Next, quantum-classical correspondence in intrinsic decoherence dynamics is examined via purities and reduced density matrices in both the position and energy representations. Dependence of the correspondence on the nature of the coupling potentials and on the initial conditions are discussed. Decoherence effects on quantum and classical dynamics in reactive scattering problems are investigated. Through the study of dynamics of the isotopic analogues of the collinear H + H2 reaction and transmission over simple one-dimensional barrier potentials, the role of decoherence in improving quantum-classical correspondence is identified with suppressing resonance and tunnelling. Finally, the efficiency of 1+3 photon phase control in the presence of decoherence effects phase is carefully examined in several model cases which include from a population inversion in a two-level bound system to IBr photodissociation. Further, the ways to overcome the control loss caused by dephasing are discussed.
Next, quantum-classical correspondence in intrinsic decoherence dynamics is examined via purities and reduced density matrices in both the position and energy representations. Dependence of the correspondence on the nature of the coupling potentials and on the initial conditions are discussed. Decoherence effects on quantum and classical dynamics in reactive scattering problems are investigated. Through the study of dynamics of the isotopic analogues of the collinear H + H2 reaction and transmission over simple one-dimensional barrier potentials, the role of decoherence in improving quantum-classical correspondence is identified with suppressing resonance and tunnelling. Finally, the efficiency of 1+3 photon phase control in the presence of decoherence effects phase is carefully examined in several model cases which include from a population inversion in a two-level bound system to IBr photodissociation. Further, the ways to overcome the control loss caused by dephasing are discussed.
Decoherence effects on quantum and classical dynamics in reactive scattering are examined using a Caldeira-Leggett type model. Through a study of dynamics of the collinear H+H2 reaction and the transmission over simple one-dimensional barrier potentials, we show that decoherence leads to improved agreement between quantum and classical reaction and transmission probabilities, primarily by increasing the energy dispersion in a well defined way. Increased potential nonlinearity is seen to require larger decoherence in order to attain comparable quantum-classical agreement.
Decoherence effects on quantum and classical dynamics in reactive scattering are examined using a Caldeira-Leggett type model. Through a study of the dynamics of the collinear H + H2 reaction and the transmission over simple one-dimensional barrier potentials, we show that decoherence leads to improved agreement between quantum and classical reactions and transmission probabilities, primarily by increasing the energy dispersion in a well-defined way. Increased potential nonlinearity is seen to require larger decoherence in order to attain comparable quantum-classical agreement.
In this thesis, we discuss the possibilities for suppression of decoherence, the loss of purity in an open quantum system, and the related process of dephasing. In the first chapter, we review the literature on the subject of open system dynamics, decoherence and methods of decoherence suppression. In the second chapter, we focus on the specific case of a rotationally hot diatomic molecule as an example of an open quantum system, where molecular vibrational wavepackets are subject to dephasing due to rovibrational coupling. We report analytical and numerical results addressing whether the dephasing rate can be controlled by adjustment of the initial wavepacket phases. It appears that over long timescales, phase-only control is not possible, but for earlier timescales the possibility of phase-only control of dephasing remains. In addition, we point out that the time-dependence of the dephasing process depends significantly upon the degeneracy of the rotational environment states. In the final chapter, we discuss the same system, but apply a qualitatively different method of dephasing suppression based on the nonlinear resonance effect in a driving field. We extend previous work on the topic (Shapiro et al. [1]) by considering the effect of using a train of laser pulses as the driving field, in place of a two-colour continuous-wave laser field. We demonstrate that the pulse train method can be more effective at suppressing dephasing than the two-colour CW case.
Tunneling is a supreme quantum effect. Every introductory text [1] on quantum mechanics gives the paradigm example of a particle tunneling through a one-dimensional potential barrier despite having a total energy less than the barrier height. Indeed, the reader typically works through a number of exercises, all involving one-dimensional potential barriers of one form or another modeling several key physical phenomena ranging from atom transfer reactions to the decay of α-particles [2]. However, one seldom encounters coupled multidimenisonal tunneling in such texts since an analytical solution of the Schro¨dinger equation in such cases is not possible. Interestingly, the richness and complexity of the tunneling phenomenon manifest themselves in full glory in the case of multidimensional systems [3]. Thus, for instance, the usual one-dimensional expectation of increasing tunneling splittings as one approaches the barrier top from below is not necessarily true as soon as one couples another bound degree of freedom to the tunneling coordinate. In the context of molecular reaction dynamics, multidimensional tunneling can result in strong mode-specificity and fluctuations in the reaction rates [4]. In fact, a proper description of tunneling of electrons and hydrogen atoms is absolutely essential [5,6] even in molecular systems as large as enzymes and proteins. Although one usually assumes tunneling effects to be significant in molecules involving light atom transfers, it is worth pointing out that neglecting the tunneling of even a heavy atom like carbon is the difference between a reaction occurring or not occurring. In particular, one can underestimate rates by nearly hundred orders of magnitude [7]. Interestingly, and perhaps paradoxically, several penetrating insights into the nature and mechanism of multidimensional barrier tunneling have been obtained from a phase-space perspective [8,9]. The contributions by Creagh, Shudo and Ikeda, and Takahashi in the present volume provide a detailed account of the latest advances in the phasespace-based understanding of multidimensional barrier tunneling.
The famous Nils Bohr's quantum-classical correspondence principle states that the classical mechanics is a limiting case of the more general quantum mechanics. This implies that ``under certain conditions" quantum laws of motion become equivalent to classical laws. One of the conditions is fairly obvious: the corresponding classical action should be very large as compared with the Planck's constant. But this condition is not sufficient. Suppression of effects of quantum interference ("decoherence") is the phenomenon of primary importance for understanding of the Bohr's principle. Being, in essence, of quite general nature, this problem takes on special significance in the case of non-linear classically chaotic quantum systems. Whereas the rapid decay of phase correlations is an underlying feature of the classical dynamical chaos, the "quantum chaos" by itself is not capable of destroying the quantum phase coherence. Strictly speaking, any initially pure quantum state remains pure during an arbitrary long unitary evolution. Basically, formation of incoherent mixed states (decoherence) results only from the process of preparation of a mixed initial state or interaction with a noisy environment. Just the decoherence brigdes the quantum and classical worlds. Peculiarities of the time behavior of Peres fidelity, state purity, Shanon and von Neumann entropies are analyzed in detail. We demonstrate the ways the decoherence shows up in periodically driven systems that can be associated with Ramsey-type interferomentry experiments with ion traps. Finally, decoherence in ballistic electron quantum transport caused by interaction with a disordered environment is considered.
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular, the classicality of early-time intrinsic decoherence dynamics is explored analytically using a second-order perturbative treatment, and an interesting connection between decoherence rates and the stability nature of classical trajectories is revealed in a simple approximate classical theory of intrinsic decoherence dynamics. The results offer deeper insights into decoherence, dynamics of quantum entanglement, and quantum chaos.