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Molecular Physics

Quantum beats in the phosphorescence of a photo-excited triplet state

R.A. Schadee, C.J. Nonhof, Jan Schmidt, J.H. van der Waals

Published Jul 1, 1977• 10 citations
Publisher

Abstract

We have observed quantum beats in the phosphorescence of tetramethylpyrazine-d 12 in a durene host crystal where the two upper spin components (тz, тy) decay via a common radiative channel. The initial phase coherence required to make the beats observable was created by a 1/2π microwave pulse resonant with the тz-тy transition at 857 MHz. When, after a few microseconds, the phase coherence is lost it can be restored by a second microwave pulse and the beats then appear as an echo signal: from this experiment one obtains a dephasing time T 2=1·2 μs.

DOI
10.1080/00268977700101611

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Physical Review Letters•Jul 31, 1989•231 citations
We have observed quantum beats in the phosphorescence of tetramethylpyrazine-d 12 in a durene host crystal where the two upper spin components (тz, тy) decay via a common radiative channel. The initial phase coherence required to make the beats observable was created by a 1/2π microwave pulse resonant with the тz-тy transition at 857 MHz. When, after a few microseconds, the phase coherence is lost it can be restored by a second microwave pulse and the beats then appear as an echo signal: from this experiment one obtains a dephasing time T 2=1·2 μs.
A method for monitoring the time development of the coherent components in a multilevel system using an observable which can measure only the relative populations in the levels is presented. Using standard density matrix formulation, expressions are obtained for the conventional and this new ’’probe’’ pulse method. For several of the more common coherence experiments, optically detected magnetic resonance of molecular excited triplet states is used to illustrate the principles. The effect of coherent averaging of relaxation terms in the spin Hamiltonian is discussed and specifically applied to excited triplet states in zero field. Finally, experimental results of coherence measurements are presented along with a detailed description of the apparatus and methods used.
An expression for the probability of time-resolved three-photon ionization via coherently excited resonant states of a molecular system is derived in the perturbative density matrix formalism with the aid of the Liouville space Feynman diagram. It is shown how the time evolution of the molecular coherence in the first resonant state can be detected as a function of the delay time between the pumping and probing lasers through the probing two-photon ionization process. The three-photon ionization process consists of the simultaneous and sequential processes which are classified by the Liouville space Feynman diagrams. The possibility of appearance of quantum beats in the pump–probe three-photon ionization is discussed by performing model calculations of the probability of ionization. The role of the direct and redistributed processes is discussed. The redistributed process is induced by intramolecular processes in the resonant state. The theoretical treatment is applied to the (1+2) three-photon ionization of pyrazine observed by Knee et al. It is demonstrated that the fast decay component (110 ps) of the pyrazine spectra originates from the intramolecular dephasing of the vibronic coherence created by the pumping pulse laser, and this component appears only when the redistributed process (the ionization process through triplet levels) is absent.
In recent years, transient four-wave mixing (FWM) techniques have been used to investigate the dephasing times of non-equilibrium carriers in semiconductor heterostructures by monitoring the decay of the macroscopic polarization. Initially, this decay was measured by temporally-integrating the scattered FWM signal as a function of time delay between two (or more) pump pulses. More recently, the macroscopic polarization decay has been measured by time-resolving the FWM signal by cross correlating it with an ultrashort laser pulse via frequency up-conversion in a nonlinear crystal. When excitons with slightly different energies are excited, oscillations (or beats) have been observed both in the time-integrated FWM signal and in the time-resolved FWM signal. Such beats have been observed, for example, between light- and heavy-hole excitons and between excitons in wells of different widths. Both the spectral behavior1 of the time-integrated FWM signal and the temporal behavior2 of the time-resolved signal have been shown to allow the distinction between the polarization interference associated with two independent oscillators and the quantum beats associated with two coupled oscillators which share a common level. In addition, it has been demonstrated3 that the quantum beats produced by incident pulses with parallel polarizations are exactly out of phase (by π) with the beats produced by orthogonally polarized pulses. In each case1-3, the period and phase of the beats and the polarization of FWM signal were explained by using a six-level model, which excluded many-body effects, to describe the J=1/2 conduction and J=3/2 valence states. Within the last few months, however, it has been shown that a complete description of the polarization selection rules for the FWM signal requires excitation-induced dephasing4 or disorder-induced coupling of the σ + and σ – excitonic transitions5.
We develop a new theoretical treatment that can explain, for the first time to our knowledge, unexpectedly strong synchronized-quantum-beat-echo (SQBE) signals that we previously observed in the ground state of sodium atoms. The SQBE is obtained by successive application of two light-pulse trains tuned to an optical transition under the condition that the pulse repetition frequency or that of one of its harmonics is equal to the separation of a ground-state sublevel pair. The theory is developed for weak optical pumping for which the duration of the light-pulse trains is much longer than the spontaneous decay time of the excited state. We show that the echo is formed effectively as a result of nonuniform depopulation from the sublevel pair to the other levels because of frequency-selective optical pumping during the rapid spontaneous decay of the excited state. Details of the experiment with sodium atoms are described also.
Abstract The spin echo [1 ] discovered by Erwin Hahn in 1950 is one of the most sophisticated phenomena in physics. It demonstrates the fact that the decay of coherence due to the inhomogeneous broadening can be recovered by an ingenious ‘effective time reversal’ technique. Since then, the research on coherent transients has been developed in the field of pulsed magnetic resonance [2]. The advent of the laser stimulated the studies in the optical region. Optical analogues of most of the coherent transients in magnetic resonance have been realized [ 3] except for those in solids, whose mechanisms are based on the spin temperature hypothesis [4] . Thus coherent interactions between radiation and atoms have been extensively studied and the techniques developed have been effectively used in a variety of fields. In the studies of so-called two-level problems the coherence is generated by a direct excitation of the relevant transitions by radiofrequency (r.f.), microwave, or laser fields.
Two pulse photon echoes were observed in organic dye molecules in solution using 6-fs optical pulses. The results show an initial rapid dephasing of the echo due to level multiplicity followed by quantum beaks. The temporal decay of the quantum beats is characterized by a T2{\mathrm{T}}_{2}T2​ of about 60 fs.