Quantum jumps in open cavity optomechanics and Liouvillian versus Hamiltonian exceptional points

Abstract

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.

Figures (3)

• Figure 1: Schematic of an optomechanical setup where a control laser enters the cavity from the left mirror and the intracavity mode $a$ couples with the mechanical motion of the right mirror, represented by the oscillator-mode $b$. The mechanical eigenfrequency is $\omega_m$ and $G$ is the effective (linearized) optomechanical coupling. The optical and mechanical decay rates are $\kappa$ and $\gamma$, respectively. We shall take $\omega_m \gg \kappa, G, \gamma$ in conformity with the good-cavity requirement for which taking the cavity detuning $\Delta \simeq -\omega_m$ allows us to write a beam-splitter form of the linearized Hamiltonian. The photon and phonon baths are shaded with red and blue, respectively.
• Figure 2: Behavior of the eigenvalues across the exceptional point: (a) real parts and (b) imaginary parts. Solid curves show the eigenvalue branches $\lambda_{\pm}$ while dashed curves correspond to the eigenvalue branches $\lambda_{{\rm NH},\pm}$. The vertical black lines mark the locations of the exceptional points; solid for LEP and dashed for HEP. The parameters used are $\kappa/2\pi=150~{\rm kHz}$, $\gamma/2\pi=0.1~{\rm Hz}$, $\omega_m/2\pi=1~{\rm MHz}$, and thermal occupation $n_{\rm th}=8.33\times10^{4}$.
• Figure 3: Monotonic variation of $G_{\rm EP}(\epsilon)$ between the HEP ($\epsilon=0$) and LEP ($\epsilon=1$) limits. The parameters used are $\kappa/2\pi=150~{\rm kHz}$, $\gamma/2\pi=0.1~{\rm Hz}$, and thermal occupation $n_{\rm th}=8.33\times10^{4}$.