Singular Perturbation of Quantum Stochastic Differential Equations with Coupling Through an Oscillator Mode
- First Online:
- 109 Downloads
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.
Keywordssingular perturbation quantum stochastic differential equations Hudson–Parthasarathy quantum stochastic calculus adiabatic elimination
Unable to display preview. Download preview PDF.
- 3.A. Barchielli, Continual measurements in quantum mechanics and quantum stochastic calculus, in Open Quantum Systems III: Recent Developments, S. Attal, A. Joye, C.A. Pillet, eds. (Springer, 2006), pp. 207–292.Google Scholar
- 6.L. M. Bouten, R. Van Handel and M. R. James, An introduction to quantum filtering. preprint, arXiv:math.OC/0601741 (2006).Google Scholar
- 18.E. J. McShane, Stochastic Calculus and Stochastic Models (Academic Press, 1974).Google Scholar
- 21.S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Dover, Mineola, New York, 2005).Google Scholar
- 23.F. Verhulst, Methods and Applications of Singular Perturbations (Springer, 2005).Google Scholar
- 24.P. Warszawski and H. M. Wiseman, Adiabatic elimination in compound quantum systems with feedback. Phys. Rev. A 63:013,803 (2001).Google Scholar