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The Journal of Chemical Physics

Superpositions of chiral states in the presence of electric dipole, magnetic dipole, and electric quadrupole interactions

Vikram Athalye, Arvind Kumar

Published Apr 27, 2005• 7 citations
Publisher

Abstract

This paper is a straightforward generalization of Maierle-Harris proposal regarding parity implications on the superpositions of chiral states of a molecule. It is shown that the inclusion of electric quadrupole and magnetic dipole interactions removes several of restrictions on the preparation of superpositions of mid R:L and mid R:R states of a chiral molecule. It is also found that the dephasing of mid R:L and mid R:R superpositions, due to the spontaneous emission from the chiral molecule, has opposing contributions from electric quadrupole-magnetic dipole and electric dipole interactions.

DOI
10.1063/1.1883645

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This paper is a straightforward generalization of Maierle-Harris proposal regarding parity implications on the superpositions of chiral states of a molecule. It is shown that the inclusion of electric quadrupole and magnetic dipole interactions removes several of restrictions on the preparation of superpositions of mid R:L and mid R:R states of a chiral molecule. It is also found that the dephasing of mid R:L and mid R:R superpositions, due to the spontaneous emission from the chiral molecule, has opposing contributions from electric quadrupole-magnetic dipole and electric dipole interactions.
In this paper, we consider how parity conservation limits the type of superpositions of chiral states that can be created and detected. We also show how spontaneous emission can cause the left and right hands of the superposition to become coupled to different states of the radiation field. This coupling, aside from being an interesting effect in its own right, helps to enforce the restrictions that parity conservation places upon superpositions of chiral states. Finally, we outline an analogy that exists between aspects of this work and the Einstein, Podolsky, Rosen paradox.
The superposition of chiral states of chiral molecules, as delocalized quantum states of a many-particle system, can be used for the experimental investigations of decoherence theory. In this regard, a great challenge is the precise quantification of the robustness of these superpositions against environmental effects. The methods so far proposed need the detailed specification of the internal states of the molecule, usually requiring heavy numerical calculations. Here, by using the linearized quantum Boltzmann equation and by borrowing ideas employed for analyzing other quantum systems, we present a general and simple approach, of wide applicability, which can be used to compute the dominant contribution to the decoherence rate for the superpositions of chiral states of chiral molecules, due to environmental scattering.
The electromagnetic field operators for a chiral (optically active) molecule are calculated in the Heisenberg picture, using the multipolar Hamiltonian. Interactions involving electric-dipole, magnetic-dipole, and electric-quadrupole moments are taken into account. The operators are expanded in powers of moments, and expressions correct to quadratic powers in the moments are given. Comparable contributions from diamagnetic interactions are also presented. The properties of these operators are discussed. Terms that are linear in the moments are found to act in the electron space alone; those quadratic in the moments act in both the electron and photon spaces. The operators are used to calculate the Poynting vector, from which the spontaneous emission rates for magnetic-dipole and electric-quadrupole transitions are obtained. Attention is drawn to the inverse square dependence of the Poynting vector on the distance of the field point from the source. This behavior is shown to be consistent with the requirement of local conservation of energy. The operators are used in the following paper [J. K. Jenkins, A. Salam, and T. Thirunamachandran, Phys. Rev. A 50, 4767 (1994)] to calculate dispersion energies between two optically active molecules.
In this paper we investigate the effect of many Rayleigh scattering events on decoherence of superpositions of chiral states of a molecule, by taking these events as measurement-like interactions in the sense that the scattered photon state depends on the state of the molecule—both its centre-of-mass position and its chirality. This gives rise to two contributions to decoherence: one due to the position measurement and the other due to the chirality measurement. It is found that under identical conditions, the decoherence timescale for chiral molecules can be different from that for achiral molecules depending on the chiral sensitivity of scattering.
The theory of the line shape in coherent electric quadrupole absorption and emission processes involving NNN interacting molecules is developed, both quantum mechanically and with the use of a classical model. The theory is applied to small clusters and to linear chains of molecules. As in the dipole case, the effects of the interaction include in general a splitting of each molecular transition line into a number of components, a shift of each component from the molecular transition frequency, and a broadening or narrowing of each component relative to the width of the molecular line.
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.