Third-order exceptional surface in a pseudo-Hermitian superconducting circuit

Compared with an isolated exceptional point, exceptional surfaces in non-Hermitian systems are more robust against environment noises, fabrication errors, and experimental uncertainties. Thanks to this, exceptional surfaces can be applied to enhance the sensitivity of sensors and develop new quantum techniques. Over the past few years, several works have been devoted to studying high-order exceptional surfaces. However, they are restricted to non-Hermitian systems without pseudo-Hermiticity. To date, research on high-order exceptional surfaces in pseudo-Hermitian systems still remains an untouched area. In this work, we propose a pseudo-Hermitian superconducting circuit, which consists of three circularly-coupled superconducting cavities with the balanced gain and loss. We then study the third-order exceptional surface in the proposed circuit. By investigating the eigenvalues, we find that in the parameter space, all third-order exceptional points of the circuit form a third-order exceptional line in the parity-time-symmetric case. When the parity-time-symmetric condition is extended to pseudo-Hermitian conditions, we find more third-order exceptional points, which constitute a third-order exceptional surface in the parameter space. The proposed scheme is universal and can be applied to explore third-order exceptional surfaces in other physical systems, such as optomechanical systems, cavity-magnon systems, and photonic micro-ring systems. This work is of fundamental interest in quantum mechanics and opens a way for studying high-order exceptional surfaces in pseudo-Hermitian systems.