Coherence creation

Suppose the first pulse resulted in the creation of a phase coherence across the Ai transition between the aa and a/3 states (Fig. 1.44). It is possible to transfer this phase information from the a)3 state to the )3/3 state by applying a selective it pulse across the Xi transition. The two successive pulses would therefore transfer the phase of the aa state to the )8)3 state, with the two states now becoming phase coherent with one another. 

We introduce the eigenstates and eigenvalues for the creation and annihilation operators (coherent states86) ... 

The objective of this NoE is to strengthen research in catalysis by the creation of a coherent framework of research, know-how and training between the various disciplinary catalysis communities (heterogeneous, homogeneous, and biocatalysis) with the objective of achieving a lasting integration between the main European Institutions in this area. IDECAT will create the virtual European Research Institute on Catalysis (ERIC) that is intended to be the main reference point for catalysis in Europe. 

The expectation value of H in the coherent state (7.17) can be evaluated explicitly for any Hamiltonian. However, an even simpler construction of Hd (valid to leading order in N) can be done (Cooper and Levine, 1989) by introducing intensive boson operators (Gilmore, 1981). In view of its simplicity, we report here this construction. If one divides the individual creation and annihilation operators by the square root of the total number of bosons, the relevant commutation relations become... 

As lawn historian Virginia Scott Jenkins concludes, front lawns are the product of two elements the ability and the desire to grow and tend lawn grasses. To say that a coherent lawn aesthetic had been established in the late 1900s and that the land economics of the mid-twentieth century made available the space for its creation and the condition for its desire (Chapter 2) by no means assures... 

The preparation period consists of the creation of a non-equilibrium state and, possibly, of the frequency labeling in 2D experiments. Usually, the preparation period should be designed in such a way that in the created non-equilibrium state, the population differences or coherences under consideration deviate as much as possible from the equilibrium values. During the relaxation period, the coherences or populations evolve towards an equilibrium (or a steady-state) condition. The behavior of the spin system during this period can be manipulated in order to isolate one specific type of process. The detection period can contain also the mixing period of the 2D experiments. The purpose of the detection period is to create a signal which truthfully reflects the state of the spin system at the end of the relaxation period. As always in NMR, sensitivity is a matter of prime concern. 

N. V. Vitanov, K.-A. Suominen, and B. W. Shore. Creation of coherent atomic superpositions by fractional stimulated Raman adiabatic passage. J. Phys. B, 32(18) 4535 546 (1999). 

Figure 6.1 shows simulation of the population dynamics of the two vibronic manifolds. The populations pbv>b and pcw>cw(T) after excitation are calculated for (a) the weak coupling case and (b) the strong coupling case. Figure 6.1 clearly shows the population transfer between the two electronic states due to the creation of the vibronic coherence. 

The interaction between light and matter can be viewed as the creation of a coherent quantum superposition of initial and final electron states that has an associated polarization [3], as shown in Figure 1. The coherence between states with different wave vector requires an intermediate virtual state and the presence of a coherent phonon. A transition between the initial and final states may occur when the coherence of the system is broken either due to the finite width of an optical wave packet or by scattering from the environment. The transition results in the absorption of a photon and the creation of a hot electron-hole pair. Otherwise, the photon is re-radiated with a different phase and, perhaps, polarisation. 

Figure 1. The creation, evolution, and detection of wave packets. The pump laser pulse pump (black) creates a coherent superposition of molecular eigenstates at t — 0 from the ground state I k,). The set of excited-state eigenstates N) in the superposition (wave packet) have different energy-phase factors, leading to nonstationary behavior (wave packet evolution). At time t = At the wave packet is projected by a probe pulse i probe (gray) onto a set of final states I kf) that act as a template for the dynamics. The time-dependent probability of being in a given final state f) is modulated by the interferences between all degenerate coherent two-photon transition amplitudes leading to that final state.

The results in this chapter make clear that a chiral outcome, the enhancement off j particular enantiomer, can arise by coherently encoding quantum interference infqjS mation in the laser excitation of a racemic mixture. The fact that the initial stall displays a broken symmetry and that the excited state has states that are eith jj symmetric or antisymmetric with respect to ah allows for the creation of a si position state that does not have these symmetry properties. Radiatively couplingfhf states in the superposition then allows for the transition probabilities from L and fi t differ, allowing for depletion of the desired enantiomer. 

Figure 2.9. Detail of the 0-0, b-polarized reflectivity at 5 K (cf. Fig. 2.8). The arrow indicates the threshold of creation of 46-cm phonons. Part A is due to reflection from the front face alone, part B to the total reflectivity of incoherent contributions from front and back faces, and part C to the reflectivity resulting from coherent superposition of front and back faces (oscillations).

For the HCCH and HCC segments, which are of particular interest to polyaromatic compounds, high relative sensitivity (0.5 and 0.25) was also predicted for the DEPT2-INADEQUATE pulse sequence (Figure 8 C). The main reason why this pulse sequence performs so well is that it incorporates refocusing of AP proton-carbon coherences prior to the creation of DQ carbon coherences. Its performance is also boosted by a smaller number of pulses (6 H and 7 C vs. 11 H and 10 C) and delays compared to those of the COS-INADEQUATE pulse sequence. 

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