Coherent NMR responses in spin systems with complex spectral structure

Abstract

We show that for nonresonant excitation of a quantum system, with an NMR spectrum consisting of two inhomogeneously broadened lines, by a combination of an extended and a short delta-shaped pulse, in the free-precession and spin-echo signals after the second pulse we observe the effect of doubling of the additional emission signals. We establish that the nature of this effect is due to zero beats arising when the variable oscillation frequency of the magnetic moments of the material matches the detuning of the pulse carrier frequency from the resonant frequencies of the spectral lines. Within the theory obtained, we propose a formula which we can use, if we know the times at which the additional emission signals arise, to very accurately determine the frequency shift of the lines in the complex spectrum of the material. The theoretical results agree well with experimental data on generation of multiple NMR signals in toluene, the spectrum of which consists of two non-overlapping lines.Key words: free precession and spin echo signals after the second pulse, inhomogeneous broadening, nuclear magnetic resonance, additional NMR emission signals, chemical shift, toluene.Introduction. In experimental observation of nonsteady-state coherent phenomena in condensed media, with the aim of determining the relaxation times for a quantum system, typically short (compared with the relaxation times) excitation pulses are used [1][2][3]. This circumstance automatically leads to small areas for the corresponding pulses, and makes it possible to neglect the effect of relaxation processes on the quantum system during the time of action of the pulses. In cases when the relaxation times are long, satisfying this condition is no longer critical and, as shown in [4,5], the use of long pulses (with large pulse areas) can reveal some fine features of the coherent response, for example the multiple structure of the nuclear spin echo in ferromagnets [6] and photon echo in dielectric crystals [7].Such conditions for excitation of coherent responses are interesting mainly due to the following. During excitation of a quantum system by an extended electromagnetic pulse, periodic variation in the populations of both levels occurs, leading to oscillations of the magnetic moments (nutational oscillations) with Larmor frequencies matching the carrier frequency of the external pulsed field [2,3]. In other words, during action of the pulse, the two-level atom absorbing and then emitting the energy of the variable magnetic field periodically makes a transition from the ground state to the excited state (and vice versa) with Rabi frequency ω 1 = γH 1 , where γ is the gyromagnetic ratio, H 1 is the amplitude of the external variable magnetic field. Consequently, the induced emission also will change with the same frequency. If the line is inhomogeneously broadened, then the magnetic moments with Larmor frequencies not matching the carrier frequency of the pulse will undergo nonresonant excitation and will not take part in the energy absorption process ...

Peculiarities of Rabi oscillations and free induction decay in two-component nuclear spin systems with Ising nuclei interactions

“…The SPE signals in two-component nuclear systems were theoretically studied neglecting the spin-spin interaction of nuclei [19,20,30]. However, for example in manganites with two magnetic phases (ferromagnetic and antiferromagnetic), this approximation is not applicable.…”