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: john.gough@ntu.ac.uk 3Physical Measurement and Control 266-33, California Institute of Technology, Pasadena, CA 91125, USA; e-mail: ramon@its.caltech.edu

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

UR - http://www.scopus.com/inward/record.url?scp=34247267645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34247267645&partnerID=8YFLogxK

U2 - 10.1007/s10955-007-9284-2

DO - 10.1007/s10955-007-9284-2

M3 - Article

AN - SCOPUS:34247267645

VL - 127

SP - 575

EP - 607

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3

ER -