NMR Quantum State Tomography of quadrupole nuclei

The first QST procedure dedicated to quadrupolar systems was developed by Kampermann and Veeman for spin 3/2 nuclei [8]. It is a direct adaptation from the method used for spin 1/2, but uses transition selective pulses instead of spin selective pulses. Similar to the spin 1 /2 method, the transition selective pulses are used to bring an specific set of populations and coherences to the reading position of the deviation density matrix (single quantum coherences) and after that the NMR spectrum is acquired. The transformations (transition selective pulses) that are applied to the deviation density matrix Ap in order to bring the unknown elements to the reading positions are. 

Since the pulse matrix elements are known and the line intensities, Ai, A2, and A3 can be measured, xn, X22, X33, X44 can be determined from the solution of (4.4.5). 

The expression (f )0 ] stands for the diagonal element (i th line and fcth 

The methods for QST of spin 3/2 systems as well as for coupled homonuclear spin 1/2 describe above can, in principle, be adapted for higher spin systems. However, this will certainly imply in the use of more selective pulses. 

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