TY - JOUR
T1 - Singular perturbation of quantum stochastic differential equations with coupling through an oscillator mode
AU - Gough, John
AU - Van Handel, Ramon
N1 - Funding Information:
1R.v.H. is supported by the Army Research Office under Grant W911NF-06-1-0378. 2School of Computing and Informatics, Nottingham Trent University, Nottingham, NG1 4BU, UK; e-mail: [email protected] 3Physical Measurement and Control 266-33, California Institute of Technology, Pasadena, CA 91125, USA; e-mail: [email protected]
PY - 2007/5
Y1 - 2007/5
N2 - 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.
AB - 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.
KW - Adiabatic elimination
KW - Hudson-Parthasarathy quantum stochastic calculus
KW - Quantum stochastic differential equations
KW - Singular perturbation
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U2 - 10.1007/s10955-007-9284-2
DO - 10.1007/s10955-007-9284-2
M3 - Article
AN - SCOPUS:34247267645
SN - 0022-4715
VL - 127
SP - 575
EP - 607
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 3
ER -