Cooling protocols are usually optimized through static detunings and damping rates. Here we show that exceptional-point braiding can enhance finite-time optomechanical cooling under a fixed drive-power resource. We consider an auxiliary-cavity-assisted optomechanical system whose full three-mode drift contains two second-order exceptional points. Using the same prescribed power waveform for every protocol, we optimize only the detuning trajectory while matching its duration, endpoint, range, mean, and integrated control effort. Encircling either exceptional point produces a distinct pairwise eigenbranch exchange, whereas enclosing both generates a three-branch spectral cycle. The optimized two-EP trajectory lowers the final mechanical occupation by \(19.2\%\) relative to the optimized non-enclosing class and by \(9.9\%\) relative to the best single-EP protocol. A full Bogoliubov calculation including counter-rotating Stokes processes preserves this hierarchy. These results establish multi-exceptional-point braiding as a controllable resource for finite-time mechanical state preparation.
Cooling protocols are usually optimized through static detunings and damping rates. Here we show that exceptional-point braiding can enhance finite-time optomechanical cooling under a fixed drive-power resource. We consider an auxiliary-cavity-assisted optomechanical system whose full three-mode drift contains two second-order exceptional points. Using the same prescribed power waveform for every protocol, we optimize only the detuning trajectory while matching its duration, endpoint, range, mean, and integrated control effort. Encircling either exceptional point produces a distinct pairwise eigenbranch exchange, whereas enclosing both generates a three-branch spectral cycle. The optimized two-EP trajectory lowers the final mechanical occupation by (19.2%) relative to the optimized non-enclosing class and by (9.9%) relative to the best single-EP protocol. A full Bogoliubov calculation including counter-rotating Stokes processes preserves this hierarchy. These results establish multi-exceptional-point braiding as a controllable resource for finite-time mechanical state preparation.
Multimode cavity optomechanical systems allow light to couple otherwise non-interacting mechanical resonators, enabling non-Hermitian phenomena such as exceptional points, where eigenfrequencies and eigenvectors of coupled modes coalesce. Accessing an exceptional point and its nearby parameter space is a first step towards chiral mode dynamics and topological state transfer. Diamond optomechanical devices support strong coherent optomechanical coupling required to tune resonances to an exceptional point, as well as strain-coupling to spin-defects for hybrid quantum technologies, but have not yet been used for multimode non-Hermitian physics. Here we tune to an exceptional point in a diamond optomechanical crystal, which uses structural symmetry breaking to produce two high-frequency mechanical resonances coupled to an optical cavity. The exceptional point is reached within a stable operating window below the phonon-lasing threshold, and we observe asymmetric redistribution of optomechanical damping and anti-damping between hybridized modes. These results establish diamond optomechanical crystals as a platform for non-Hermitian optomechanics, opening routes to topological mechanical dynamics in hybrid spin-phonon interfaces.
Exceptional points, where two or more eigenstates of a non-Hermitian system coalesce, are now of interest across many fields of physics, from the perspective of open-system dynamics, sensing, nonreciprocal transport, and topological phase transitions. In this work, we investigate exceptional points in cavity optomechanics, a platform of interest to diverse communities working on gravitational-wave detection, macroscopic quantum mechanics, quantum transduction, etc. Specifically, we clarify the role of quantum jumps in making a clear distinction between Liouvillian and Hamiltonian exceptional points in optomechanical systems. While the Liouvillian exceptional point arises from the unconditional Lindblad dynamics and is independent of the phonon-bath temperature, the Hamiltonian exceptional point emerges from the conditional no-jump evolution and acquires a thermal shift due to an enhanced conditional damping. Employing the thermofield formalism, we derive a unified spectral framework that interpolates between these regimes via an analytical hybrid-Liouvillian description. Remarkably, in the weak-quantum-jump regime, the exceptional point is perturbed only at the second order, highlighting the robustness of the Hamiltonian exceptional point under small hybrid perturbations. Our work reveals a continuous family of hybrid exceptional points, clarifies the operational and physical differences between the conditional and unconditional dissipative dynamics in optomechanical systems, and provides a probe for thermal baths.
We investigate how the exceptional-point structure of a dissipative cavity optomechanical system is inherited by experimentally accessible dynamical, spectral, and quantum-statistical observables. At optical-mechanical resonance, the effective non-Hermitian first-moment dynamics exhibits a second-order exceptional point, where two eigenvalues and their eigenvectors coalesce and the eigenvalue splitting follows the characteristic square-root dependence on perturbations. We show that the same square-root feature also governs transient photon and phonon populations, first-order coherence, spectral poles, and second-order intensity correlations. Below the exceptional point, the dynamics is non-oscillatory, whereas above it damped oscillations emerge together with frequency splitting of the spectral poles. At the exceptional point, the Jordan-block structure produces polynomial-exponential relaxation and a second-order spectral pole. Using the quantum regression theorem and Gaussian moment factorization, we further show that the stationary fluctuations satisfy the Siegert relation linking first- and second-order correlations. Although the zero-delay autocorrelations retain their thermal value, the finite-delay intensity correlations exhibit clear exceptional point signatures. This finding connects non-Hermitian mode coalescence with measurable dynamical and correlation observables in cavity optomechanics.
Exceptional points define branch-exchange state transfers through holomorphic continuation of non-Hermitian eigenmodes, but realizing these transfers dynamically remains difficult. Slow encircling does not generally transport the full set of instantaneous eigenstates, while shortcuts to adiabaticity can require controls outside the native experimental manifold. Here, we introduce a constrained shortcut-to-adiabaticity principle for exceptional-point braiding using native controls. In a dressed instantaneous-eigenstate frame, the available controls cancel the accessible transition channels locally, while the residual channels remain active during the evolution but are constrained to have no net accumulated effect over the closed loop. The protocol therefore targets the endpoint state transfer selected by ideal adiabatic branch exchange, rather than enforcing complete local cancellation or adiabatic following throughout the trajectory. We demonstrate the construction in a minimal two-mode non-Hermitian model equivalent, up to a trace shift and a basis convention, to the effective Hamiltonian used in dissipative-transmon exceptional-point experiments, where detuning and drive amplitude provide real controls and the relative loss imbalance fixes the non-Hermitian scale. Smooth real waveforms reshape only these controls, reproduce the branch-exchange transfer, and remain accurate under calibration errors, exceptional-point uncertainty and finite-bandwidth filtering with modest overhead.
Higher-order exceptional points (EPs) in non-Hermitian systems have attracted great interest due to their advantages in sensitive enhancement and distinct topological features. However, realization of such EPs is still a challenge because more fine-tuning parameters are generically required in quantum systems, compared to the second-order EP (EP2). Here, we propose a non-Hermitian three-mode optomechanical system in the blue-sideband regime for predicting the third-order EP (EP3). By deriving the pseudo-Hermitian condition for the proposed system, one cavity with loss and the other with gain must be required. Then we show that EP3 or EP2 can be observed when the mechanical resonator (MR) is neutral, loss, or gain. For the neutral MR, we find that two degenerate or two nondegenerate EP3s can be predicted by tuning system parameters in the parameter space, while four nondegenerate EP2s can be observed when the system parameters deviate from EP3s, which is distinguished from the previous study in the red-detuned optomechanical system. For the gain (loss) MR, we find that only two degenerate EP3s or EP2s can be predicted by tuning enhanced coupling strength. Our proposal provides a potential way to predict higher-order EPs or multiple EP2s and study multimode quantum squeezing around EPs using blue-detuned non-Hermitian optomechanical systems.
Quantum entanglement not only plays an important role in the study of the fundamentals of quantum theory, but also is considered as a crucial resource in quantum information science. The generation of macroscopic entanglement involving multiple optical and mechanical modes is a desired task in cavity optomechanics. However, the dark-mode effect is a critical obstacle against the generation of quantum entanglement in multimode optomechanical systems consisting of multiple degenerate or near-degenerate mechanical modes coupled to a common cavity mode. Here we propose an auxiliary-cavity-mode method to enhance optomechanical entanglement in a multimode optomechanical system by breaking the dark-mode effect. We find that the introduction of the auxiliary cavity mode not only assists the entanglement creation between the cavity mode and the mechanical modes, but also improves the immunity of the optomechanical entanglement to the thermal excitations by about three orders of magnitude. We also study the optomechanical entanglement in the network-coupled optomechanical system consisting of two mechanical modes and two cavity modes. By analyzing the correspondence between the optomechanical entanglement and the dark-mode effect, we find that optomechanical entanglement can be largely enhanced once the dark mode is broken. In addition, we study the mechanical entanglement and find that it is negligibly small. We also present some discussions on the experimental implementation with a microwave optomechanical setup, on the relationship between the dark-mode-breaking mechanism and the center-of-mass and relative coordinates, and on the explanation of the important role of the dark-mode breaking in the enhancement of optomechanical entanglement. Our results pave the way towards the preparation of entangled optomechanical networks and noise-resistant quantum resources.