## Abstract

We consider the geometric phase and quantum tunneling in the vicinity of diabolic and exceptional points. We show that the geometric phase associated with the degeneracy points is defined by the flux of complex magnetic monopoles. In the limit of weak coupling, the leading contribution to the real part of the geometric phase is given by the flux of the Dirac monopole plus a quadrupole term, and the expansion of the imaginary part starts with a dipole-like field. For a two-level system governed by a generic non-Hermitian Hamiltonian, we derive a formula to compute the non-adiabatic, complex, geometric phase by integrating over the complex Bloch sphere. We apply our results to study a dissipative two-level system driven by a periodic electromagnetic field and show that, in the vicinity of the exceptional point, the complex geometric phase behaves like a step-function. Studying the tunneling process near and at the exceptional point, we find two different regimes: coherent and incoherent. The coherent regime is characterized by Rabi oscillations, with a one-sheeted hyperbolic monopole emerging in this region of the parameters. The two-sheeted hyperbolic monopole is associated with the incoherent regime. We show that the dissipation results in a series of pulses in the complex geometric phase which disappear when the dissipation dies out. Such a strong coupling effect of the environment is beyond the conventional adiabatic treatment of the Berry phase.

## Full Text

### Topics from this Paper

- Vicinity Of Exceptional Points
- Complex Geometric Phase
- Exceptional Point
- Geometric Phase
- Periodic Electromagnetic Field + Show 5 more

Create a personalized feed of these topics

Get Started#### Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call### Similar Papers

- Journal of Physics A
- Oct 22, 2008

- arXiv: Quantum Physics
- Jun 23, 2008

- arXiv: Mathematical Physics
- Apr 10, 2007

- Physical Review Letters
- Feb 9, 2018

- IEEE Sensors Journal
- Jun 1, 2022

- Journal of Physics A: Mathematical and Theoretical
- Jul 27, 2007

- Results in Physics
- Aug 1, 2022

- Quantum
- Dec 22, 2022

- Mar 15, 2018

- Optics Express
- Feb 5, 2018

- arXiv: Optics
- Apr 17, 2017

- Optical and Quantum Electronics
- Aug 1, 2018

- Journal of the Optical Society of America B
- Sep 5, 2017

- Nature
- Jul 25, 2016

### Journal of Physics A: Mathematical and Theoretical

- Journal of Physics A: Mathematical and Theoretical
- Nov 24, 2023

- Journal of Physics A: Mathematical and Theoretical
- Nov 24, 2023

- Journal of Physics A: Mathematical and Theoretical
- Nov 24, 2023

- Journal of Physics A: Mathematical and Theoretical
- Nov 24, 2023

- Journal of Physics A: Mathematical and Theoretical
- Nov 24, 2023

- Journal of Physics A: Mathematical and Theoretical
- Nov 24, 2023

- Journal of Physics A: Mathematical and Theoretical
- Nov 23, 2023

- Journal of Physics A: Mathematical and Theoretical
- Nov 23, 2023

- Journal of Physics A: Mathematical and Theoretical
- Nov 22, 2023

- Journal of Physics A: Mathematical and Theoretical
- Nov 20, 2023