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Journal of the Physical Society of Japan

Double Quantum Rotary Echoes Due to Magnetic Dipolar Interaction in a Multi-Level NMR System

Hiroshi Hatanaka, Noriyuki Tabuchi

Published Apr 15, 1987• 2 citations
Publisher

Abstract

Double quantum (DQ) analogs of rotary echo due to magnetic dipolar interaction have been observed in a multi-level NMR system of 27 Al nuclei in Al 2 O 3 . Observations of the phenomena have been made with the aid of a simple digital filter which was designed for removing large wiggles superposed on the signals of DQ transient nutation and DQ rotary echo.

DOI
10.1143/jpsj.56.1323

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Bulletin of the American Physical Society•May 21, 2009•0 citations
Double quantum (DQ) analogs of rotary echo due to magnetic dipolar interaction have been observed in a multi-level NMR system of 27 Al nuclei in Al 2 O 3 . Observations of the phenomena have been made with the aid of a simple digital filter which was designed for removing large wiggles superposed on the signals of DQ transient nutation and DQ rotary echo.
Two-quantum rotary echoes predicted by Bloch like equations for two-quantum transition have been observed in a multi-level NMR system of 27 Al nuclei in Al 2 O 3 . An rf field exactly at resonance to the two-quantum transition ( Δ m =2) was turned on at t =0 and its phase was shifted by 90° at t =τ. The echo at t =2τ was observed by using the technique of transfer of coherence reported previously. Characteristic dependence of the echo width upon inhomogeneity of rf field amplitude was confirmed experimentally.
Effects of magnetic dipolar interaction between like nuclei on two-quantum (TQ) free decay were examined in a multi-level NMR system, Al in Al 2 O 3 . TQ free decay was observed using a TQ π/2-pulse followed by a probe pulse. The effect of probe pulse was carefully examined to deduce the intrinsic decay time of the TQ coherence. The second moments for two- and three-quantum transitions were calculated. The observed decay time is in good agreement with that obtained from the calculated second moment by assuming Gaussian decay. Basic equations for TQ resonance are also presented.
The phenomenon of transfer of coherence and the effect of level shift caused by two-quantum (TQ) excitation were studied on 27Al^{27}\mathrm{Al}27Al nuclei in Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​. Transfer of coherence between two single-quantum (SQ) transitions and that between SQ and three-quantum transitions were examined. It was observed that the coherences transfer periodically with frequency equal to one-half the TQ transient nutation frequency accompanied by phase shifts caused by the level shift. Experimental results are in good agreement with theoretical predictions. The effect of magnetic dipole interaction was also studied. A precise measurement was made on the shift of TQ resonance frequency and it was confirmed that no shift exists on the TQ resonance frequency contrary to the prediction based on the three-level model.
The first observation of optical rotary echoes, the optical analog of rotary spin echoes, is reported. Rotary echoes are produced in a quantum-mechanical two-level system which is driven resonantly (nutation effect) by a coherent field that suffers a sudden phase retardation. The initial nutation transient dephases, because of an inhomogeneity in either the driving field or the transition frequency of the sample, and then rephases to form an echo following the phase-shifting pulse. Hence, optical rotary and photon echoes are similar processes---the former being an interference in nutation and the latter an interference in free precession. Perturbative solutions of the Bloch equations are derived for the case where inhomogeneous dephasing arises from Doppler broadening and the Rabi frequency exceeds the homogeneous damping rate. Observations of the optical rotary echo in I2{\mathrm{I}}_{2}I2​ vapor are facilitated by the technique of laser frequency switching, which generates precise phase shifts in the optical field. The measurements corroborate detailed theoretical predictions.
Rotary echoes are employed to study excitation dynamics in many-body Rydberg systems. In this method, a phase reversal of a narrow-band excitation field is applied at a variable time during the excitation pulse. The visibility of the resulting echo signal reveals the degree of coherence of the excitation process. Rotary echoes are measured for several n D 5/2 Rydberg levels of rubidium with principal quantum numbers near n =43, where the strength of electrostatic Rydberg-atom interactions is modulated by a Forster resonance. The Rydberg-atom interactions are shown to diminish the echo visibility, in agreement with recent theoretical work. The equivalence of echo signals with spectroscopic data is demonstrated.