We develop a theory of quantum beats in molecular fluorescence taking into account collision effects (such as pure dephasing due to elastic collision) without invoking the Markoff approximation. Model calculations of the time dependent fluorescence from molecules with two excited levels are performed in order to see how the non-Markoffian character in the collision process exerts influence upon the quantum beat pattern. It is suggested that if the pure dephasing between the excited states is a Markoffian ‘‘the degree of modulation of the beats’’ decreases exponentially with time; if it is in the static limit the degree of modulation of the beats decreases as a Gaussian function (the non-Markoffian behavior in the quantum beats). A given case can be classified as either Markoffian or non-Markoffian, depending on the relative magnitudes of the collision duration time τc, the beat frequency ω, and the coupling strength v which is characteristic of the pure dephasing process. The Markoff approximation holds only if the condition ω<v<1/τc is satisfied; the non-Markoffian behavior appears in the quantum beat pattern when ω>v, even if v2τ2c<1 .
We develop a theory of quantum beats in molecular fluorescence taking into account collision effects (such as pure dephasing due to elastic collision) without invoking the Markoff approximation. Model calculations of the time dependent fluorescence from molecules with two excited levels are performed in order to see how the non-Markoffian character in the collision process exerts influence upon the quantum beat pattern. It is suggested that if the pure dephasing between the excited states is a Markoffian ‘‘the degree of modulation of the beats’’ decreases exponentially with time; if it is in the static limit the degree of modulation of the beats decreases as a Gaussian function (the non-Markoffian behavior in the quantum beats). A given case can be classified as either Markoffian or non-Markoffian, depending on the relative magnitudes of the collision duration time τc, the beat frequency ω, and the coupling strength v which is characteristic of the pure dephasing process. The Markoff approximation holds only if the condition ω<v<1/τc is satisfied; the non-Markoffian behavior appears in the quantum beat pattern when ω>v, even if v2τ2c<1 .
Based on the master equation approach, an expression for the time dependent fluorescence intensity has been derived taking into account both collision effects resulting from the elastic and inelastic scattering from the heat bath and the statistical properties of the incident light. The degree of coherence for the molecular eigenstates is defined. The pure dephasing constant between the excited states attenuates the degree of coherence for the molecular eigenstates during and after the light pulse duration; on the other hand, the pure dephasing between the ground and excited states attenuates it during the pulse duration. A separable nonstationary correlation function for the incident radiation field is introduced to investigate the effects of the field coherence on the time dependent fluorescence. Model calculations of the quantum beats in the fluorescence from molecules with two levels in the excited state in the weak radiation field have been performed to demonstrate the effects of the dephasing constants and the field coherence as well as those of the population decay constants.
When a diatomic molecule is photodissociated on a singlet molecular potential energy surface to give two singlet atoms, one of which is electronically excited, the atoms are left in pure angular momentum states referred to the molecular quantization axis. Transformation of such pure states to a laboratory frame of reference gives atomic wave functions that are described as coherent superpositions of states. Application of an external magnetic field to an ensemble of excited atoms causes quantum beats, or, alternately, a Hanle effect to appear in the fluorescence emitted by the atoms. Calculations show that the interference effects are observed only for certain geometrical arrangements of the electric vector of the photodissociating radiation, the external field, and the polarization direction accepted by the fluorescence detector. The expressions for the fluorescence intensity show that the phase and modulation depth of the quantum beat can be used to determine the asymmetry parameter for recoil of the photofragments.
It is the aim of this note to show that, even under fixed excitation wavelength and bandwidth, the fluorescence time profile of a given molecule may exhibit a sudden and drastic qualitative change between smooth, purely exponential, and periodically structured quantum beat decay if appropriate external conditions are continuously varied. This abrupt change is analogous to a nonequilibrium phase transition which occurs at a bifurcation point of a suitable order parameter, identified to be the beat frequency, whose branching is governed by a tunable level width which turns out to be the appropriate control parameter for the transition.
We study theoretically quantum statistical and spectral properties of the resonance fluorescence of a single atom or system with angular momentum $J=1/2\ensuremath{-}{J}^{\ensuremath{'}}=1/2$ driven by a monochromatic linearly polarized laser field, due to quantum interference among its two antiparallel $\ensuremath{\pi}$ transitions. A magnetic field parallel to the laser polarization is applied to break the degeneracy (Zeeman effect). In the nondegenerate case, the $\ensuremath{\pi}$ transitions evolve at different generalized Rabi frequencies, producing quantum beats in the intensity and the dipole-dipole, intensity-intensity, and quadrature-intensity correlations. For a strong laser and large Zeeman splitting the beats have mean and modulation frequencies given by the average and difference, respectively, of the Rabi frequencies, unlike the beats studied in many spectroscopic systems, characterized by a modulated exponential-like decay. Further, the Rabi frequencies are those of the pairs of sidebands of the Mollow-like spectrum of the system. In the two-time correlations, the cross contributions, i.e., those with products of probability amplitudes of the two $\ensuremath{\pi}$ transitions, have a lesser role than those from the interference of the probability densities. In contrast, there are no cross terms in the total intensity. We also consider nonclassical and non-Gaussian properties of the phase-dependent fluorescence for the cases of weak to moderate excitation and in the regime of beats. The fluorescence in the beats regime is nonclassical, mainly from third-order dipole fluctuations, which reveal them to be also strongly non-Gaussian, and their quadrature spectra show complex features around the Rabi frequencies. For small laser and Zeeman detunings, a weak to moderate laser field pumps the system partially to one of the ground states, showing slow decay in the two-time correlations and a narrow peak in the quadrature spectra.
The transient four-wave mixing signal from a three-level system coupled to a bath of harmonic oscillators is calculated in the short-pulse limit. This allows an examination of the non-Markovian effects on the relaxation processes in the excited levels between which beating occurs. In particular, it is possible to distinguish between oscillations which are due to oscillatory dephasing, a consequence of the memory effects, and oscillations due to the quantum beats. This also allows one to analyze how these two kinds of oscillations are mixed together. We show that we not only have an amplitude modulation of the beats as in the Markovian case but also deformations of the beats for short delays between the exciting light pulses. These deformations are a consequence of the nonequilibrium motion of the surroundings of the system under optical excitation. \textcopyright{} 1996 The American Physical Society.
We present a theoretical treatment of the coherent three-level beat signals occurring in the transient response of a Doppler-broadened molecular system with coupled closely spaced levels resonating with an intense monochromatic cw laser field. When the degenerate levels of the molecular system are suddenly split by means of an external Stark or Zeeman field, the transmitted laser radiation exhibits decaying beats at frequencies related to the level splitting or Raman frequency. This effect has been the subject of earlier theoretical analyses, but some relevant aspects such as the velocity integration, were not taken into account. A perturbation treatment, complete to third order in laser field strength, is used to calculate the velocity-integrated induced polarization and the corresponding reradiated field. The calculation takes into account both Raman-type processes, which lead to transient oscillations at the Raman frequency ${\ensuremath{\omega}}_{21}$, and population-saturation effects. In particular, population-induced transient oscillations at half the Raman frequency, $\frac{{\ensuremath{\omega}}_{21}}{2}$, are predicted. The relative importance of the various oscillations is analyzed as a function of the laser detuning and other parameters, including velocity-changing collisions. The relationship between the three-level beat signals and the well-known quantum-beat effect studied in fluorescence is explored.