Multiple-Quantum Direct Detection

After briefly considering the relevant results pertinent to multiple-quantum direct detection (Sec. 7.2.1), we derive the combination device response for the general multiple-quantum photomixing process (including the important two-quantum case) in Section 7.12. In Section 7.2.3, we obtain the SNR for a receiver using a multiphoton optical heterodyne device, and compare it with the SNR for conventional optical heterodyne detection. The results of a two-photon experiment are presented in Section 7.2.4, while a suggested setup for future experiments, as well as the applicability of the scheme in general, is reserved for Section 7.2.5. 

The ordinary photoeffect was discovered by Hertz in 1887 and explained in terms of the absorption of a single quantum of light by Einstein in his now famous work published in 1905 [7.17], It was not until 1959, however, that the relationship between the statistics of an arbitrary incident radiation field and the emitted photoelectrons was firmly established by Mandel [7.18]. Consideration of the general photodetection process in terms of quantum-electrodynamic coherent states of the radiation field was undertaken by Glauber [7.19] in 1963, and by Kelley and Kleiner [7.20] in 1964, and provides a convenient starting point for calculations involving multiple-photon as well as single-photon absorptions. 

Multiple-quantum photoemission, being a higher-order effect, is most easily observed in the absence of ordinary (first-order) photoemission. For the two- 

Theoretical work has focused on two aspects of the problem perturbation theory and other calculations of the transition probabilities in the material, and the effect on the transition probability of the statistical nature of the radiation field. Makinson and Buckingham [7,29] were the first to predict the second-order effect and calculate its magnitude based on a surface model of photoemission this work was expanded by Smith [7.30], Bowers [7.31], and Adawi [7.32], The analogous volume calculation was performed by Bloch [7.33] and later corrected by Teich and Wolga [7.24, 25], 

All of the models predict a two-quantum dc photocurrent (expressed in amperes) proportional to the square of the incident radiation power P and inversely proportional to the irradiated area A. Using the results of a number of authors [7.24, 25, 30-33], we can therefore write the double-quantum dc photocurrent as 

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HMQC //ctcronuclear multiple quantum coherence. A proton-detected, 2-D technique that correlates protons to the carbons they are directly attached to. 

Heterocorrelations can be detected both in direct and reverse modes. In the latter mode, dramatic enhancements of sensitivity can be achieved owing to the larger sensitivity of protons with respect to heteronuclei. In the most common heterocorrelation pulse sequences for reverse detection, called heteronuclear multiple quantum coherence (HMQC) (Fig. 8.2G) [25,26], H-I3C MQ (multiple quantum) coherence is generated by first applying a 90° pulse on protons and, after a time t chosen equal to 1/2 J[j, by applying a 90° pulse on carbon (Fig. 8.19). 

The second 90° 13C pulse converts the ZQC and DQC back into antiphase H SQC, which is refocused by the final 1/(2J) delay just as it is in the HSQC experiment. This is an important theme that occurs in many of the more sophisticated NMR experiments multiple-quantum coherences (DQC and ZQC) cannot be directly observed, but they can be created from SQC, allowed to precess, and converted back to measurable SQC. The multiple-quantum coherences can be detected then, but only indirectly. Multiple quantum coherence is essential to the DQF-COSY and DEPT experiments as well, so even though it is difficult to understand it is very important in modern NMR and cannot be ignored. 

The sensitivity gain of proton detected Heteronuclear Multiple-Quantum Coherences (HMQ.C) experiments, as compared with direct heteronuclear detected ones and with polarization transfer techniques like INEPT [22-24] using heteronuclear detection, can be calculated [27,28] for the Sn, Sn and Sn isotopes (Table 3). 

It has been pointed out that the central ( 2, transition does not experience any first-order quadrupole interaction. The absence of first-order broadening effects is a general property of symmetric (m, - m) transitions. There are cases where this can be a distinct advantage, the most direct instance being for integer spin nuclei (e.g. D and both 1=1) where there is no ( /2, — /2) transition. The main problem is to excite and detect such higher-order transitions, for which there are two separate approaches. The sample may either be irradiated and detected at the multiple quantum frequency (called overtone spectroscopy) or the MQ transition can be excited and a 2D sequence used to detect the effect on the observable magnetisation. 

Connectivity information and spectral editing may be performed by combining crosspolarization (CP) and MQMAS. These include direct CP from a spin-j to the quadrupolar spin and subsequently its detection with MQMAS scheme. CP can be performed by polarizing either the CT of the quadrupolar nucleus followed by an inverse split- MQMAS scheme, allowing the incorporation of FAM pulses,or by directly polarizing the multiple-quantum transitions during the CP contact time. ° °... 

The transverse magnetisation we observe directly in an NMR experiment is known as single quantum coherence. Multiple quantum coherence, however, cannot be directly observed because it induces no signal in the detection coil. For multiple quantum coherence to be of use to us, it must be transferred back into signal quantum coherence by the action of rf pulses. The concept of coherence is developed further in Chapter 5. 

Is the probe direct, or inverse The former is good for direct observation with or without INEPT enhancement. The latter will give poor signaTto-noise in direct experiments since the sample does not fill the coil space, but is much preferred for indirect detection via, for example, a heteronuclear multiple quantum coherence (HMQC) or heteronuclear single quantum coherence (HSQC) experiment. 

The inverse-detected 2D NMR experiments that have been discussed to this point have all been discrete, single-purpose experiments, e.g. correlating protons with their directly bound heteronucHde (typically or N). There are another class of inverse-detected 2D NMR experiments that are generally referred to as hyphenated 2D experiments. These are experiments that first establish one type of correlation, followed by an additional experiment segment that then pursues a further spectroscopic task. Predecessors of the inverse-detected variants of these experiments were the HC-RELAY (proton—carbon heteronuclear relayed coherence transfer) experiments pioneered by Bolton [151—155]. Examples of these include, but are by no means hmited to HXQC-COSY and -TOCSY [156—158], -NOESY [159], -ROESY [160], and more recent gradient variants [161] etc., where X = S (single) or M (multiple) quantum variants of the experiments. 

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