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AIP conference proceedings

Spectral properties of two-mode two photon process

M. M. Ashraf

Published Jan 1, 2001• 0 citations
Publisher

Abstract

Spectral properties of an atom interacting with two modes of quantized field are described-Two types of spectra are investigated-Fluorescent and Output spectra. It is shown that both the spectra are sensitive to coupling strengths, which affect the two-photon transition probability. In case of equal coupling strength ratio (r=1), the fluorescent spectra exhibit a transition from asymmetric to symmetric two-peak structure and the output spectra demonstrate a single peak. The single peak of output spectrum resembles with a two-photon signal of linearly polarized light.

DOI
10.1063/1.1370692

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Spectral properties of an atom interacting with two modes of quantized field are described-Two types of spectra are investigated-Fluorescent and Output spectra. It is shown that both the spectra are sensitive to coupling strengths, which affect the two-photon transition probability. In case of equal coupling strength ratio (r=1), the fluorescent spectra exhibit a transition from asymmetric to symmetric two-peak structure and the output spectra demonstrate a single peak. The single peak of output spectrum resembles with a two-photon signal of linearly polarized light.
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.
This article investigates the interaction of a pair of two-level atoms with a quantized radiation field in an ideal cavity, taking into account the dipole-dipole interaction between the two atoms. One-photon and two-photon transitions are treated. It is found that the spectra have eight completely asymmetric peaks in both cases. For an intense field in both processes, a striking feature with five asymmetrically distributed peaks is recorded if ga γ where ga is the dipole-dipole coupling constant and γ is the detector's width. If the atoms' coupling is weak and the spectrometer's resolution is low, say ga < γ, then only a three-peak structure can be obtained.
We focus on the influence of multiphoton effect on the fluorescence spectrum and photon statistics of the bichromatically driven two-level atomic system. The influence of the multiphoton effect of the weaker driving field on the system and spontaneous emission are revealed by Schrieffer-Wolff perturbation theory, respectively. The physical origin of the multiphoton process affecting the fluorescence spectral asymmetry characteristics is fully investigated by studying the population distribution and the dressed atomic transition weight. Further, the suppression condition of the central peak of the central band is investigated. The photon statistical properties of the system are revealed by studying the frequency-resolved correlations between different sidepeaks and the central peak and sidepeak, respectively. In particular, the physical picture of the asymmetry of the two-photon correlation signal that is affected by the multiphoton process of the weaker driving field affecting the timing detection is fully revealed by the two methods of correlation moment and conditional quantum state, respectively. These results of ours provide a theoretical approach for studying multiphoton processes in multichromatically driven quantum systems, as well as for developing quantum simulation techniques such as spin locking.
Emission spectra of a pair of effective two-level atoms interacting with two modes of the cavity field through Raman interaction are studied, where the interaction of each atom with the field may be different. The spectra with two modes of the cavity field being initially in various number states are analysed in detail. It is found that emission spectra manifest following new properties: When mode 1 of the cavity field is in vacuum state and the other is in the weak field , the spectrum shows symmetric ten peaks and six peaks alternately, with the increase of R=g2/g1, which reflects the different Raman interacting intensities of two atoms with the cavity field more sensitively compared with the spectrum of two atoms in a single-mode cavity. The spectrum with 01=1, n2=50 and n1 = 50, n2=1 reflects the different positions of mode 1 and mode 2 of cavity field interacting with two atoms through Raman process. Finally, the symmetric 16-peaks structure of the spectrum is explained.
We have studied the fluorescence spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes are equal to the two atomic transition frequencies, respectively. The Green's function formalism has been used to calculate the excitation spectrum of the system. An expression for the spectral function describing the excitation spectrum of the system has been derived in a closed form in the limit of high photon densities. Numerical computation of the expression for the spectral function indicates that at each transition frequency there may exist either one pair or two pairs or three pairs of sidebands, in addition to the central peak, depending upon the relative strength of the Rabi frequencies involved.
We have studied the fluorescent spectra arising from the interaction of a four-level atom with a strong bichromatic field and a weak signal field simultaneously. The atomic system consists of two upper excited states \ensuremath{\Vert}3〉 and \ensuremath{\Vert}4〉 and two lower states \ensuremath{\Vert}1〉 and \ensuremath{\Vert}2〉 and the two laser fields, whose frequency modes ${\ensuremath{\omega}}_{a}$ and ${\ensuremath{\omega}}_{b}$ are initially populated, operate between the states \ensuremath{\Vert}2〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}4〉 and \ensuremath{\Vert}2〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}3〉, respectively. Using the Green-function formalism and a model Hamiltonian, where all the free and interacting fields are quantized, we have studied the transitions \ensuremath{\Vert}4〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 and \ensuremath{\Vert}3〉\ensuremath{\leftrightarrows}\ensuremath{\Vert}1〉 of the signal field in the limit of high photon densities of both laser fields. The expression of the spectral function for the \ensuremath{\Vert}1〉\ensuremath{\rightarrow}\ensuremath{\Vert}4〉 transition describes stimulated one-photon and three-photon processes, respectively. The one-photon spectra near the frequency \ensuremath{\omega}\ensuremath{\approxeq}${\ensuremath{\omega}}_{41}$ of the signal field consist of a central peak and two pairs of sidebands whose intensities take always positive and negative values indicating that attenuation and amplification (stimulated emission) of the signal field takes place at the frequencies in question, respectively. The spectral function for the three-photon process near the frequency \ensuremath{\omega}\ensuremath{\approxeq}${\ensuremath{\omega}}_{41}$-2${\ensuremath{\omega}}_{a}$ describes two pairs of sidebands whose intensities are always negative implying that strong amplification of the signal field occurs. The computed one-photon and three-photon spectra are presented graphically for different values of Rabi frequencies and detunings of both laser fields, respectively. Then using a classical description of both laser fields, the spectral functions describing one-photon and three-photon processes are calculated and the derived results are compared with the corresponding ones when the fields are quantized. It is found that the results obtained when the fields are quantized and in the limit of high photon densities describe the classical as well as the quantum nature of the photons which is lost in the classical treatment.