Recently one of the authors published a paper concerning the exact quantum mechanical description of pressure-induced four-wave mixing in which the exact expression of the transition probability was found.1 In this approach, a formal solution for the problem of multifield interacting with a single multilevel atom is presented by treating the fields fully quantized and the states in a dressed atomic picture. If we think of the four-wave mixing experiments as a case where the ω a , ω b , and ω c waves are sent into the medium with the fourth wave at ω p generated by the mixing, the output amplitude should be proportional to the component of the polarization fluctuating at the frequency of ω p . Based on these results, we obtained an exact quantum mechanical expression for the polarization tensor. This paper intends to explore the photon number (intensity) dependence of the polarization tensor (susceptibility) and give a comparison of the line shapes for low and high intensity of the incoming three beams. Specifically, the corresponding terms for the 31st, 32nd and 33rd terms in the Bloembergen classical expression for the susceptibility tensor will be investigated in detail.2 For no dissipation we will plot and analyze the amplitude of the polarization component at ω p .
The fluorescence of a two-level atom embedded into a two-dimensional photonic crystal is considered under the assumption that the electronic transition frequency ω 10 is close to the photonic mode frequency ω 0 in the saddle critical point of the photonic spectrum. In this case, the density of photonic states has a logarithmic peak, which manifests itself in a considerable rearrangement of the fluorescence spectrum. The Green’s function of the electron-photon system, which contains the description of the dynamics of spectroscopic transitions and the shape of fluorescence spectra, is obtained in the rotating field approximation. Using the Green’s function, the frequency-dependent Lamb shift and the broadening of the atomic transition are calculated. The shape of the fluorescence spectra is studied. At a large oscillator strength of the atomic transition, the fluorescence line splits into two components in the vicinity of the singularity caused by the saddle critical point. This splitting is associated with a specific Fano-type resonance between the discrete spectrum (the atomic states) and the continuum (the dispersion of photons with a saddle critical point). At small detunings δ = ω 10 -ω 0 , the components of the fluorescence line have considerably different intensities. As δ increases, the spectral positions of the strong and weak components tend to the frequencies of the atomic transition and the saddle point, respectively. The results obtained show that two-level atoms (or quantum dots) can be used as specific probes of the band spectra of photonic crystals.
Two-photon resonant optical processes, using potassium ns2S1/2 states (7 ≤ n ≤ 20), are investigated in detail by a pulsed dye laser. About 100 coherent lines between 288–422 nm are generated through the processes ωUV ± ωIR = 2ωL and [Formula: see text]. The strongest lines (near mP–4S transitions) are formed by parametric oscillation and are generally split into components that are frequency shifted relative to atomic transitions. About 70 lines are generated by six-wave mixing processes and 15 other lines by four-wave mixing processes. The wavelengths, relative intensities of the lines, and the components of the strongest lines are explained with a theoretical analysis based on the wave equation, atomic polarization, and phase-match condition for both wave-mixing processes and parametric oscillations.
The dynamics of quantum solitons in an Ising-like S=(1/2 antiferromagnet on finite linear chains with spins N (\ensuremath{\le}15) is studied by integrating the Schr\"odinger equation of motion. Space-time correlation functions
Szz(r,t) and their Fourier transforms, i.e., dynamical structure factor
Szz(q,\ensuremath{\omega}), are calculated for both even and odd N. A slow but large oscillation of
Szz(r,t) is seen, which gives a direct evidence of the occurrence of propagating domain walls, i.e., solitons. The oscillation leads to a low-energy component of
Szz(q,\ensuremath{\omega}) whose line shape greatly depends on whether N is even or odd and on the temperature. We analyze in detail the dependence of soliton number in the line shape and give a plausible conjecture that
Szz(q,\ensuremath{\omega}) for N=\ensuremath{\infty} should exhibit a very broad double maximum at low temperatures. We estimate
Szz(q,\ensuremath{\omega}) at various temperatures. Our results reproduce experimental observations of
Szz(q,\ensuremath{\omega}) on
CsCoCl3 and
CsCoBr3 very well over a wide temperature range.