Coherence Level Scheme

The concept of longitudinal and transverse magnetization must be extended if the discussion of multi-pulse experiments is to include multiple quantum states and coherence transfer. The concept of coherence, the transition between two eigenstates, is preferable to using the expression transverse magnetization. Each transition may involve 

6 the coherence order of different spin system states are listed for a two-spin system. 

For completeness the transverse (Iix, Iiy, l2x. I2y) longitudinal magnetization are explicitly listed in Table 2.6 although the later discussion of coherences does not differentiate between these states or any other coherence state of the same order. Coherence order or more precisely the coherence pathway is an important concept in the design of a phase program or gradient selection used in pulse sequences. In addition to simple coherence suppression in ID sequences, these procedures are also used for frequency discrimination and for the measurement of pure absorption spectra in 2D experiments. 

Coherence transfer pathways (CT pathway) fall in the domain of spherical product operators instead of CARTESIAN operators. Before proceeding any further it is recommended to a necomer to read section 2.2.2 and for addition information references [2.20 - 2.31]. To illustrate the use of coherence transfer pathways in coherence selection, three pulse sequences will be examined. 

The one-pulse experiment A one-pulse experiment consists of an excitation pulse, often with a 90° tilt angle and phase 0 or 2 for the first two scans. According to the conventions in section 2.2 the phase values corresponds to the x-axis (phase value 0, phase shift cp = nil) and the y-axis (phase value 1, phase shift (p = 0). The coherence 

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Fig. 2.4 Alternative coherence level schemes for the heteronuclear polarization transfer step of a l C, IR spin system.

Coherence level scheme of a ID l C, IH HMQC pulse sequence using the p scale. 

For even-even ground state bands the additive constant is 1 /2, but in general it is not straightforward to deduce reliable spins through this method [29]. However, this approach is often usefiil to give an indication of the expected angular momentum and can be used in conjunction with other experimental constraints to construct a coherent level scheme. 

Figure 5 JO. The coherence level diagram for a single-pulse ID experiment. The solid line represents the coherence transfer pathway of the detected magnetisation. The dotted line represents the mirror image pathway that is rejected by the quadrature detection scheme.

This section examines the theoretical approach to pulse sequences using the density matrix method and product operator formalism. It also looks at the pictorial representations of coherence levels and energy level schemes. This section summarizes the terms and methods that provide the arguments for a particular pulse sequence layout. The concepts introduced in this section are used in chapter 5 when discussing possible improvements to a specific pulse sequence. 

Figure B2.3.8. Energy-level schemes describing various optical methods for state-selectively detecting chemical reaction products left-hand side, laser-induced fluorescence (LIF) centre, resonance-enhanced multiphoton ionization (REMPI) and right-hand side, coherent anti-Stokes Raman spectroscopy (CARS). The ionization continuum is denoted by a shaded area. The dashed lines indicate virtual electronic states. Straight arrows indicate coherent radiation, while a wavy arrow denotes spontaneous emission.

In molecules, as noted by de Vries and Wiersma, the application of free induction decay to study optical dephasing may be frustrated by the presence of an intermediate triplet state. The level scheme, which is representative for most molecules with an even number of electrons, is shown in Fig. 26. For an applied laser field E =EQCOs t-k ), that is resonant with the (2 <- 1) transition, we may write, in the RWA approximation, the following steady-state density matrix equations, which describe the coherent decay after laser frequency switching ... 

Fig. 7.9 (a) Level scheme illustrating the coherent excitation of levels 11) and 2) by a short pulse, (b) Quantum beats observed in the fluorescence decay of two coherently excited levels. Insert Fourier spectrum l o)) of (b) with o) 2 = Ejh... 

Fig. 7.15 STIRAP (a) A-level scheme (b) coherent excitation of high-lying levels (c) spatial overlay of pump and Stokes pulses (d) populations (N(t)) of the three levels (e) experimental arrangement (f) measurement of the population N3 by LIP [888]...

For a theoretical explanation of the signal we consider a simplified level scheme with four sublevels in the ground and four in the excited state (see Fig. 1). This corresponds to an atomic system with angular momentum J = Y and a nuclear spin I =. A complete treatment of the Cs case would require to calculate with 32 sublevels in minimum. However, we can expect that the reduced level system already includes the essential coherence phenomena and in principle shows the same structure only with slightly modified amplitudes for the oscillations. 

This chapter continued the debate on the relation between holistic approaches to reduction (Chap. 8), with an eye on the relation between reduction and forms of unification, and it applied the explication proposed here to issues such as reduction and grounding, reduction and intervention, reduction and physicalism, and reduction and the notion of scientific levels. One notion of a scientific level is tied to modes of presentations, in a way that can, again, be illuminated referring to property structures. Unification is to be expected in reductions We subsume apparently different phenomena under one coherent conceptual scheme, achieve ontological unification and epistemic as well as explanatory unification. Reduction is a cognate, or a version of grounding, and knowledge of true reduction statements has an impact on the set of intended interventions we have access to. 

Fig. 4. Energy level scheme, transition frequencies, and coherence transfer in pulsed ELDOR experiments, (a) Sitnation before the pump pulse, (b) Situation after the pump pulse.

Fig.11.23a,b. Quantum beat spectroscopy, (a) Level scheme illustrating coherent excitation of levels 1 and 2 with a short broad-band pulse, (b) Fluorescence intensity showing a modulation of the exponential decay... 

Just as above, we can derive expressions for any fluorescence lifetime for any number of pathways. In this chapter we limit our discussion to cases where the excited molecules have relaxed to their lowest excited-state vibrational level by internal conversion (ic) before pursuing any other de-excitation pathway (see the Perrin-Jablonski diagram in Fig. 1.4). This means we do not consider coherent effects whereby the molecule decays, or transfers energy, from a higher excited state, or from a non-Boltzmann distribution of vibrational levels, before coming to steady-state equilibrium in its ground electronic state (see Section 1.2.2). Internal conversion only takes a few picoseconds, or less [82-84, 106]. In the case of incoherent decay, the method of excitation does not play a role in the decay by any of the pathways from the excited state the excitation scheme is only peculiar to the method we choose to measure the fluorescence (Sections 1.7-1.11). 

In examining numerical approximations it is as well to bear in mind the general qualitative conclusion of our brief examination of symmetry constraints. In broad terms the result was the simpler the model the more severe the effect of any constraint on the variation principle. This result cannot be carried over directly and used in numerical work since numerical approximation schemes can rarely be brought into a sufficiently coherent logical and mathematical form for analysis. Nevertheless it seems likely that this result can be used as a guideline — a rule of thumb . We therefore expect that the imposition of formal constraints and consistency requirements (derived from a higher level of approximation or the exact solution) on numerical approximation schemes is likely to have far-reaching consequences — particularly on the... 

Accurate measurements of the frequency-resolved transverse spin relaxation T2) of Rb NMR on single crystals of D-RADP-x (x = 0.20, 0.25, 0.30, 0.35) have been performed in a Bq field of 7 Tesla as a function of temperature. The probe head was placed in a He gas-flow cryostat with a temperature stability of 0.1 K. To obtain the spin echo of the Rb - 1/2 -o-+ 1/2 central transition we have used the standard (90 - fi - 180y -ti echo - (2) pulse sequence with an appropriate phase-cycling scheme to ehminate quadrature detection errors and unwanted coherences due to pulse imperfections. To avoid sparking in the He gas, the RF-field Bi had to be reduced to a level where the 7T/2-pulse length T90 equalled 3.5 ps at room temperature. 

G. Gerber The o>3 = 3 and w scheme has been experimentally explored by Dan Elliott using CW laser radiation and by Bob Gordon using nanosecond radiation. I would like to know the viewpoint of Prof. Rice about what we would learn additionally by using ultrafast laser pulses. In ultrashort laser excitation, the individual levels under consideration are coherently coupled. 

Prof. H. Neusser introduced the term coherent ionization dip. Talking about the coherence in an ionization process we should distinguish two different schemes. One scheme is based on two-frequency coherent control of a two-level A scheme (see Fig. 1), which was discussed by Prof. H. Neusser. 

If J" —> J excitation is accompanied or followed by deexcitation J —> J" in a stimulated emission process (SEP), then the population efficiency of the level can be increased considerably. It is now known [248, 347] that the process might be made more effective by applying the A-configuration scheme in which the first-step (J" — J ) excitation pulse is applied after the second-step (J — J") pulse which, at first glance, seems surprising. This process is called stimulated Raman scattering by delayed pulses (STIRAP). The population transfer here takes place coherently and includes coordination of the Rabi nutation phase in both transitions. 

Figure 1 Schematic representation of a time-resolved coherent Raman experiment, (a) The excitation of the vibrational level is accomplished by a two-photon process the laser (L) and Stokes (S) photons are represented by vertical arrows. The wave vectors of the two pump fields determine the wave vector of the coherent excitation, kv. (b) At a later time the coherent probing process involving again two photons takes place the probe pulse and the anti-Stokes scattering are denoted by subscripts P and A, respectively. The scattering signal emitted under phase-matching conditions is a measure of the coherent excitation at the probing time, (c) Four-photon interaction scheme for the generation of coherent anti-Stokes Raman scattering of the vibrational transition.

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