Diabolical points in coupled active cavities with quantum emitters

Abstract

In single microdisks, embedded active emitters intrinsically affect the cavity mode of microdisks, which results in a trivial symmetric backscattering and a low controllability. Here we propose a macroscopical control of the backscattering direction by optimizing the cavity size. The signature of positive and negative backscattering directions in each single microdisk is confirmed with two strongly coupled microdisks. Furthermore, the diabolical points are achieved at the resonance of two microdisks, which agrees well with the theoretical calculations considering backscattering directions. The diabolical points in active optical structures pave a way to implement quantum information processing with geometric phase in quantum photonic networks.Diabolical points (DPs) and exceptional points (EPs) describe degeneracies of systems depending on parameters [1,2]. EPs refer to degeneracies of non-Hermitian system with coalescent eigenstates, which is quite popular in the system with gain and loss such as PT-symmetry systems [3][4][5]. DPs means the degeneracy of Hermitian system with twofold orthognal eigenstates. Compared to EPs with gain and loss, DPs have more practical feasibility, provide the geometric phase with controlled phase shift and also introduce new approaches to studying topological or quantum DP behaviors [6][7][8][9][10][11]. Thus, photons in photonic structures at DPs have potential applications in the quantum information and quantum computation [12][13][14][15]. Meanwhile, active emitters in photonic structures are essential for the coherent electron-photon interface to implement quantum information processing in the quantum photonic network [16][17][18][19][20]. However, DPs or EPs of backscattering in optics can be achieved inoptical structures with a few defects or scatterers individually controlled [21][22][23].While in active cavities with multiple quantum emitters, the quantum emitters affect the cavity mode as scatterers themselves [24,25]. The random positions of multiple emitters cause the system to be hard to control. More importantly, the multiple scatterers result in the symmetric backscattering in a single microdisk [26,27]. The symmetric backscattering forbids any degeneracy with only trivial eigenstates, thus the coherent interface between electrons and photons at DPs is hard to achieve.Single microdisks have two-dimensional Hamiltonians based on the clockwise (CW) and counterclockwise (CCW) modes [28]. The symmetric backscattering results in the splitting between eigenstates, corresponding to the absolute value of backscattering coupling strength.Previous works on active microdisks mainly focused on the splitting in the spectrum, and further investigations are limited by the low controllability [29][30][31]. In contrast, two strongly coupled microdisks have supermodes with four-dimensional Hamiltonians. The detuning between microdisks can be controlled, during which not only the absolute value but also the sign of backscattering coupling strength can be investigated. This feature makes...

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