Exact Solutions of strongly interacting Models in Quantum Optics

• Applicant: Dr. Daniel Braak
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Mathematics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 439943572

The following results have been published during the first funding period: 1.) Exact determination of phase diagram and exceptional spectrum of the anisotropic quantum Rabi model with the aid of the G-function technique. 2.) Clarification of the hidden symmetry in the asymmetric quantum Rabi model which was surmised in 2011. Identification of the symmetry group and derivation of several theorems on the symmetry generator found by Mangazeev et al. in 2021. 3.) Metrological properties of the non-linearly coupled (two-photon) quantum Rabi model (2pQRM) at the critical point. Close to the collapse instability, the model exhibits a measurement precision enhanced by several orders of magnitude compared to the linear model. Moreover, the adiabatic sweep can be done in finite time. The non-linear system turned out to be far superior to the linearly coupled system with regard to quantum metrology. 4.) The G-function technique has been generalized to systems with irregular singular points, one example being the 2pQRM. The G-function for the 2pQRM conjectured by Chen et al. in 2012 has been derived rigorously with this method, together with a conjecture made by Ng et al. in 1999. To complete the theory it is necessary to solve the case with degenerate exponents of second kind. This degeneracy appears in the anharmonic oscillator, driven systems described by Floquet theory and the Rabi-Stark model (RSM) at the critical point. Preliminary numerical results indicate that the RSM possesses bound states embedded into a continuum like the atomic Stark Hamiltonian. This phenomenon could now be treated exactly in the quantum optical context. Moreover, the RSM should exhibit similar advantages for quantum metrology as the 2pQRM. These shall be investigated using the theory of G-functions, together with the excited state quantum phase transition which has been numerically detected in the RSM.

• DFG Programme: Research Grants
• International Connection: China, Italy
• Cooperation Partners: Professor Dr. Qing-Hu Chen; Dr. Simone Felicetti; Professor Dr. Zu-Jian Ying