In the last few years, much attention has been paid to exceptional surfaces (ESs) owing to various important physical phenomena and potential applications. However, high-order ESs inpseudo-Hermitian systems have not been reported until now. Here, we study the high-order ES in a pseudo-Hermitian superconducting (SC) circuit system. In our proposal, the SC circuit system is composed of three circularly coupled SC cavities, where the gain and loss are balanced. According to the eigenvalue properties of the pseudo-Hermitian Hamiltonian, we derive the general pseudo-Hermitian conditions for the ternary SC system. In the special pseudo-Hermitian case with parity-time symmetry, all third-order exceptional points (EP3s) of the SC system form a third-order exceptional line in the parameter space. Under the general pseudo-Hermitian conditions, more EP3s are found, and all EP3s are located on a surface, i.e., a third-order exceptional surface is constructed. Moreover, we also investigate the eigenvalues of the pseudo-Hermitian SC circuit around EP3s. Our work opens up a door for exploring high-order ESs and related applications in pseudo-Hermitian systems.
We propose an experimentally accessible superconducting quantum circuit, consisting of two coplanar waveguide resonators (CWRs), to enhance the microwave squeezing via parametric down-conversion(PDC). In our scheme, the two CWRs are nonlinearly coupled through a superconducting quantum interference device embedded in one of the CWRs. This is equivalent to replacing the transmission line in a flux-driven Josephson parametric amplifier (JPA) by a CWR, which makes it possible to drive the JPA by a quantized microwave field. Owing to this design, the PDC coefficient can be considerably increased to be about tens of megahertz, satisfying the strong-coupling condition. Using the Heisenberg-Langevin approach, we numerically show the enhancement of the microwave squeezing in our scheme. In contrast to the JPA, our proposed system becomes stable around the critical point and can generate stronger transient squeezing. In addition, the strong-coupling PDC can be used to engineer the photon blockade.
A cavity quantum electrodynamical (QED) system beyond the strong-coupling regime is expected to exhibit intriguing quantum phenomena. Here we report a direct measurement of the photon-dressedqubit transition frequencies up to four photons by harnessing the same type of state transitions in an ultrastrongly coupled circuit-QED system realized by inductively coupling a superconducting flux qubit to a coplanar-waveguide resonator. This demonstrates a convincing observation of the photon-dressed Bloch-Siegert shift in the ultrastrongly coupled quantum system. Moreover, our results show that the photon-dressed Bloch-Siegert shift becomes more pronounced as the photon number increases, which is a characteristic of the quantum Rabi model.