Superposition states preparation

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,... 

Since the two pulses are temporally distinct, it is convenient to deal with their effects consecutively. After the first pulse is over, the superposition state prepared by the E r) pulse is given in first-order perturbation theory as... 

An unresolved absorption spectrum /(w) results from the evolution of P(r) in Eq. (4.6) and, thus, C(t) for a finite time T. The spectrum /(w) and P(f) are still related according to Eqs. (4.16) and (4.23), but the integration limits become T and —T. As (r) and, thus, C(r) are followed for longer times the resolution of /(w) is improved. Consider the preparation of a coherent superposition state prepared by a transform limited pulsed laser as described in section 2.1. For a short pulse width the superposition will contain many eigenstates that is, the number of n in Eq. (4.5) will be larger. If (0 is followed in time by a probe laser, /(w) can be calculated from Eq. (4.23). The... 

The external control parameters are now 0 - 0 and x, which are the relative phase and amplitude ratio due to both the superposition state preparation and subsequent applied fields. The functional form of Eq. (11) prevents analytic determination of the most general conditions under which the yield in channel q=2 is an extremum. However, if the molecule is such that... 

As in classical mechanics, the outcome of time-dependent quantum dynamics and, in particular, the occurrence of IVR in polyatomic molecules, depends both on the Flamiltonian and the initial conditions, i.e. the initial quantum mechanical state I /(tQ)). We focus here on the time-dependent aspects of IVR, and in this case such initial conditions always correspond to the preparation, at a time of superposition states of molecular (spectroscopic) eigenstates involving at least two distinct vibrational energy levels. Strictly, IVR occurs if these levels involve at least two distinct... 

In a first time iirterval of the scheme (A3.13.46), a superposition state is prepared. This step... 

From a theoretical perspective, the object that is initially created in the excited state is a coherent superposition of all the wavefunctions encompassed by the broad frequency spread of the laser. Because the laser pulse is so short in comparison with the characteristic nuclear dynamical time scales of the motion, each excited wavefunction is prepared with a definite phase relation with respect to all the others in the superposition. It is this initial coherence and its rate of dissipation which determine all spectroscopic and collisional properties of the molecule as it evolves over a femtosecond time scale. For IBr, the nascent superposition state, or wavepacket, spreads and executes either periodic vibrational motion as it oscillates between the inner and outer turning points of the bound potential, or dissociates to form separated atoms, as indicated by the trajectories shown in Figure 1.3. 

Control over the a, and production of the desired superposition states can be achieved by several routes. One nice way is to utilize the reactants from an earlier photodissociation step, altering the af by any of a number of coherent control scenarios [2] for this piereactive step. Consider then preparing n, 0) via a prereactive stage in which an adduct AB, made up of a structureless atom A and the molecular fragment B, is photodissociated. The AB is assumed to be initially in a pure state of energy Eg and the photodissociation is carried out with a coherent source. Under these circumstances photodissociation produces B in a linear combination of internal states. For... 

Consider now preparation of the generalized superposition states [Eq. (7.5)] where for simplicity we limit consideration to a superposition of two states. To do so we examine the scattering of A and B, each previously prepared in the laboratory in a superposition state. The wave functions of A and B in the laboratory frame, ij/A and t//B, are of the general form ... 

Further, as discussed in Section 3.1, the inability to control the product ratio by shaping the pulse can be overcome by photodissociating not just one EX) bound . state but a superposition of several bound states )) (as was done, e.g., with bichro-, matic control). Such a superposition state can be created separately by an initial preparation pulse, as in the case of pump-dump control scenario Sections 3.5 and. 4.1). Alternatively, the superposition state can be created by the photolysis pulse itself (by, e.g., a stimulated Raman process), provided that the bandwidth of the -pulse is comparable to the energy spacings between the Ef) levels. r, ... 

The proposed mechanism is thermal excitation of the Rh-C stretch mode causes the CO-stretching mode transition frequency to shift a small amount, Am, as shown in Fig. 7A. During the time period in which the Rh-C mode is excited, the initially prepared CO superposition state pre-cesses at a higher frequency, as indicated by the dashed arrow in Fig. 7A. Thus, a phase error develops. For a small Am and a short r, the phase error is on the order of rAm < 1. In the slow-exchange, weak coupling limit, the pure dephasing contribution to the linewidth from repeated excitation and relaxation of the low-frequency mode is (51,52) ... 

Finally, we should mention the possibility of coherent excitation transfer when the donor-acceptor interaction is strong, but the coupling of the system to the thermal bath is weak. The resulting two-level weakly damped system lends itself to the time-dependent density-matrix approach [33], which is essentially identical to the familiar spin-1/2 treatment in magnetic resonance. Under certain circumstances, coherence effects can be important for singlet energy transfer, because the donor states are populated instantaneously by direct photoexcitation. With a sufficient band width of the excitation source (e.g., ultrashort femtosecond pulses), quantum superposition states can be prepared in a coherent fashion even in condensed media at room... 

Here we analyze a measurement-assisted generation of a superposition state. This is in line with the intentions of earlier proposals such as preparation by means of continuous photodetection, [Ogawa 1991], or via state reduction in a Mach-Zehnder interferometer containing a Kerr medium, [Gerry 1999], In order to implement the Zeno-limit evolution given by Eq. (85), we assume in the Hamiltonian (63) for simplicity 6 = 0 and the parameter c to be sufficiendy large such that for some detected ancilla state I I o) the condition ( I ol l I o) = 7oo = cos 0 = — c-1 a can be fulfilled. This yields for... 

Gerry [29] has proposed a similar method based on a dispersive interaction of the atoms with a cavity mode prepared in a coherent state a). The atoms enter the cavity in superposition states... 

However, the preparation of the superposition state requires that the atoms have different transition frequencies. Beige et al. [32] have proposed a scheme in which the superposition state <1>) can be prepared in a system of two identical atoms placed at fixed positions inside an optical cavity. 

This result is a generalization of the 100% modulation of b-type decays in the two-level case. Just as in the two-level case, the result ensures that Iy(0+) = 0 when y, a. This, in turn, is a reflection of the fact that only a> contributes to the initially prepared superposition state, T(t)>. 

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...

Holme and Hutchinson suggest tuning two, or several, lasers to nearly degenerate molecular eigenstates. By adjusting the strength of the field at each frequency, they are able to combine these two molecular eigenstates with arbitrary coefficients, and thereby prepare a desired superposition state. These workers have focused on applications to local mode overtones, where field-free evolution would lead to relaxation into an intramolecular bath. 

Figure 36. Comparison of Tannor-Rice, Holme-Hutchinson. and Brumer-Shapiro selectivity schemes, (a) Tannor-Rice scheme uses two pulses, where each pulse is wide enough in frequency to excite a superposition of many vibrational levels, (h) Holme-Hutchinson scheme uses two monochromatic photons to prepare a superposition state on the excited-state surface (c) Brumer-Shapiro scheme uses one photon to prepare a superposition state on the ground-state surface then two additional photons to excite the superposition state to the excited state surface. 

Quantum-beat spectroscopy (see Sections 9.2.1, 9.2.2 and 9.3.2 and reviews by Lombardi, 1988, and by Hack and Huber, 1991) requires preparation of a coherent superposition state, > composed of two eigenstates, +, M)... 

The word coherence has also been used in the description of radiationless processes (RP) in molecules in the gasphase. In the so-called molecular eigenstate basis set-description of RP, the initial state prepared after flash excitation can be written as a superposition of quasistationary states ... 

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. 

---