Quantum states coherence

Fig. 2 (a) Populations of the ground electronic state of the adsorbate without delayed dissipation for two vibrational levels r = vg = 0,1, Pg>r and their sum Pg (b) Results with delayed dissipation, versus time. Here the alternating populations of states r = vg = 0,1 show quantum state coherence. 

In the present section, we concentrate on coherent preparation by irradiation with a properly chosen laser pulse during a given time interval. The quantum state at time t may be chosen to be the vibrational ground... 

The present chapter has no ambition to cover all these topics. We focus solely on the information content of the two-pathway coherent control approach, where the energy-domain, single quantum states approach to the control problem simplifies the phase information and allows analysis at the most fundamental level. We regret having to limit the scope of this chapter and thus exclude much of the relevant literature. We hope, however, that this contribution will entice the reader to explore related literature of relevance. 

Nakamura, Y., Pashkin, Y.A. and Tsai, J.S. (1999) Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature, 398, 786-788. 

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. 

A quantum state loses quantum coherence (decoheres) when Sqd wave functions are peaked along classical trajectories. And it decoheres when each trajectory loses quantum coherence with its neighbors. Quantum decoherence is realized when the diagonal term density matrix dominates over the off-diagonal term (fts-... 

To make the ideas sharper consider the case of two quasi degenerate quantum states of the active precursor and successor complexes. The discussion made around equation (57) holds true here too. The activated complex will be the place of a coherent electro-nuclear fluctuation that will go on forever, unless there are quantum states belonging to the relaxation channels of Hc(i) and Hc(j). Note that the mechanisms of excitation to get into the quantum activated complex and those required to relax therefrom are related to the actual rate, while the mechanism of interconversion is closely connected with an... 

One of the possibilities is to replace the evolution of the single-quantum states by the multiple-quantum ones during extended evolution periods. As theoretically predicted by Griffey and Redfield [34] and experimentally demonstrated by Grzesiek and Bax [35], keeping a spin pair in the state of multiple-quantum coherence (MQ) eliminates most of the dipolar contribution to the spin-spin relaxation. With the X-H (X is a heteronucleus) spin pairs, this is partially offset by a higher rate of proton cross-relaxation in the transverse plane with the remote H spins. Since the MQ coherences consist of transverse... 

Bergmann, K., Theuer, H., and Shore, B. W.. 1998. Coherent population transfer among quantum states of atoms and molecules. Rev. Mod. Phys. 1 (3) 1003-25. 

Einstein s laws of absorption and emission describe the operation of lasers. The luminescence of minerals, considered in this book, is a spontaneous emission where the luminescence is independent of incident radiation. In a stimulated emission the relaxation is accomplished by interaction with a photon of the same energy as the relaxation energy. Thus the quantum state of the excited species and the incident photon are intimately coupled. As a result the incident and the emitted photons will have the same phase and propagation direction. The emitted light of stimulated emission is therefore coherent as opposed to the... 

The underlying issue is broader Coherent control was originally conceived for closed systems, and it is a priori unclear to what extent it is applicable to open quantum systems, that is, systems embedded in their ubiquitous environment and subject to omnipresent decoherence effects. These may have different physical origins, such as the coupling of the system to an external environment (bath), noise in the classical fields controlling the system, or population leakage out of a relevant system subspace. Their consequence is always a deviation of the quantum-state evolution (error) with respect to the unitary evolution expected... 

Coherent excitation of quantum systems by external fields is a versatile and powerful tool for application in quantum control. In particular, adiabatic evolution has been widely used to produce population transfer between discrete quantum states. Eor two states the control is by means of a varying detuning (a chirp), while for three states the change is induced, for example, by a pair of pulses, offset in time, that implement stimulated Raman adiabatic passage (STIRAP) [1-3]. STIRAP produces complete population transfer between the two end states 11) and 3) of a chain linked by two fields. In the adiabatic limit, the process places no temporary population in the middle state 2), even though the two driving fields - pump and Stokes-may be on exact resonance with their respective transitions, 1) 2)and... 

As illustrated earlier in the text (Figure 10.5), molecules released from the centrifuge generate an oscillatory Raman signal, characteristic of the coherent rotation with well-defined relative phase relation between the quantum states inside a rotational wave packet. Time-resolved coherent Raman response from a wave packet centered at A = 69 in oxygen is plotted at the bottom of Figure 10.9a. Knowing the wave packet composition from the state-resolved detection discussed above. 

B. A. Hess The reason that macroscopic motions display coherence is that they are in most cases at the classical limit of quantum dynamics. In this case, a suitable occupation of quantum states ensures that quantum mechanical expectation values equal the classical value of an observable. In particular, the classical state of an electromagnetic field (the coherent state) is one in which the expectation value of the operator of the electromagnetic field equals the classical field strengths. 

Here coherence occurs only for three low-lying quantum states. The... 

The surface-hopping trajectories obtained in the adiabatic representation of the QCLE contain nonadiabatic transitions between potential surfaces including both single adiabatic potential surfaces and the mean of two adiabatic surfaces. This picture is qualitatively different from surface-hopping schemes [2,56] which make the ansatz that classical coordinates follow some trajectory, R(t), while the quantum subsystem wave function, expanded in the adiabatic basis, is evolved according to the time dependent Schrodinger equation. The potential surfaces that the classical trajectories evolve along correspond to one of the adiabatic surfaces used in the expansion of the subsystem wavefunction, while the subsystem evolution is carried out coherently and may develop into linear combinations of these states. In such schemes, the environment does not experience the force associated with the true quantum state of the subsystem and decoherence by the environment is not automatically taken into account. Nonetheless, these methods have provided com-... 

Equation (7.75) defines what is meant by a so-called coherent sum of quantum states. The diagonal terms resemble the incoherent sum in Eq. (7.74) the values of the populations cn 2 are, however, determined by the laser pulse. The off-diagonal terms are called interference terms these terms are the key to quantum control. They are time dependent and we use the term coherent dynamics for the motion associated with the coherent excitation of quantum states. A particular simple form of Eq. (7.75) is obtained in the special case of two states. Then... 

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