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The Journal of Chemical Physics

Sudden change of shape of time-dependent molecular fluorescence intensity as a nonequilibrium phase transition

K. Lendi

Published Feb 1, 1985• 4 citations
Publisher

Abstract

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.

DOI
10.1063/1.448487

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arXiv:2010.08081•Journal of Physics B Atomic Molecular and Optical Physics•Oct 20, 2021•24 citations
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 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.
The effects of different laser line shapes on the intensity and spectrum of resonance fluorescence from a two-level atom are investigated. The laser model considered is that of an ideal single-mode laser operating high above threshold, with constant amplitude and undergoing phase-frequency fluctuations analogous to Brownian motion. As the correlation time of the frequency fluctuations increases from zero to infinity, the laser line shape changes from Lorentzian to Gaussian in a continuous way. It is shown that for intermediate and strong fields, the average intensity of fluorescence in the case of a resonant broadband Lorentzian line shape is higher than that in the case of a Gaussian line shape with the same bandwidth and total power. This is in contrast to the weak-field case where the higher peak power of the Gaussian line shape makes it more effective than the Lorentzian line shape. It is also shown that in the case of a nonzero frequency correlation time (non-Lorentzian line shape) the intensity of fluorescence undergoes non-Markovian fluctuations. In relation to the spectrum of resonance fluorescence, it is shown that as the line shape is varied from Lorentzian to Gaussian the following changes take place: In the case of off-resonance excitation, the asymmetry of the spectrum decreases. In the case of resonant excitation, the center-peak to side-peak height ratio for the triplet structure increases. Moreover, the recently predicted center-line dip, which develops in the spectrum in the case of broadband excitation when the Rabi frequency and the bandwidth are nearly equal, becomes increasingly deeper.
We compute the time-dependent spectrum of fluorescence by two-level atoms after a strong resonant exciting laser pulse is turned off abruptly. The behavior of the "delayed" three-peaked spectrum is shown to be dependent on the natural lifetime of the upper state and on the bandwidth of the interferometer used in the measurement. A prompt increase in the central-peak intensity and an oscillating decay in the two side peaks are predicted to occur immediately after the laser is turned off. These are manifestations of the "undressing" of the atomic states. Our calculation permits consideration of the question of the speed of the undressing and its observation.
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.
Abstract In this work, we give a quantitative answer to the question: how sudden or how adiabatic is a frequency change in a quantum harmonic oscillator (HO)? We do that by studying the time evolution of a HO which is initially in its fundamental state and whose time-dependent frequency is controlled by a parameter (denoted by ϵ ) that can continuously tune from a totally slow process to a completely abrupt one. We extend a solution based on algebraic methods introduced recently in the literature that is very suited for numerical implementations, from the basis that diagonalizes the initial Hamiltonian to the one that diagonalizes the instantaneous Hamiltonian. Our results are in agreement with the adiabatic theorem and the comparison of the descriptions using the different bases together with the proper interpretation of this theorem allows us to clarify a common inaccuracy present in the literature. More importantly, we obtain a simple expression that relates squeezing to the transition rate and the initial and final frequencies, from which we calculate the adiabatic limit of the transition. Analysis of these results reveals a significant difference in squeezing production between enhancing or diminishing the frequency of a HO in a non-sudden way.