najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/22208054201785559566najo-594Research ArticlePHYSICSФИЗИКАSpectral properties of spontaneous photon emission by a material twolevel system in a parabolic cavityAlberG.

Darmstadt, 64289

chizhov@theor.jinr.ruChizhovA. V.

JoliotCurie, 6, Dubna, 141980

Universitetskaya, 19, Dubna, 141980

Institut f¨ur Angewandte Physik, Technische Universit¨at DarmstadtGermanyBogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research; Dubna State University, UniversitetskayaRussian Federation20171208202585559–566Copyright © Alber G., Chizhov A.V., 20252025Alber G., Chizhov A.V.Alber G., Chizhov A.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/594

The spectral properties of a photon spontaneously emitted by a material twolevel system, modelling an atom or ion, in a parabolic cavity are investigated. In particular, we concentrate on the special case of a motionless twolevel system positioned exactly at the focus of a parabolic cavity with a dipole moment oriented along the symmetry axis of this cavity. Treating the corresponding atomfield coupling in the dipoleand rotating wave approximation, it is demonstrated that inside the parabolic cavity the position and frequency dependence of the spectrum of the spontaneously emitted photon exhibits interesting interference patterns. These patterns are explored in detail with the help of a photon path representation of the firstorder electric field correlation function. In the radiation, zone the spatial behavior of the spectrum reveals strong interference in particular at distances from the twolevel system of the order of the focal length of the parabola. With increasing distances, these interference patterns decay except for an undepleted component surrounding the symmetry axis at an almost constant radius. Furthermore, the maximum of the frequency dependence of the spectrum exhibits a positiondependent frequency shift with respect to the atomic resonance frequency.

cavity QEDspontaneous emissionThis work is supported by the Heisenberg–Landau Program (JINR, Russia).ReferencesBruss D., Leuchs G. Lectures on Quantum Information. WileyVCH, Weinheim, 2008.Bruss D., Leuchs G. Lectures on Quantum Information. WileyVCH, Weinheim, 2008.Haroche S., Raimond J.M. Exploring the Quantum: Atoms, Cavities and Photons. Oxford UP, Oxford, 2006.Haroche S., Raimond J.M. Exploring the Quantum: Atoms, Cavities and Photons. Oxford UP, Oxford, 2006.Jaynes E.T., Cummings F.W. Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proceedings of the IEEE, 1963, 51 (1), P. 89–109.Jaynes E.T., Cummings F.W. Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proceedings of the IEEE, 1963, 51 (1), P. 89–109.Paul H. Induzierte Emission bei starker Einstrahlung. Annalen der Physik, 1963, 466 (7–8), P. 411–412.Paul H. Induzierte Emission bei starker Einstrahlung. Annalen der Physik, 1963, 466 (7–8), P. 411–412.Schleich W.P. Quantum Optics in Phase Space. WileyVCH, Weinheim, 2001.Schleich W.P. Quantum Optics in Phase Space. WileyVCH, Weinheim, 2001.Maiwald R., Golla A., et al. Collecting more than half the fluorescence photons from a single ion. Phys. Rev. A, 2012, 86 (4), 043431–5.Maiwald R., Golla A., et al. Collecting more than half the fluorescence photons from a single ion. Phys. Rev. A, 2012, 86 (4), 043431–5.Trautmann N., Bernad J.Z., et al. Generation of entangled matter qubits in two opposing parabolic mirrors. Phys. Rev. A, 2014, 90 (6), 063814–9.Trautmann N., Bernad J.Z., et al. Generation of entangled matter qubits in two opposing parabolic mirrors. Phys. Rev. A, 2014, 90 (6), 063814–9.Purcell E.M. Spontaneous emission probabilities at radio frequencies. Phys. Rev., 1946, 69 (8), P. 681.Purcell E.M. Spontaneous emission probabilities at radio frequencies. Phys. Rev., 1946, 69 (8), P. 681.Alber G. Photon wave packets and spontaneous decay in a cavity. Phys. Rev. A, 1992, 46 (9), R5338–R5341.Alber G. Photon wave packets and spontaneous decay in a cavity. Phys. Rev. A, 1992, 46 (9), R5338–R5341.Alber G., Bernad J.Z., et al. QED with a parabolic mirror. Phys. Rev. A, 2013, 88 (2), 023825–11.Alber G., Bernad J.Z., et al. QED with a parabolic mirror. Phys. Rev. A, 2013, 88 (2), 023825–11.Abramowitz M., Stegun I. A. Handbook of Mathematical Functions. Dover, New York, 1965.Abramowitz M., Stegun I. A. Handbook of Mathematical Functions. Dover, New York, 1965.Eberly J.H., W´odkiewicz K. The timedependent physical spectrum of light. J. Opt. Soc. Am., 1977, 67 (12), P. 1252–1261.Eberly J.H., W´odkiewicz K. The timedependent physical spectrum of light. J. Opt. Soc. Am., 1977, 67 (12), P. 1252–1261.

The authors declare that there are no conflicts of interest present.