Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems
arXiv:2205.13416 · doi:10.1088/1751-8121/acb1de
Abstract
In this work, we study the counterdiabatic driving scheme in pseudo- and antipseudo- Hermitian systems. By discussing the adiabatic condition for non-Hermitian system, we show that the adiabatic evolution of state can only be realized in the non-Hermitian system which possesses real energy spectrum. Therefore, the counterdiabatic driving scheme to reproduce an exact evolution of an energy eigenstate needs either real energy spectrum or dropping its parts of dynamic phase and Berry phase. In this sense, we derive the adiabatic conditions and counterdiabatic driving Hamiltonians for the pseudo-Hermitian Hamiltonian which possesses either real or complex energy spectrum and the antipseudo-Hermitian Hamiltonian which possesses either imaginary or complex energy spectrum. We also find the condition to get self-normalized energy eigenstates in pseudo- and antipseudo- Hermitian system and derive the well-defined population of bare states on this energy eigenstate. Our results are illustrated by studying the counterdiabatic driving for a non-Hermitian three level system, and a perfect population transfer with loss or gain is realized.
9pages, 6figures
References in corpus (16)
- Making Sense of Non-Hermitian Hamiltonians
- Shortcut to adiabatic passage in two and three level atoms
- Observation of parity-time symmetry breaking in a single spin system
- Lewis-Riesenfeld invariants and transitionless tracking algorithm
- Fast atomic transport without vibrational heating
- PT-Symmetric Wave Chaos
- Transient energy excitation in shortcuts to adiabaticity for the time dependent harmonic oscillator
- Fast ground-state cooling of mechanical resonator with time-dependent optical cavities
- Shortcut to adiabatic population transfer in quantum three-level systems: effective two-level problems and feasible counter-diabatic driving
- Non-Hermitian shortcut to stimulated Raman adiabatic passage
- Berry-phase blockade in single-molecule magnets
- Higher-order exceptional point in a pseudo-Hermitian cavity optomechanical system
- Shortcut to Adiabatic Passage in a Waveguide Coupler with Allen-Eberly scheme
- Resonant shortcuts for adiabatic rapid passage with only -field control
- Higher-order exceptional point in a blue-detuned non-Hermitian cavity optomechanical system
- High-fidelity multistate STIRAP assisted by shortcut fields