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arXiv:0808.3148 · Physical Review Letters

Photoinduced Separation of Chiral Isomers in a Classical Buffer Gas

Boris Z. Spivak, Anton V. Andreev

Published Feb 13, 2009• 30 citations
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Abstract

We develop a theory of photoinduced drift of chiral molecules or small particles in classical buffer gases. In the absence of a magnetic field there exists a flux of chiral molecules, provided the electromagnetic field is circularly polarized. It has opposite signs for different chiral isomers. In the presence of a magnetic field the flux can be also induced by a linearly polarized (or unpolarized) electromagnetic field. The magnitude of the flux is not proportional to either linear or orbital momentum of the electromagnetic field.

DOI
10.1103/physrevlett.102.063004

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We develop a theory of photoinduced drift of chiral molecules or small particles in classical buffer gases. In the absence of a magnetic field there exists a flux of chiral molecules, provided the electromagnetic field is circularly polarized. It has opposite signs for different chiral isomers. In the presence of a magnetic field the flux can be also induced by a linearly polarized (or unpolarized) electromagnetic field. The magnitude of the flux is not proportional to either linear or orbital momentum of the electromagnetic field.
We explore the spatial enantioseparation of gaseous chiral molecules for the cyclic three-level systems coupled with three electromagnetic fields. Due to molecular rotations, the specific requirements of the polarization directions of the three electromagnetic fields lead to the space-dependent part of the overall phase of the coupling strengths. Thus, the overall phase of the coupling strengths, which differs with $\ensuremath{\pi}$ for the enantiomers in the cyclic three-level model of chiral molecules, varies intensely in the length scale of the typical wavelength of the applied electromagnetic fields. Under the induced gauge potentials resulting from the space-dependent part of the overall phase and the space-dependent intensities of coupling strengths, we further show spatial enantioseparation for typical parameters of gaseous chiral molecules.
Light-induced drift of optically active atoms in a buffer gas is a consequence of the unequal diffusive frictions suffered by the excited and the ground-state atoms. This drift can be used to create an ``optical piston,'' in which the active atoms are pushed forward by light through the semipermeable membrane of the buffer gas. Normally, optical piston effect is studied when the active atoms are neutral in a confined one-dimensional situation. We present a detailed theory of this phenomenon when the active atoms are charged and a magnetic field is applied for ``tuning'' the direction as well as the magnitude of the drift, thus removing the necessity of confinement. Our study is in different geometries of the light beam and the magnetic field, first in the weak collision model, and then for the strong collision and the Boltzmann-Lorentz models.
Abstract An achiral system bathed in an intense beam of circularly polarized light shows chiral behaviour which may be detected with an auxiliary beam of polarized light. In this paper, expressions are derived for differential absorption rates, optical rotation of a plane polarized probe beam and circular differential scattering intensities. The theory of these two, three and four photon processes is developed by using quantum electrodynamics in electric dipole approximation. Two types of circular dichroism are distinguished: (a) the transition exhibiting induced dichroism is one-photon allowed, with chirality induced by scattering of the laser beam, or (b) the transition is two-photon allowed with absorption of a photon from each beam. In both, the induced circular dichroism is linearly dependent on the intensity of the inducing beam. Circular dichroism of type (a) is also discussed from the dressed-molecule viewpoint, and it is shown how a canonical transformation may be used to recover the results more simply. The possibility of observing Doppler-free circular dichroism is indicated. The induced optical rotation is analysed as a two-state process with transitions involving change of polarization only. The angle of rotation is linearly dependent on the intensity of the intense beam; its sign depends on the helicity. It is shown that, for non-forward Rayleigh scattering of the probe beam in the presence of an intense beam of light, the scattering intensity depends on the relative helicities of the two beams, and the differential intensity is proportional to the incident intensities.
We examine spin-resolved photoionization of randomly oriented chiral molecules via circularly polarized light, and revisit earlier predictions of Cherepkov (J. Phys. B: Atom. Mol. Phys. 16, 1543, 1983). We will show that the dynamical origin of spin- and enantio-sensitive observables arise from two intrinsic mechanisms that are quantified by two pseudovectors stemming from the geometric properties of the photoionization dipoles in spin space and in real space, and an extrinsic mechanism which is a directional bias introduced by the well-defined direction of light polarization. These mechanisms arise solely from electric dipole interactions. Consequently, this means that the ten independent parameters that was earlier predicted by Cherepkov to fully describe spin-resolved photoionization of chiral molecules can be reduced as moments of these three pseudovectors. We also find that the molecular pseudoscalars describing the spin- and enantio-sensitive components of the yield can be described by the flux of these pseudovectors through the energy shell, which changes sign upon switching enantiomers. Our results provide compact expressions for these observables which provide an intuitive picture on what determines the strength of these spin- and enantio-sensitive observables. The approach can be readily generalized to photoexcitation, multiphoton processes, and arbitrary field polarizations. Regardless of the specific driving conditions, the resulting spin- and enantio-sensitive observables are still controlled by the same three pseudovectors, underscoring their universal role as the primary generators of chirality-induced spin asymmetries, emphasizing their fundamental geometric origin and the universality of the mechanism identified here.
Chiral materials possess some unusual properties which make them interesting for useful applications in nanophotonics. In this work, we review the basic techniques used to achieve electromagnetically induced chirality in initially isotropic materials and mention some of their novel operations. Next, we investigate the transmission characteristics of two different multi-level atomic models in which chirality is introduced by magnetoelectric cross coupling of external electromagnetic fields with atomic transitions, leading to quantum coherence. The left-(lcp) and right-circularly polarized (rcp) beams, the two eigenmodes of a chiral medium, are shown to transmit in an anti-symmetric manner with respect to the probe field detuning and control field magnitude variations. This selective transmission of a particular mode at specific detunings may find applications in optical isolation and storage. We further demonstrate that the driving control fields and their effective phase can be used as tuning knobs to manipulate the medium's birefringence and the transmission of the eigenmodes.
The decoherence of a two-state tunneling molecule, such as a chiral molecule or ammonia, due to collisions with a buffer gas is analyzed in terms of a succession of quantum states of the molecule satisfying the conditions for a consistent family of histories. With $\ensuremath{\hbar}\ensuremath{\omega}$ the separation in energy of the levels in the isolated molecule and $\ensuremath{\gamma}$ a decoherence rate proportional to the rate of collisions, we find for $\ensuremath{\gamma}\ensuremath{\gg}\ensuremath{\omega}$ (strong decoherence) a consistent family in which the molecule flips randomly back and forth between the left- and right-handed chiral states in a stationary Markov process. For $\ensuremath{\gamma}<\ensuremath{\omega}$ there is a family in which the molecule oscillates continuously between the different chiral states, but with occasional random changes of phase, at a frequency that goes to zero at a phase transition $\ensuremath{\gamma}=\ensuremath{\omega}$. This transition is similar to the behavior of the inversion frequency of ammonia with increasing pressure, but will be difficult to observe in chiral molecules such as D2{}_{2}2​S2{}_{2}2​. There are additional consistent families both for $\ensuremath{\gamma}>\ensuremath{\omega}$ and for $\ensuremath{\gamma}<\ensuremath{\omega}$. In addition, we relate the speed with which chiral information is transferred to the environment to the rate of decrease of complementary types of information (e.g., parity information) remaining in the molecule itself.