Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optica Acta International Journal of Optics

Nonlinear and Stimulated Effects in Resonance Fluorescence of One and Two Two-level Atoms

Vladislav Cheltsov

Published Jan 1, 1986• 10 citations
Publisher

Abstract

The resonance fluorescence spectrum of one and two two-level atoms in an ideal cavity with one resonant mode is investigated as a function of the initial excitation of the system. The analysis is carried out in the Stark representation with respect to the cavity's field and in first-order perturbation theory with respect to the fluorescence field. In the absence of the field of the cavity (n c = 0) and under an initial excitation of one atom only, the spectrum consists of two lines which are symmetrical with respect to ωa. In all other cases the spectrum has a central line at ωa and other lines at ωa ± 2 Ω. The intensity of the higher (ωa ± 4 Ω) harmonics is small and decreases as 1/ 2 c c with increasing n>c. The nonlinearity of the interaction hamiltonian results in the parametric (with respect to the field of the cavity) amplification of the ωa + 2 Ω harmonic and the attenuation of the ωa − 2 Ω harmonic. The stimulated emission of the ωa ± 2 Ω harmonics, vanishing in a strong (n c » 1) field, is shown to exist for two atoms.

DOI
10.1080/713821854

Related papers

Nonlinear and stimulated effects in resonance fluorescence of one and two atoms

Vladislav Cheltsov

The Stark representation of the resonator field and the first order of perturbation theory of the fluorescence field are used to study the fluorescence spectrum of one and two two-level atoms in an ideal resonator as a function of the initial excitation of the system. It is shown that in the absence of resonator photons (nc = 0) the spectrum obtained for initial excitation of one atom consists of two lines located symmetrically relative to the central frequency ωα. In all other cases the spectrum consists of the central harmonic ωα and of ωα ± 2Ω satellites (Ω is the Rabi frequency). The intensity of collective higher harmonics ωα ± 4Ω is low and it falls on increase in the resonator field as I/nc2. The nonlinearity of the interaction Hamiltonian results in parametric amplification of the ωα + 2Ω harmonics and in attenuation of the ωα–2Ω harmonics. In the case of two atoms it is possible to achieve stimulated fluorescence at the harmonics ωα ± 2Ω.

Soviet Journal of Quantum Electronics•May 31, 1986•0 citations

Resonance Fluorescence from a two-level artificial atom strongly coupled to a single-mode cavity

Zhihui Peng, He, D., Y. Zhou +8 more

We experimentally demonstrate the resonance fluorescence of a two-level artificial atom strongly coupled to a single-mode cavity field. The effect was theoretically predicted thirty years ago by Savage [Phys. Rev. Lett. 63, 1376 (1989)]. The system consists of a superconducting qubit circuit and a one-dimensional transmission line resonator. In addition, a one-dimensional transmission line strongly coupled to the atom serves as an open space. The effect takes place, when a microwave field is applied to the cavity, which in turn is resonantly coupled to the atom. The fluorescence spectrum is measured via the emission into the transmission line. We find that the central peak is determined by the atom spontaneous emission to the open space and the widths of side peaks are largely determined by the coherent interaction between the atom and the cavity, that is, the fluorescence spectrum here is very different from that of the Mollow triplet. We also derive analytical form for the spectrum. Our experimental results agree well with theoretical calculations.

arXiv:2202.12080•Feb 24, 2022•1 citation

Higher harmonics in collective resonance fluorescence

Vladislav Cheltsov

The Stark representation of a strong external resonant field and the third order of perturbation theory of the fluorescence field are used to show that the probability of emission of the (ωa + 4Ω) harmonic (ωa and Ω are the atomic and Rabi frequencies) of collective resonance fluorescence of a pair of two-level atoms is equal to γ2/384, where γ is the width of the spontaneous emission line of a single atom.

Soviet Journal of Quantum Electronics•May 31, 1984•0 citations

Two-atom resonance fluorescence

Constantine Mavroyannis

The excitation spectrum arising from the interaction between two identical atoms (molecules), one of which is excited in the presence of a resonant strong electromagnetic field (pump field), is investigated. The excitation spectrum is found to consist of those describing the symmetric and antisymmetric modes, respectively. The form of both spectra depends on the relation between the distance $R$ separating the atoms and the wavelength $\ensuremath{\lambda}$ of the transition from the ground state to the excited state. For $R<\ensuremath{\lambda}$, and when certain conditions prevail, the spectral function for the symmetric modes consists of three Lorentzian lines describing the central peak and the two sidebands whose radiative widths are equal to ${\ensuremath{\gamma}}_{0}$, $\frac{3{\ensuremath{\gamma}}_{0}}{2}$, and $\frac{3{\ensuremath{\gamma}}_{0}}{2}$, which are twice the corresponding ones arising from an isolated single atom interacting with the pump field. For the antisymmetric modes the central peak has a $\ensuremath{\delta}$-function distribution indicating the stability of the mode in question, while, when certain conditions are satisfied, the two sidebands are described by Lorentzian lines each having a radiative width of the order of $\frac{{\ensuremath{\gamma}}_{0}}{2}$, which is equal to the natural linewidth for a photon spontaneously emitted from an isolated atom. For both the symmetric and antisymmetric modes, the dipole-dipole interaction between the atoms brings about small energy shifts. For $R>\ensuremath{\lambda}$, apart from the small energy shifts caused by the dipole-dipole interaction, the spectral functions for symmetric and antisymmetric modes are similar to that for the single atom interacting with the pump field.

Physical Review A•Jul 1, 1978•70 citations

One- and two-photon resonance fluorescence of a three-level atom at high photon densities

Constantine Mavroyannis, M. P. Sharma

We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.

Molecular Physics•Apr 20, 1981•4 citations

Higher Harmonics in Cooperative Resonance Fluorescence

Vladislav Cheltsov

In the Stark representation, in third-order perturbation theory with respect to fluorescence, it is shown that probability of the ωa + 4Ω harmonic emission in the cooperative fluorescence of two two-level atoms is small and proportional to γ2 / Ω2, Ω2 / ω2 a, contributions to this probability from non-resonant processes being of the order of γ2 / ω2 a.

Optica Acta International Journal of Optics•Oct 1, 1984•4 citations
The resonance fluorescence spectrum of one and two two-level atoms in an ideal cavity with one resonant mode is investigated as a function of the initial excitation of the system. The analysis is carried out in the Stark representation with respect to the cavity's field and in first-order perturbation theory with respect to the fluorescence field. In the absence of the field of the cavity (n c = 0) and under an initial excitation of one atom only, the spectrum consists of two lines which are symmetrical with respect to ωa. In all other cases the spectrum has a central line at ωa and other lines at ωa ± 2 Ω. The intensity of the higher (ωa ± 4 Ω) harmonics is small and decreases as 1/ 2 c c with increasing n>c. The nonlinearity of the interaction hamiltonian results in the parametric (with respect to the field of the cavity) amplification of the ωa + 2 Ω harmonic and the attenuation of the ωa − 2 Ω harmonic. The stimulated emission of the ωa ± 2 Ω harmonics, vanishing in a strong (n c » 1) field, is shown to exist for two atoms.
The Stark representation of the resonator field and the first order of perturbation theory of the fluorescence field are used to study the fluorescence spectrum of one and two two-level atoms in an ideal resonator as a function of the initial excitation of the system. It is shown that in the absence of resonator photons (nc = 0) the spectrum obtained for initial excitation of one atom consists of two lines located symmetrically relative to the central frequency ωα. In all other cases the spectrum consists of the central harmonic ωα and of ωα ± 2Ω satellites (Ω is the Rabi frequency). The intensity of collective higher harmonics ωα ± 4Ω is low and it falls on increase in the resonator field as I/nc2. The nonlinearity of the interaction Hamiltonian results in parametric amplification of the ωα + 2Ω harmonics and in attenuation of the ωα–2Ω harmonics. In the case of two atoms it is possible to achieve stimulated fluorescence at the harmonics ωα ± 2Ω.
We experimentally demonstrate the resonance fluorescence of a two-level artificial atom strongly coupled to a single-mode cavity field. The effect was theoretically predicted thirty years ago by Savage [Phys. Rev. Lett. 63, 1376 (1989)]. The system consists of a superconducting qubit circuit and a one-dimensional transmission line resonator. In addition, a one-dimensional transmission line strongly coupled to the atom serves as an open space. The effect takes place, when a microwave field is applied to the cavity, which in turn is resonantly coupled to the atom. The fluorescence spectrum is measured via the emission into the transmission line. We find that the central peak is determined by the atom spontaneous emission to the open space and the widths of side peaks are largely determined by the coherent interaction between the atom and the cavity, that is, the fluorescence spectrum here is very different from that of the Mollow triplet. We also derive analytical form for the spectrum. Our experimental results agree well with theoretical calculations.
The excitation spectrum arising from the interaction between two identical atoms (molecules), one of which is excited in the presence of a resonant strong electromagnetic field (pump field), is investigated. The excitation spectrum is found to consist of those describing the symmetric and antisymmetric modes, respectively. The form of both spectra depends on the relation between the distance RRR separating the atoms and the wavelength $\ensuremath{\lambda}$ of the transition from the ground state to the excited state. For $R<\ensuremath{\lambda}$, and when certain conditions prevail, the spectral function for the symmetric modes consists of three Lorentzian lines describing the central peak and the two sidebands whose radiative widths are equal to ${\ensuremath{\gamma}}_{0}$, $\frac{3{\ensuremath{\gamma}}_{0}}{2}$, and $\frac{3{\ensuremath{\gamma}}_{0}}{2}$, which are twice the corresponding ones arising from an isolated single atom interacting with the pump field. For the antisymmetric modes the central peak has a $\ensuremath{\delta}$-function distribution indicating the stability of the mode in question, while, when certain conditions are satisfied, the two sidebands are described by Lorentzian lines each having a radiative width of the order of $\frac{{\ensuremath{\gamma}}_{0}}{2}$, which is equal to the natural linewidth for a photon spontaneously emitted from an isolated atom. For both the symmetric and antisymmetric modes, the dipole-dipole interaction between the atoms brings about small energy shifts. For $R>\ensuremath{\lambda}$, apart from the small energy shifts caused by the dipole-dipole interaction, the spectral functions for symmetric and antisymmetric modes are similar to that for the single atom interacting with the pump field.
We consider the possible physical processes that may arise in a three-level atom when only two of its levels interact with a strong electromagnetic field and when the atomic transition frequency is nearly equal to once and twice the frequency of the laser field, respectively. There have been found pronounced cooperative effects in the spectrum of the two-level system, which is in resonance with the laser field, arising from the presence of the third level. The excitation spectra describing the transitions from the first excited state into the second excited state and from that to the ground state consist, apart from the two central peaks, of two pairs of sidebands which are induced by the laser field of the neighbouring system. Detailed expressions of the spectral functions for the physical processes of one- and two-photon resonance fluorescence have been derived and discussed in the limit of high photon densities. The excitation spectrum of the low frequency modes has been considered and discussed in detail. It is found that quantum beats in spontaneous emission may appear in the spectra of the one- and two-photon resonance fluorescence arising from the interference between the two atomic transition frequencies and the frequency of the laser field. The importance of the low frequency modes that occur in the processes in question has been pointed out.