Quantum beat fluorescence intensity

Stark and Zeeman polarization quantum beats are discussed in Section 6.5.3. An external electric or magnetic field destroys the isotropy of space. As a result, the amplitudes for two transition sequences J", M" — J, M = M" 1 —> J ", M" interfere, and the intensity of X or Y (but not Z) polarized fluorescence is modulated at (Fj M =M"+i — Ejim =M"-i)/h. However, it is not necessary to destroy the isotropy of space in order to observe polarization quantum beats. 

In particular, the laboratory frame orientation of the transition moment for spontaneous fluorescence evolves in time. The intensities of z— and (x,y) — polarized fluorescence are modulated 7t/2 out of phase, but the intensity of the total x + y + z polarized fluorescence is not modulated. This is the physical basis for polarization quantum beats (Aleksandrov, 1964 Dodd, et al., 1964) and Rotational Coherence Spectroscopy (Felker and Zewail, 1995). 

The reason for the name population quantum beats is that the signal intensity (fluorescence, REMPI), integrated over all solid angles and polarization states, oscillates in time after the preparation pulse. It appears as if the population prepared in the excited state at t = 0 vanishes and returns periodically (see Fig. 9.5) (Felker and Zewail, 1984). In fact, the population does not oscillate, but the radiative capability of the time-evolving state prepared at t = 0, k(t), does oscillate. 

This intensity can either be monitored in a time-resolved fashion after pulsed excitation in the constant magnetic field B quantum beats, Sect. 7.2), or the time-integrated fluorescence intensity is measured as a function of B (level crossing), where the excitation may be pulsed or cw. 

We have already discussed quantum-beat spectroscopy (QBS) in connection with beam-foil excitation (Fig.6.6). There the case of abrupt excitation upon passage through a foil was discussed. Here we will consider the much more well-defined case of a pulsed optical excitation. If two close-lying levels are populated simultaneously by a short laser pulse, the time-resolved fluorescence intensity will decay exponentially with a superimposed modulation, as illustrated in Fig. 6.6. The modulation, or the quantum beat phenomenon, is due to interference between the transition amplitudes from these coherently excited states. Consider the simultaneous excitation, by a laser pulse, of two eigenstates, 1 and 2, from a common initial state i. In order to achieve coherent excitation of both states by a pulse of duration At, the Fourier-limited spectral bandwidth Au 1/At must be larger than the frequency separation ( - 2)/ = the pulsed excitation occurs at... 

In Zeeman quantum-beat measurements oscillations superimposed on an exponential decay of the fluorescence light intensity are observed. In experiments on ytterbium atoms with zero nuclear spin the beat frequency for the 6sl9d D2 state was 31.52 MHz for a flxed magnetic field, in which the beat frequency for the signal from the 6s6p P state (with known Qj value = 1.493) was 46.05 MHz. What is the gj value of the 6sl9d Z>2 state Is the result expected Discuss what can be learned from measurements of Lande gj factors. 

If two or more closely spaced molecular levels are simultaneously excited by a short laser pulse, the time-resolved total fluorescence intensity emitted from these coherently prepared levels shows a modulated exponential decay. The modulation pattern, known as quantwn beats is due to interference between the fluorescence amplitudes emitted from these coherently excited levels. Although a more thorough discussion of quantum beats demands the theoretical framework of quantum electrodynamics [11.33], it is possible to understand the basic principle by using more simple argumentation. 

Fig.11.23a,b. Quantum beat spectroscopy, (a) Level scheme illustrating coherent excitation of levels 1 and 2 with a short broad-band pulse, (b) Fluorescence intensity showing a modulation of the exponential decay... 

The Fourier transform of the time-resolved fluorescence intensity I(t) yields its spectral distribution I(o)) with sub-Doppler resolution. Figure 11.24 illustrates as an example quantum beats measured by ANDRA et al. [11.19] in the fluorescence following the excitation of three hfs levels in the 6p P3/2 state of the ion. Either a tunable dye laser crossed perpen-... 

A short pump pulse excites coherently different upper levels. The time evolution of the superposition of states following the coherent excitation causes time-dependent changes of the complex susceptibility x of the sample. Similar to the quantum beats in the fluorescence intensity the susceptibility x(t) is found to contain oscillating nonisotropic contributions which can be readily detected by placing the sample between crossed polarizers and transmitting a probe pulse with variable delay (see also Sect.10.3 on polarization spectroscopy). Even a cw broadband dye laser can be used for probing if the probe intensity transmitted by the polarizer is monitored with sufficient time resolution. 

The time resolved fluorescence intensity measured in a quantum beat experiment, can be represented by... 

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