Beyond adiabatic elimination: A hierarchy of approximations for multi-photon processes

  • Vanessa Paulisch
  • Han Rui
  • Hui Khoon Ng
  • Berthold-Georg Englert
Regular Article


In multi-level systems, the commonly used adiabatic elimination is a method for approximating the dynamics of the system by eliminating irrelevant, nonresonantly coupled levels. This procedure is, however, somewhat ambiguous and it is not clear how to improve on it systematically. We use an integro-differential equation for the probability amplitudes of the levels of interest, which is equivalent to the original Schrödinger equation for all probability amplitudes. In conjunction with a Markov approximation, the integro-differential equation is then used to generate a hierarchy of approximations, in which the zeroth order is the adiabatic-elimination approximation. It works well with a proper choice of interaction picture; the procedure suggests criteria for optimizing this choice. The first-order approximation in the hierarchy provides significant improvements over standard adiabatic elimination, without much increase in complexity, and is furthermore not so sensitive to the choice of interaction picture. We illustrate these points with several examples.


Relevant State Rabi Frequency Probability Amplitude Rabi Oscillation Interaction Picture 
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Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Vanessa Paulisch
    • 1
  • Han Rui
    • 2
  • Hui Khoon Ng
    • 2
    • 3
  • Berthold-Georg Englert
    • 2
    • 4
  1. 1.Fakultät für PhysikLudwig-Maximilians-UniversitätMunichGermany
  2. 2.Centre for Quantum TechnologiesNational University of SingaporeSingaporeSingapore
  3. 3.Applied Physics LabDSO National LaboratoriesSingaporeSingapore
  4. 4.Department of PhysicsNational University of SingaporeSingaporeSingapore

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