Non-Hermitian topological effects are of crucial importance both in fundamental physics and applications. Here we discover the gain-loss-induced hybrid second-order skin-topological effect and the $\mathcal{P}\mathcal{T}$ phase transition in skin-topological modes. By studying a non-Hermitian Haldane model, we find that the topological edge modes are localized on a special type of corner, while the bulk modes remain extended. Such an effect originates from the interplay between gain, loss, and the chiral edge currents induced by the nonlocal flux, which can be characterized by considering the properties of the edge sites as a one-dimensional chain. We establish a relation between the skin-topological effect and the $\mathcal{P}\mathcal{T}$ symmetries belonging to different edges. Moreover, we discover the $\mathcal{P}\mathcal{T}$ phase transition with the emergence of exceptional points between pairs of skin-topological modes. Our results pave the way for the investigation of non-Hermitian topological physics and $\mathcal{P}\mathcal{T}$ phase transition in higher-dimensional systems.

Cavity optomechanical systems enable interactions between light and mechanical resonators, providing a platform both for fundamental physics of macroscopic quantum systems and for practical applications of precision sensing. The resonant enhancement of both mechanical and optical response in the cavity optomechanical systems has enabled precision sensing of multiple physical quantities, including displacements, masses, forces, accelerations, magnetic fields, and ultrasounds. In this article, we review the progress of precision sensing applications using cavity optomechanical systems. The review is organized in the following way: first we will introduce the physical principles of optomechanical sensing, including a discussion of the noises and sensitivity of the systems, and then review the progress in displacement sensing, mass sensing, force sensing, atomic force microscope (AFM) and magnetic resonance force microscope (MRFM), accelerometry, magnetometry, and ultrasound sensing, and introduce the progress of using quantum techniques especially squeezed light to enhance the performance of the optomechanical sensors. Finally, we give a summary and outlook.

Cooling of mesoscopic mechanical resonators represents a primary concern in cavity optomechanics. In this Letter, in the strong optomechanical coupling regime, we propose to dynamically control the cavity dissipation, which is able to significantly accelerate the cooling process while strongly suppressing the heating noise. Furthermore, the dynamic control is capable of overcoming quantum backaction and reducing the cooling limit by several orders of magnitude. The dynamic dissipation control provides new insights for tailoring the optomechanical interaction and offers the prospect of exploring mesoscopic quantum physics.

Squeezed spin states possess unique quantum correlation or entanglement and are significantly promising for advancing quantum information processing and quantum metrology. In recent back-to-back publications [C. Gross et al., Nature (London) 464, 1165 (2010) and Max F. Riedel et al., Nature (London) 464, 1170 (2010)], reduced spin fluctuations are observed leading to spin squeezing at $-8.2$ and $-2.5\mathrm{dB}$, respectively, in two-component atomic condensates exhibiting one-axis-twisting interactions. The noise reduction limit for the one-axis twisting scales as $\propto 1/N^{2/3}$, which for a condensate with $N\sim {10}^3$ atoms is about 100 times below the standard quantum limit. We present a scheme using repeated Rabi pulses capable of transforming the one-axis-twisting spin squeezing into the two-axis-twisting type, leading to Heisenberg limited noise reduction $\propto 1/N$ or an extra tenfold improvement for $N\sim {10}^3$.

We propose a hybrid photonic-plasmonic resonant structure which consists of a metal nanoparticle (MNP) and a whispering-gallery-mode (WGM) microcavity. It is found that the hybrid mode enables a strong interaction between the light and matter, and the single-atom cooperativity is enhanced by more than two orders of magnitude compared to that in a bare WGM microcavity. This improvement originates from two aspects: the MNP offers a highly enhanced local field in the vicinity of an emitter, and, interestingly, the high-Q property of WGMs can be maintained in the presence of the MNP. Thus the present system has advantages over a single microcavity or a single MNP, and holds potential in quantum optics, nonlinear optics, and highly sensitive biosensing.