Rotational superposition state

Varying other parameters, such as the width of the pulses, also has substantial effect on product control. For example, the effect of exciting more vib-rotational levels in the E electronic state by using a broader pump pulse is shown in Figure1, t 3.27, where AkfJ = 60 cm-1 and A2co = 100 cm-1. The superposition state prepared by the first pulse consists of the v = 14, 15 and J 21,23 levels, where the pulse is] centered at 2, = 803.88 nm, corresponding to the frequency halfway between the,... 

Figure 5.3 Contour plot of I yield [I /(I + I )] for two color photodissociation of a fi CH3I superposition state composed of bound states with vibrational and rotational qua numbers (v, J) — (0, 2) and (1,2) excited with frequencies a>1 = 41,579 cm-1 and 1 41,163 cm-1. Contours increase, in increments of 0.04 from the center well . (Taken Fig. 1, Ref [175].)...

We have previously suggested (9a, 1 0) a rotational isomeric state model to explain the solution thermochromism exhibited by the un-branched alkyl substituted polysilylenes. This model treats the absorption spectrum as a superposition of the spectra of Isolated... 

As previously discussed, if two or more excited eigenstates can combine in absorption with a common ground-state level, then these eigenstates can be excited so as to form a coherent superposition state. The superposition state, in turn, can give rise to quantum beat-modulated fluorescence decays. All this, of course, lies at the heart of the theory of vibrational coherence effects. However, it also implies that the same experimental conditions under which vibrational coherence effects are observed should allow for the observation of rotational coherence effects. That is, since more than one rotational level in the manifold of an excited vibronic state can combine in absorption with a single ground-state ro-vibrational level, then in a picosecond-resolved fluorescence experiment rotational quantum beats should obtain. 

Figure 45. Schematic representation of the preparation and detection of rotational coherence in a molecule. The case depicted corresponds to the linearly polarized excitation (polarization vector ,) of a symmetric top molecule in ground-state ro-vibronic level S0v0 J0K0M0) to those rotational levels of the excited vibronic state 15,1 ,) allowed by the rotational selection rules germane to a parallel-type transition moment. The excitation process creates a superposition state of three rotational levels, the coherence properties of which can be probed by time resolving the polarized fluorescence (polarization it) to the manifold of ground-state ro-vibronic levels S0vf JfKfMfy, or by probing with a second, variably time-delayed laser pulse (polarization...

Now consider the temporal behavior of polarization-analyzed (polarization vector if) fluorescence from this superposition state to all possible rotational eigenstates of the ground vibronic level ISqPj-). This fluorescence decay is... 

The first step in a unimolecular reaction involves energizing the reactant molecule above its decomposition threshold. An accurate description of the ensuing unimolecular reaction requires an understanding of the state prepared by this energization process. In the first part of this chapter experimental procedures for energizing a reactant molecule are reviewed. This is followed by a description of the vibrational/rotational states prepared for both small and large molecules. For many experimental situations a superposition state is prepared, so that intramolecular vibrational energy redistribution (IVR) may occur (Parmenter, 1982). IVR is first discussed quantum mechanically from both time-dependent and time-independent perspectives. The chapter ends with a discussion of classical trajectory studies of IVR. 

States of unimolecular reactants prepared by collisional energization and chemical activation, reactions (1) and (2), can also be viewed as incoherent superposition states. The most specific excitation will occur when the collision partners are in specific vibrational/rotational states and the relative translational energy is highly resolved. However, even for this situation it is difficult to avoid preparing a superposition state since the collisions have a distribution of orbital angular momentum. 

As described above, a pulsed laser with a sufficiently narrow pulse width will overlap a group of vibrational/rotational eigenstates and will prepare a coherent superposition, Eq. (4.5), of some or all of these eigenstates in a molecule. This superposition state evolves in time and is thus identified as (t). Its time dependence is given by the equation of motion (Merzbacher, 1970) ... 

Single-qubit rotations can be accomplished with optical or microwave fields. The initial states of two individual sites a and b can be prepared in a superposition state, for example, using jt/2 Raman pulses. 

A good way to get into this superposition state would be to couple two neighboring rotation states via microwaves, as in Ref. [10]. 

Much of the previous section dealt with two-level systems. Real molecules, however, are not two-level systems for many purposes there are only two electronic states that participate, but each of these electronic states has many states corresponding to different quantum levels for vibration and rotation. A coherent femtosecond pulse has a bandwidth which may span many vibrational levels when the pulse impinges on the molecule it excites a coherent superposition of all tliese vibrational states—a vibrational wavepacket. In this section we deal with excitation by one or two femtosecond optical pulses, as well as continuous wave excitation in section A 1.6.4 we will use the concepts developed here to understand nonlinear molecular electronic spectroscopy. 

A microwave pulse from a tunable oscillator is injected into the cavity by an anteima, and creates a coherent superposition of rotational states. In the absence of collisions, this superposition emits a free-mduction decay signal, which is detected with an anteima-coupled microwave mixer similar to those used in molecular astrophysics. The data are collected in the time domain and Fourier transfomied to yield the spectrum whose bandwidth is detemimed by the quality factor of the cavity. Hence, such instruments are called Fourier transfomi microwave (FTMW) spectrometers (or Flygare-Balle spectrometers, after the inventors). FTMW instruments are extraordinarily sensitive, and can be used to examine a wide range of stable molecules as well as highly transient or reactive species such as hydrogen-bonded or refractory clusters [29, 30]. 

The calculation method and equations presented in the previous sections are for Newtonian fluids such that the flow due to screw rotation and the downstream pressure gradient can be solved independently, that is, via the principle of superposition. Since most resins are highly non-Newtonian, the rotational flow and pressure-driven flow in principle cannot be separated using superposition. That is, the shear dependency of the viscosity couples the equations such that they cannot be solved independently. Potente [50] states that the flows and pressure gradients should only be calculated using three-dimensional (3-D) numerical methods because of the limitations of the Newtonian model. 

Finally, the rules of angular momentum construction can be made as if the system had spherical symmetry. The reason is that the invariance to rotation of the I-frame leads to angular momentum conservation. Once all base states have been constructed, the dynamics is reflected on the quantum state that is a linear superposition on that base. As the amplitudes change in time, motion of different kinds result. 

Although it is possible with the adiabatic following of STIRAP to produce not only complete population transfer but also, through fractional STIRAP [16], any superposition of quantum states 1 and 3, so too is it possible to design a series of rotations that will produce an arbitrary change of polarization. However, in both cases, the full change of variables (quantum state or polarization) is more robust than a partial change. 

In order to check our imaging procedure we have to first stimulate the fluorescence emitted by excited polarized (and unpolarized) Na2 wavepackets. In these simulation we assume that the molecule, which exists initially in a (Xvg,jg) Na2 (X1 5 ) vib-rotational state, is excited by a pulse to a superposition of (xs) vib-rotational states belonging to the Na2(B IIu) electronic-states. 

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