Method of integro-differential equations in quantum optics

Gadomsky, O. N.; Krutitsky, K. V.

doi:10.1088/1355-5111/9/3/008

Cited by 5 publications

(6 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, as pointed out above, we can separate out the positronic polarizing field, which in some cases cannot be neglected compared with its electronic counterpart. In view of the correspondence between Eqn (5.11) and the classical integral equation, it can be argued that the positronic polarizing field can be interpreted as an additional current in Maxwell's equations [19]. The electronic polarizing field in the electric dipole approximation is well known in optics: this is a field of dipoles which is entirely due to electronic states in the spectrum of interacting atoms.…”

Section: Integral Equation For Photon Propagation In a System Of Elecmentioning

confidence: 99%

See 1 more Smart Citation

Two electron problem and the nonlocal equations of electrodynamics

Gadomskiǐ

2000

Phys.-Usp.

View full text Add to dashboard Cite

A survey is offered for the current knowledge of nonlocal electrodynamic equations which in some cases (e.g., in solving boundary value problems in optics) can replace Maxwell's equations. The nonlocal equations are derived using the semi-classical or quantum-electrodynamic approaches. The former involves an expansion of retarded potentials in appropriate parameters and a subsequent transition, to terms of orderto quantum mechanical operators in the Lagrangian of a system of moving charges. The latter approach is to consider second-and third-order quantum electrodynamic effects for two hydrogen-like atoms arbitrarily far apart. Various nonlocal equations are derived for the propagation of photons and electromagnetic waves in spin systems, dielectrics, and metals, taking into account a variety of quantum transitions and intermediate states in the spectrum of the interacting atoms. By combining nonlocal field equations with relevant constitutive equations, a number of typical boundary-value optical problems are solved for semi-infinite media, superthin films, and for objects whose linear dimensions are much smaller than the light wavelength.

show abstract

Section: Integral Equation For Photon Propagation In a System Of Elecmentioning

confidence: 99%

“…This can be achieved [19,42] by applying the quantum analogue of the Ewald ± Oseen extinction theorem, which Ð unlike in Ref. [35] Ð enables one to solve the three-dimensional boundary value problem.…”

Section: X23mentioning

confidence: 99%

Two electron problem and the nonlocal equations of electrodynamics

Gadomskiǐ

2000

Phys.-Usp.

View full text Add to dashboard Cite

show abstract

“…Substituting Eqs. (10) to (12) into the Hamiltonian (4) and the evolution equations (7), it is easy to notice that all these equations contain an effective dipole-dipole coupling of atoms responsible for near-zone local-field effects [24]. Expression (10) is not a final solution for the observable field but it is an operator relation having sense only in the combination with the Heisenberg equations (7).…”

Section: Evolution Equationsmentioning

confidence: 99%

“…For a collective of atoms, when g = 0, the system of equations (35) becomes nonlinear, and its solutions essentially depend on the value of the atom-atom coupling parameter g, defined in Eq. (24).…”

Section: Liberation Of Lightmentioning

confidence: 99%

Coherent effects under suppressed spontaneous emission

Yukalov

2001

The European Physical Journal D

View full text Add to dashboard Cite

An ensemble of resonance atoms is considered, which are doped into a medium with well developed polariton effect, when in the spectrum of polariton states there is a band gap. If an atom with a resonance frequency inside the polariton gap is placed into the medium, the atomic spontaneous emission is suppressed. However, a system of resonance atoms inside the polariton gap can radiate when their coherent interaction is sufficiently strong. Thus the suppression of spontaneous emission for a single atom can be overcome by a collective of atoms radiating coherently. Conditions when such collective effects can appear and their dynamics are analysed.

show abstract

“…The angular distribution of the spontaneously emitted photons is also investigated. We thereby rely on the mathematical formalism developed in [13,22], but in contradistinction to the works [18,19] the electromagnetic field will be quantized. A comparison with experiments cannot be made because, as far as we know, there are no such experiments.…”

Section: Introductionmentioning

confidence: 99%

Boundary effects influencing single-atom spontaneous emission in a linear atomic chain

Krutitsky¹,

Audretsch²

1998

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

As a contribution to quantum optics in the vicinity of surfaces we study the single atom spontaneous emission in a linear chain of two-level atoms. The electromagnetic field is thereby treated with the help of integro-differential equations which take into account the interaction with the other atoms in the chain. The life time of the excited atom, the frequency shift of the atomic transition and the angular distribution of emitted photons are worked out. They depend on the position of the emitting atom. As compared with the single atom in free space, considerable modifications occur for atoms a few interatomic distances away from the ends of the chain. * Permanent address:

show abstract

Method of integro-differential equations in quantum optics

Cited by 5 publications

References 29 publications

Two electron problem and the nonlocal equations of electrodynamics

Two electron problem and the nonlocal equations of electrodynamics

Coherent effects under suppressed spontaneous emission

Boundary effects influencing single-atom spontaneous emission in a linear atomic chain

Contact Info

Product

Resources

About