Journal of Statistical Physics

, Volume 127, Issue 3, pp 575-607

First online:

Singular Perturbation of Quantum Stochastic Differential Equations with Coupling Through an Oscillator Mode

  • John GoughAffiliated withSchool of Computing and Informatics, Nottingham Trent University Email author 
  • , Ramon van HandelAffiliated withPhysical Measurement and Control 266-33, California Institute of Technology

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We consider a physical system which is coupled indirectly to a Markovian resevoir through an oscillator mode. This is the case, for example, in the usual model of an atomic sample in a leaky optical cavity which is ubiquitous in quantum optics. In the strong coupling limit the oscillator can be eliminated entirely from the model, leaving an effective direct coupling between the system an the resevoir. Here we provide a mathematically rigorous treatment of this limit as a weak limit of the time evolution and observables on a suitably chosen exponential domain in Fock space. The resulting effective model may contain emission and absorption as well as scattering interactions.


singular perturbation quantum stochastic differential equations Hudson–Parthasarathy quantum stochastic calculus adiabatic elimination