective phenomena (synchronization, locking effects) in nonlinear systems, and to control chaos.

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In this paper, we apply the technique of back-action cooling to investigate the effects of both optical and mechanical nonlinearities in optomechanical cooling systems. It is shown that cooling of the nanomechanical oscillator to its ground state is limited by the effects of these nonlinearities. The qualitative result is justified quantitatively by comparing, for the same parameters, our analytical minimum phonon number with the experimental one.

We study steady-state continuous variable entanglement in a three-mode optomechanical system consisting of an active optical cavity (gain) coupled to a passive optical cavity (loss) supporting a mechanical mode. For a driving laser which is blue-detuned, we show that coupling between optical and mechanical modes is enhanced in the unbroken-PT -symmetry regime. We analyze the stability and this shows that steady-state solutions are more stable in the gain and loss systems. We use these stable solutions to generate distant entanglement between the mechanical mode and the optical field inside the gain cavity. It results in a giant enhancement of entanglement compared to what is generated in the single lossy cavity. This work offers the prospect of exploring quantum state engineering and quantum information in such systems. Furthermore, such entanglement opens up an interesting possibility to study spatially separated quantum objects.

We propose a scheme to generate robust stationary continuous-variable entanglement in optomechanical systems, based on geometrical nonlinearity that occurs for large mechanical displacements. Such nonlinearity is often used to correct the dynamics of the systems in the strong coupling regime. It appears that geometrical nonlinearity enhances the entanglement and shifts its maximum towards high detuning values. Using the experimental parameters, we find that such a scheme generates a very robust entanglement against thermal decoherence even at room temperature. Our results show that geometrical nonlinearity affects entanglement as the optomechanical quantum interface.

In recent experiments, the re-thermalization time of the mechanical resonator is stated as the limiting factor for quantum applications of optomechanical systems. To explain the origin of this limitation, an analytical nonlinear investigation supported by the recent successful experimental laser cooling parameters is carried out in this work. To this end, the effects of geometrical and the optical nonlinearities on the squeezing are studied and are in a good agreement with the experimental results. It appears that highly squeezed state are generated where these nonlinearities are minimized and that high nonlinearities are limiting factors to reach the quantum ground state.

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