Vacuum Rabi Splitting and Quantum Fisher Information of a Non-Hermitian Qubit in a Single-Mode Cavity
arXiv:2412.16770 · doi:10.1103/m7kc-vc9h
Abstract
A natural extension of the non-Hermitian qubit is to place it in a single-mode cavity. This setup corresponds to the quantum Rabi model (QRM) with a purely imaginary bias on the qubit, exhibiting parity-time () symmetry. In this work, we first solve the -symmetric QRM using the Bogoliubov operator approach. We derive the transcendental function responsible for the exact solution, which can also be used to precisely identify exceptional points. The adiabatic approximation previously used can be easily formulated within this approach by considering transitions between the same manifolds in the space of Bogoliubov operators. By further considering transitions between the nearest-neighboring manifolds, we can analytically obtain more accurate eigensolutions. Moreover, these simple corrections can capture the main features of the dynamics, where the adiabatic approximation fails. Furthermore, the rich characteristics of the vacuum Rabi splitting in the emission spectrum are predicted. The width of the peaks increases with the coupling strength and the imaginary biases, reflecting the nature of open quantum systems. Additionally, we identify a {quantum-criticality-enhanced} effect by calculating the quantum Fisher information. Near the exceptional points, the quantum Fisher information in the -symmetric QRM is significantly higher than that of the non-Hermitian qubit component. This may open a new avenue for enhancing quantum sensitivity in non-Hermitian systems by incorporating coupling with an additional degree of freedom, enabling more precise parameter estimation.
13 pages, 9 figures
References in corpus (27)
- Making Sense of Non-Hermitian Hamiltonians
- Non-Hermitian Physics
- Multiple Rabi Splittings under Ultra-Strong Vibrational Coupling
- Dynamic framework for criticality-enhanced quantum sensing
- Observation of a quantum phase transition in the quantum Rabi model with a single trapped ion
- Critical parametric quantum sensing
- Observation of -symmetric quantum coherence in a single ion system
- Global sensing and its impact for quantum many-body probes with criticality
- Experimental measurement of the divergent quantum metric of an exceptional point
- PT spectroscopy of the Rabi problem
- Fundamental Sensitivity Limits for non-Hermitian Quantum Sensors
- Critical Quantum Metrology in the Non-Linear Quantum Rabi Model
- The hidden symmetry of the asymmetric quantum Rabi model
- -symmetric, non-Hermitian quantum many-body physics -- a methodological perspective
- Hidden symmetry and tunnelling dynamics in asymmetric quantum Rabi models
- Attempt to find the hidden symmetry in the asymmetric quantum Rabi model
- Toward Heisenberg Scaling in Non-Hermitian Metrology at the Quantum Regime
- Quantum parameter estimation of non-Hermitian systems with optimal measurements
- Generalized adiabatic approximation to the quantum Rabi model
- Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians
- Identifying non-Hermitian critical points with quantum metric
- PT-symmetric quantum Rabi model
- Third-order exceptional point in an ion-cavity system
- Quantum Fisher information and polaron picture for identification of transition coupling in quantum Rabi model
- General symmetry operators of the asymmetric quantum Rabi model
- -symmetric quantum Rabi model: Solutions and exceptional points
- Analytical Study of the Non-Hermitian Semiclassical Rabi Model