Coherent superpositions of states

We use a7r/2 — vr — vr/2 pulse sequence to coherently divide, deflect and finally recombine an atomic wavepacket. The first vr/2 pulse excites an atom initially in the l,p) state into a coherent superposition of states l,p) and 2,p + hkeff). If state 2) is stable against spontaneous decay, the two parts of the wavepacket will drift apart by a distance hkT/m in time T. Each partial wavepacket is redirected by a vr pulse which induces the transitions... 

From the point of view of the study of dynamics, the laser has three enormously important characteristics. Firstly, because of its potentially great time resolution, it can act as both the effector and the detector for dynamical processes on timescales as short as 10 - s. Secondly, due to its spectral resolution and brightness, the laser can be used to prepare large amounts of a selected quantum state of a molecule so that the chemical reactivity or other dynamical properties of that state may be studied. Finally, because of its coherence as a light source the laser may be used to create in an ensemble of molecules a coherent superposition of states wherein the phase relationships of the molecular and electronic motions are specified. The dynamics of the dephasing of the molecular ensemble may subsequently be determined. 

Ultrafast laser excitation gives excited systems prepared coherently, as a coherent superposition of states. The state wave function (aprobabihty wave) is a coherent sum of matter wave functions for each molecule excited. The exponential terms in the relevant time-dependent equation, the phase factors, define phase relationships between constituent wave functions in the summation. 

The matter wave function is formed as a coherent superposition of states or a state ensemble, a wave packet. As the phase relationships change the wave packet moves, and spreads, not necessarily in only one direction the localized launch configuration disperses or propagates with the wave packet. The initially localized wave packets evolve like single-molecule trajectories. 

This experimental work on the dissociation of excited Nal clearly demonstrated behavior one could describe with the vocabulary and concepts of classical motions.The incoherent ensemble of molecules just before photoexcitation with a femtosecond laser pump pulse was transformed through the excitation into a coherent superposition of states, a wave packet that evolved as though it represented a single vibrationally activated molecule. 

B. Kohler My question to T. Softley ties in to one of the major themes of the meeting, namely coherence. In your presentation you briefly mentioned that it may be important to consider an initially coherent superposition of states in the preparation step of experiments on highly excited Rydberg states. Several groups have now prepared coherent electronic wavepackets using picosecond (and shorter) pulses. Would this kind of an initial state be useful for any of the classes of pulsed-field ionization experiments that you have described ... 

In spite of the apparent obviousness of the beat effect in optical radiation at pulsed excitation, it was only registered and studied comparatively recently. At the beginning of the 1960s Aleksandrov [3] and, independently, Dodd and coworkers [119] discovered beats in atomic emission. It may be pointed out that this, and the related phenomenon of beat resonance, was predicted by Podgoretskii [313], as well as by Dodd and Series [118]. The phenomenon was treated on the basis of well-known fundamental concepts on coherent superposition of states, and was named accordingly quantum beats. These ideas are amply expounded in reviews and monographs [4, 5, 6, 71, 96, 120, 146, 182, 188, 343, 348, 388]. 

Recent experimental studies on interference effects in solution, and on collisional vibrational energy transfer between molecules in solution, provide some insight into the molecular time scales of these relaxation events. For example [171], the time scale for transfer of population to die vibrational modes in liquid CH3OH is on thd order of 5 to 15ps [172], Further, studies of the preparation of coherent superpositions of states in solution show that phase coherences of molecules exist in solution for time scales greater than 100 fs [173, 174], -- i... 

The target part of the entrance-channel state Ovoko) is a coherent superposition of magnetic substates defined by an arbitrary choice of coordinate frame. It is transferred into another fully-coherent superposition of states in the exit channel ivjkj). The scattering amplitude is defined as a generalisation of (4.46), so that its absolute square is the corresponding... 

D. Resonant Processes—Creation of Coherent Superposition of States—Half-Scrap... 

Transfer to a Coherent Superposition of States VI. State-Selectivity by Bichromatic Pulses... 

If one takes an area different from ji, it leads to a final coherent superposition of states. For example, in the case of a one-photon process, one has [using formula (254) with a = 0 and fl = po ... 

When the processes involve a zero-field resonance, one has to add the ingredient of lifting of degeneracy. This means that we have to consider the dynamics starting (or ending) near the conical intersection in a direction not parallel to the Cl = 0-plane. This can be seen in Fig. 6 where the surfaces of Fig. 2 have been redrawn for positive detunings (case of a one-photon resonance). When the dynamics starts this way, it is characterized by two adiabatic paths, one on each surface. They will lead in general to coherent superpositions of states. 

We analyze two kinds of paths which, starting in state 11 0), will lead to a coherent superposition of states ... 

This process leading to a coherent superposition of states has been suggested in Ref. 63 and named half-scrap, since it is very similar to the scrap process except it starts (or ends) in resonance. 

Formally, we describe the state of the particle during the propagation as a coherent superposition of states, in particular of position states, that are classically mutually exclusive. A classical object will either take one or the other path with certainty. A quantum object cannot be said to do that since the in-... 

An essential property of such a coherently coupled three-level system is the existence of a dark state D) as an eigenstate of the system. This state generally occurs if both laser fields have the same resonance detuning with respect to the corresponding transition, that is, if the two-photon demning is zero. The state is dark in the sense that it is decoupled from the excited state e) and thus not influenced by its radiative decay. The dark state can be understood as a coherent superposition of state a) and state b),... 

The central point to simulate decoherence is to generate independent MD simulations on the PESs of the two electronic states of interest. To have a nonzero overlap at time 1 = 0 (a coherent superposition of states), these MD simulations will share the same initial conditions (positions and momentum). In later times the classical nuclei will feel different forces on the two PESs and will diverge over time. Once the two trajectories have been carried out, the function can be calculated using the values of xy, X2j, Py, xy, and IsK 2 evaluated along the diverging trajectories. This operation is repeated with different initial conditions to sample the desired thermodynamics ensemble. 

Nondiagonal terms in Equation [14] produce a macroscopic polarization Pjj(t) departs from zero at equilibrium and includes an oscillatory term at the frequency co y. The existence of a nondiagonal term Pij(t) 0 is linked to the creation of a coherent superposition of states i and / due to the perturbation. This coherence is broken through the interaction with the molecules of the bath, with a rate constant of the order of F y= I/T2. Usually this dephasing is much faster than the energy relaxation and T2 Ti. 

Many exciting questions remain in gas phase reaction dynamics. The goal of bond and state selective chemistry is still not fully realized, although this type of control has been observed in the local mode H-I-H20 system [18, 19]. An interesting new approach for chemical control involves preparing reactants in a coherent superposition of states [24], for which some theory already exists [25]. In applying these techniques to complex reactive systems, one hopes that the hard won coherence is not lost before the reaction proceeds. 

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