Adiabatic passage in the presence of noise

@article{Noel2012AdiabaticPI,
  title={Adiabatic passage in the presence of noise},
  author={Thomas W. Noel and Matthew R. Dietrich and Nathan Kurz and Gang Shu and J. Wright and Boris B. Blinov},
  journal={Physical Review A},
  year={2012},
  volume={85},
  pages={023401}
}
Now add to this Hamiltonian a term that couples the two states, yielding a new Hamiltonian H � . The eigenstates of H � will exhibit an avoided crossing as a function of ω. Consider suchacoupledsysteminitiallyinaneigenstateof H with ω set such that the energy splitting between the states is much larger than the coupling energy. If ω is now varied sufficiently slowly across the energy level crossing, the system will adiabatically 
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