Tuned amplitudes approximation

For this purpose, the cantilever tune menu is opened and a frequency sweep is performed. From the probe manufacturers data sheet, the resonance frequency is approximately known, e.g., 300 kHz. Hence, we excite the lever with low power (drive amplitude 25 mV) and sweep the frequency for 30 kHz around the expected resonance frequency of 300 kHz. In advanced AFM set-ups, the resonance frequency may also be independently determined before the tuning by a thermal tune (please consult the corresponding manual for details the procedure is globally reviewed in Sect. 2.2.5). 

Figure Ila shows how an ideal cosine amplitude modulation of the RF carrier wave could be approximated by a rectangular RF pulse scheme, which is much easier to implement. Such a scheme comprises of pulses with alternating phases of 0° and 180° and is referred to as FAM. As was already mentioned, the modulation frequency should be tuned such that Vm matches tq, at least during part of the excitation. Due to the sample spinning, the quadrupolar splitting of many crystallites will pass through the v n value. It was shown that mismatches between and the powder i/qS do not create large phase distortions and simultaneous adiabatic and direct coherence transfer processes result in relatively pure MQ SQ transfers. By pure we mean that no significant phase dispersions are observed when looking at the transfer of each crystallite separately.

The pulse envelope of the laser is given by f(t), the Rabi frequencies for the various transitions are and the laser detuning is denoted by A. Solution of these equations by numerical integration has been given by Parker and Stroud for the case of a laser pulse of duration 6-10 psec with a central frequency tuned to n = 85. The sum over states involves 60 n 100. After the excitation the amplitudes will be constant except for a very slow spontaneous decay. The time evolution to a good approximation will therefore be the oscillatory free evolution i.e. 

Modern NMR spectrometry uses the pulsed Fourier method, in which a carefully shaped pulse of radio-frequency energy, tuned to the characteristic NMR frequency called the Larmor frequency (co), is pumped into the sample. The sample then responds by sending out a very much weaker signal called a free-induction decay (FID). This FID signal appears at the same Larmor resonance frequency but with an amplitude that decays approximately as a decreasing exponential. Depending on a number of experimental parameters, the FID time constant may range from milliseconds to seconds. 

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