We are excited to announce the next seminar in ANZAMP’s seminar series, next week’s seminars by Xilin Lu and Zimin Li titled “Hidden Symmetry in Generalisations of the Quantum Rabi Model” and “Generalized adiabatic approximation to the quantum Rabi model”, respectively, abstracts below.
Date: 15 June 2021
Time: 12:00 pm
The seminar will be presented via Zoom: https://unimelb.zoom.us/j/81213691522
Speaker 1: Xilin Lu
Title: Hidden Symmetry in Generalisations of the Quantum Rabi Model
Abstract: The hidden ℤ2 symmetry in the asymmetric quantum Rabi model (AQRM) was recently uncovered in (J. Phys. A 54 12LT01) by constructing the corresponding symmetry operators. From this result, we propose an ansatz to determine symmetry operators for generalisations of the AQRM. We successfully applied this ansatz to the following cases: the anisotropic AQRM, the asymmetric Rabi–Stark model (ARSM), the anisotropic ARSM and the biased Dicke model with small number of qubits. Furthermore, from our results on the biased Dicke model, we conjectured and proved the explicit expression of the hidden ℤ2 symmetry operator for arbitrary number of qubits.
Speaker 2: Zimin Li
Title: Generalized adiabatic approximation to the quantum Rabi model
Abstract: A generalized adiabatic approximation (GAA) is developed to calculate the eigenvalues of the excited states of the quantum Rabi model (QRM). The adiabatic approximation (AA) is widely used to treat the QRM in the limit where the qubit frequency is smaller than the harmonic frequency. However, the level crossings in the spectrum of the QRM predicted by the AA are determined by the zeros of Laguerre polynomials, which deviate from the exact points. We generalize the AA based on the similarity between the exact solutions of the level crossings and the Laguerre polynomials. By construction, the GAA always has exact exceptional energy and approximates the regular spectrum with rather good agreement in a larger parameter regime. The GAA offers a framework to deal with the light–matter interaction models in a simple but accurate manner. Furthermore, the GAA is applied to the AQRM and the conical intersections in the energy landscape are correctly recovered. The geometric phases around these conical intersections are calculated analytically as an illustrative example.