Nuclear coherence generator

The remote-echo detector is shown in Figure 11. In this method the electron spin echo at the end of the pulse sequence, which uses Vi < recho formation an additional nil pulse transfers the electron coherence to longitudinal magnetization. The echo amplitude information can thus be stored for a time interval up to the order of T. After a fixed time delay h < T l, the z-magnetization is read out using a two-pulse echo sequence with a fixed time interval X2 > r. Remote echo detection can be applied to many experiments, including three-pulse ESEEM and HYSCORE, and thus can eliminate blind spots with an appropriate choice of small ri. Note, however, that it may suffer from reduced sensitivity due to the increased sequence time. 

In this section we describe selected time-domain ENDOR experiments where the free evolution of nuclear coherence is recorded. These experiments consist of at least three building blocks a nuclear coherence generator, a free evolution period for the nuclear coherence, and a nuclear coherence detector. 

The pulse sequenees for a Davies-type, a Mims-type, and a Chirp-ENDOR-HYSCORE are shown in Figure 24 [82]. In the Davies-type sequence (a), the nuclear coherence generator consists of the first m.w. and r.f. chirp pulse, followed by a variable free evolution time T, and the nuclear coherence detector consisting of the second r.f chirp pulse and the m.w. primary echo sequence. The time-domain trace is thus measured by incrementing T and recording the echo intensity. FT gives the ENDOR spectrum. The Mims-type sequence, shown in Figure 24b, functions in a similar way. 

Considering the resolution of the nuclear frequency spectrum, this two-pulse echo experiment is not optimal. The nuclear frequencies are here measured as differences of frequencies of the ESR transitions, so that the line widths correspond to those of ESR transitions. The nuclear transitions have longer transverse relaxation times Tin and thus smaller line widths. In fact, if the second mw pulse is changed from a n pulse to a Ji/2 pulse, coherence is transferred to nuclear transitions instead of forbidden electron transitions. This coherence then evolves for a variable time T and thus acquires phase v r or vpT. Nuclear coherence cannot be detected directly, but can be transferred back to allowed and forbidden electron coherence by another nil pulse. The sequence (jt/2)-x-(Jt/2)-r-(jt/2)-x generates a stimulated echo, whose envelope as a function of T is modulated with the two nuclear frequencies v and vp. The combination frequencies v+ and v are not observed. The modulation depth is also 8 211. The lack of combination lines simplifies the spectrum and the narrower lines lead to better resolution. There is also, however, a disadvantage of this three-pnlse ESEEM experiment. Depending on interpulse delay x the experiment features blind spots. Thus it needs to be repeated at several x values. 

The key requirements for ISRS excitation are the existence of Raman active phonons in the crystal, and the pulse duration shorter than the phonon period loq1 [19]. The resulting nuclear oscillation follows a sine function of time (i.e., minimum amplitude at t=0), as shown in Fig. 2.2e. ISRS occurs both under nonresonant and resonant excitations. As the Raman scattering cross section is enhanced under resonant excitation, so is the amplitude of the ISRS-generated coherent phonons. 

Optical detection offers the most conventional technique to time-resolve the coherent phonons. It includes four-wave mixing [8], transient reflectivity [9,10] and transmission [7] measurements, as well as second harmonic generation (SHG) [15,32]. Coherent nuclear displacement Q induces a change in the optical properties (e.g., reflectivity R) of the crystal through the refractive index n and the susceptibility y,... 

In general, the motion of M in the rotating frame follows from the classical torque exerted on it by Beff. The effect of an rf pulse is then to tip M away from the z axis and to generate a component in the x y plane. As viewed from the laboratory frame of reference, this component precesses in the xy plane and induces an electrical signal at frequency w in a coil placed in this plane. As the nuclear moments that make up M precess, they lose phase coherence as a result of interactions among them and magnetic field inhomogeneity effects, as described in Section 2.7. Thus Mxy decreases toward its equilibrium value of zero, and the... 

So far, biexponential relaxation has been the only aspect of the behaviour of quadrupolar nuclei which has distinguished them from the classical model of nuclear magnetism. This is because all the density matrices generated have contained only single-quantum elements, which behave classically in response to rf pulses. The order of multiple-quantum coherence for a density matrix element ernm is n — m for the special case of a single spin. The coherence pattern for a spin- density matrix is thus,... 

Light amplification by stimulated emission of radiation was first demonstrated by Maiman in 1960, the result of a population inversion produced between energy levels of chromium ions in a ruby crystal when irradiated with a xenon flashlamp. Since then population inversions and coherent emission have been generated in literally thousands of substances (neutral and ionized gases, liquids, and solids) using a variety of incoherent excitation techniques (optical pumping, electrical discharges, gas-dynamic flow, electron-beams, chemical reactions, nuclear decay). 

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). 

---