Reversible dephasing effect

In case of anisotropic motions (an anisotropic fluid), the quadrupolar interaction is partially time-averaged to a residual tensor. This residual interaction A modulates the time relaxation function via a reversible dephasing MYt)=exp[-t/T2]cosAt. For motions uniaxial around a symmetry axis, the effect on the spectrum is to split the resonance line into a symmetric doublet with a splitting (in frequency units) ... 

State now involves a dissipative irreversible decay into the effective continuum of levels < >/. Questions concerning the precise nature of the prepared state, the contribution from the reversible dephasing processes at intermediate energies, and the role of intramolecular vibrational relaxation at high enough energies are central to the understanding of infrared multiphoton dissociation processes in isolated molecules. ... 

Electron spin echo spectroscopy (ESE) monitors the spontaneous generation of microwave energy as a function of the timing of a specific excitation scheme, i.e. two or more short resonant microwave pulses. This is illustrated in Fig. 7. In a typical two-pulse excitation, the initial n/2 pulse places the spin system in a coherent state. Subsequently, the spin packets, each characterized by their own Larmor precession frequency m, start to dephase. A second rx-pulse at time r effectively reverses the time evolution of the spin packet magnetizations, i.e. the spin packets start to rephase, and an emission of microwave energy (the primary echo) occurs at time 2r. The echo ampHtude, as a fvmction of r, constitutes the ESE spectrum and relaxation processes lead to an irreversible loss of phase correlation. The characteristic time for the ampHtude decay is called the phase memory time T. This decay is often accompanied by a modulation of the echo amplitude, which is due to weak electron-nuclear hyperfine interactions. The analysis of the modulation frequencies and ampHtudes forms the basis of the electron spin echo envelope modulation spectroscopy (ESEEM). 

The coherent dynamics are reversible since the system is isolated and there are no bath modes in the simplified one-dimensional model. Therefore, if the two electronic states are coherently excited by a Unearly polarized pulse, the dynamic behaviors are invariant with respect to change in the direction of polarization, = 1 (e+) or = —1 (e ). Time-dependent behavior of PcuiW with e+ (e ) is the same as Pbo,w t) with = — 1 ( = 1). In real molecules with many vibrational degrees of freedom, the invariance is broken, and dephasing time of the vibrational coherence in lower excited state b is shorter than that in higher state c because multimode effects induced by potential couplings and/or anharmonicity play a much more dominant role in lower state b than in higher state c. 

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