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Physical review. B, Condensed matter

Transfer of coherence and effect of level shift caused by two-quantum excitation in a multilevel NMR system

Hiroshi Hatanaka, Tsuneo Hashi

Published Apr 1, 1983• 8 citations
Publisher

Abstract

The phenomenon of transfer of coherence and the effect of level shift caused by two-quantum (TQ) excitation were studied on $^{27}\mathrm{Al}$ nuclei in ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$. 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.

DOI
10.1103/physrevb.27.4095

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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 {\mathrm{Al}}_{2}$${\mathrm{O}}_{3}. 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.
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.
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.
The wealth of quantum coherence effects depending on the orientation of external magnetic field, the polarization of coupling and probe lights, and the Rabi frequency of the coupling beam are studied in transition ${F}_{e}=2\ensuremath{\leftrightarrow}{F}_{g}=3$ of Cs D2{\mathrm{D}}_{2}D2​ line. The split of electromagnetically induced transparency (EIT) resonances on two or three resonances determined by the different combination of the polarization of interaction lights and the direction of applied magnetic fields is obtained. The shifting and widening of the EIT resonances with the strength of the magnetic field (i.e., Zeeman splitting in the upper and lower levels) and Rabi frequency of the coupling beam increasing are also discussed. It may develop into the potential application for tunable multichannel optical information storage. On the other hand, an explanation of observed asymmetry of spectra by laser frequency offset from the optical resonance is given with theoretical calculation, which is in good agreement with the experimental results.
Multiple quantum (MQ) NMR methods1 are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian1 describing MQ NMR dynamics is related to the flip-flop Hamiltonian of a one-dimensional spin system in the approximation of the nearest neighbor interactions. As a result, it is possible to organize quantum state transfer along a linear chain. MQ NMR experiments are performed on quasi-one-dimensional chains of 19F nuclei in calcium fluorapatite Ca5(PO4)3F. Relaxation of the MQ NMR coherences is considered as the simplest model of decoherence processes. A theory of the dipolar relaxation of the MQ NMR coherences in one-dimensional systems is developed. A good agreement of the theoretical predictions and the experimental data is obtained.
Pulsed radio-frequency transient phenomena of resonant two-level spins are often described by the Bloch equations where the phenomenological dipole (T2{T}_{2}T2​) and population (T1{T}_{1}T1​) decay times appear. A similar description has been carried over recently into the microwave and infrared regions as well. At visible-ultraviolet wavelengths, however, a more general solution is required because the transition levels do not constitute an isolated system and also spontaneous emission can no longer be disregarded. As a consequence, the lower (1) and upper (2) transition levels are characterized by vastly different decay rates (${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$) and the lifetime T1{T}_{1}T1​ is no longer a defined quantity. In view of laser-induced coherent transient phenomena now being observed, we present general solutions of the density-matrix equations of motion for an optically resonant two-level system in contact with a multilevel reservoir where ${\ensuremath{\gamma}}_{1}\ensuremath{\ne}{\ensuremath{\gamma}}_{2}$. Particular and perturbative solutions involving intensity-dependent damping and frequency shifts are included with applications to echo and nutation phenomena.
Experimentally achievable conditions where only weak off-resonant fields are used to excite coherence in a two-level system are explored. A brief review of previous theoretical results useful in treating multifrequency irradiation sequences is provided. Using an approximation method based on the Floquet formalism we derive an expression for the effective field strength as a function of the phases and amplitudes of the applied irradiation fields. Some of these results are rederived and/or explained in a simplified manner. Under conditions of four-frequency irradiation, three-photon excitation of a two-level system in NMR is experimentally demonstrated on the spin-1/2 system of the 31P nucleus in phosphoric acid. The behavior of the three-photon resonance is explored as a function of all important experimental parameters. The results of these tests conform closely to the theoretical predictions. Possible uses of multifrequency irradiation schemes in NMR are suggested.