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arXiv:1006.3123

Distinguishability and Chiral Stability: Effects of Decoherence and Intermolecular Interactions

Heekyung Han, David M. Wardlaw

Published Jun 16, 2010• 0 citations
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Abstract

We examine the effect of decoherence and intermolecular interactions (chiral discrimination energies) on the chiral stability and the distinguishability of initially pure versus mixed states in an open chiral system. Under a two-level approximation for a system, intermolecular interactions are introduced by a mean-field theory, and interaction between a system and an environment is modeled by a continuous measurement of a population difference between the two chiral states. The resultant equations are explored for various parameters, with emphasis on the combined effects of the initial condition of the system, the chiral discrimination energy and the decoherence. We focus on factors affecting the distinguishability as measured by population difference between the initially pure and mixed states and on the chiral stability as measured by the purity decay.

DOI
10.48550/arxiv.1006.3123

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We examine the effect of decoherence and intermolecular interactions (chiral discrimination energies) on the chiral stability and the distinguishability of initially pure versus mixed states in an open chiral system. Under a two-level approximation for a system, intermolecular interactions are introduced by a mean-field theory, and interaction between a system and an environment is modeled by a continuous measurement of a population difference between the two chiral states. The resultant equations are explored for various parameters, with emphasis on the combined effects of the initial condition of the system, the chiral discrimination energy and the decoherence. We focus on factors affecting the distinguishability as measured by population difference between the initially pure and mixed states and on the chiral stability as measured by the purity decay.
We examine the effect of decoherence and intermolecular interactions (chiral discrimination energies) on the chiral stability and the distinguishability of initially pure versus mixed states in an open chiral system. Under a two-level approximation for a system, intermolecular interactions are introduced by a mean-field theory, and interaction between a system and an environment is modeled by a continuous measurement of a population difference between the two chiral states. The resultant equations are explored for various parameters, with emphasis on the combined effects of the initial condition of the system, the chiral discrimination energies, and the decoherence in determining: the distinguishability as measured by a population difference between the initially pure and mixed states, and the decoherence process; the chiral stability as measured by the purity decay; and the stationary state of the system at times long relative to the time scales of the system dynamics and of the environmental effects.
We examine how initial coherences in open chiral systems affect distinguishability of pure versus mixed states and purity decay. Interaction between a system and an environment is modeled by a continuous position measurement and a two-level approximation is taken for the system. The resultant analytical solution is explored for various parameters, with emphasis on the interplay of initial coherences of the system and dephasing rate in determining the purity decay and differences in the time evolution of pure versus mixed initial states. Implications of the results for several fundamental problems are noted.
We study the tunnel dynamics of a chiral molecule between its left (L) and right (R) conformations, under the global effect of collisional decoherence together with the effect of a mean-field generated by the environment where an energetic difference, K, between homochiral and heterochiral interactions is assumed. We show that this decoherence leads unavoidably to equal populations of the L and R chiral conformations even for a high enough value of K which tends to keep localized an initial chiral state. However, we also show that K contributes to the stabilization of an initial L or R state for times that could be many orders of magnitude larger than the tunneling time, in the case the decoherence rate is much greater than the tunneling rate. In this case, an estimation of this stabilization time and a critical tunneling time is made. Even in the case in which the tunneling rate is greater than the decoherence rate, the effect of K is to keep localized the initial chiral state for times greater than the tunneling time. A possible slight chiral asymmetry is also considered.
In the mean-field theory, the stabilization of chiral molecules is understood as a quantum phase transition where the mean-field ground state of molecules changes from the achiral eigenstate of the molecular Hamiltonian to one of the degenerated chiral states due to the increase of the intermolecular interaction. Starting from the many-body Hamiltonian of the molecular gases with electric dipole-dipole interactions, we give static Gross-Pitaevskii equations without free parameters in the vibrational dimension to explore the achiral-chiral transitions of chiral molecules. We find that the achiral-chiral transitions can be classified into two categories: in one category the mean-field ground state changes continuously with the increase of the intermolecular interaction, in the other category the mean-filed ground state changes discontinuously. In order to summarize our results, we give the mean-field phase diagram of the achiral-chiral transitions.
In the mean-field theory, the stabilization of polar chiral molecules is understood as a quantum phase transition where the mean-field ground state of molecules changes from the achiral eigenstate of the molecular Hamiltonian to one of the degenerated chiral states as the increase of the intermolecular interaction. Starting from the many-body Hamiltonian of the molecular gases with electric dipole-dipole interactions, we give the static nonlinear Schr\"odinger equations without free parameters to explore the achiral-chiral transitions of polar chiral molecules. We find that the polar chiral molecules of different species can be classified into two categories: At the critical point for the achiral-chiral transition, the mean-field ground state changes continuously in one category and changes discontinuously in the other category. We further give the mean-field phase diagram of the achiral-chiral transitions for both two categories.
We study in the framework of the Schrodinger equation the effect of intermolecular interactions on the tunneling racemization of the active molecule. The active molecule is assumed as a two-level system and the left-right isomerism is viewed in terms of a double-bottomed harmonic potential well. The active molecule is assumed to be embedded in a gas, liquid or solid, submitted to a perturbing potential U created by the molecules of the sample. In our model we take into account the difference of energy E due to the weak interactions between the left (L) and right (R) configurations. We have shown that when E is equal to zero the system cannot be optically stable: the optical activity tends asymptotically to zero in the case of dilute gases or compressed gases and liquids or oscillates periodically around zero when the molecules are isolated or submitted to a static potential. Only when E is different of zero the system can be optically stable depending on the strength parameters of the potential U and on the magnitude of the spontaneous tunneling.