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Journal of Physics B Atomic Molecular and Optical Physics

Decoherence of superposition of molecular chiral states due to Rayleigh scattering

Vikram Athalye, Arvind Kumar

Published May 24, 2006• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/39/12/002

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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 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.
In this study, we apply the monitoring master equation describing decoherence of internal states to an optically active molecule prepared in a coherent superposition of nondegenerate internal states interacting with thermal photons at low temperatures. We use vibrational Raman scattering theory up to the first chiral-sensitive contribution, i.e., the mixed electric-magnetic interaction, to obtain scattering amplitudes in terms of molecular polarizability tensors. The resulting density matrix is used to obtain elastic decoherence rates.
We investigate the decoherence of superpositions of hyperfine states of Be ions due to spontaneous scattering of off-resonant light. We find that, contrary to conventional wisdom, elastic Rayleigh scattering can have majour contributions to decoherence when compared to the effect of inelastic Raman scattering. 1. Summary Minimizing the effects of decoherence is a central challenge in many quantum physics experiments. In the case of ion trap quantum computing [1] a majour contribution to decoherence comes from the off-resonant scattering of the controlling light beams. It is often assumed that the decoherence process is dominated by in-elastic Raman scattering, since in that case the scattered photon has a different frequency from the incoming photon, and consequently carries with it information regarding the internal state of the ion [2, 3]. This leads to decoherence of that internal state. On the otherhand since Rayleigh scattering does not carry this information it is assumed to not lead to comparable decoherence. Here we show that under certain circumstances the Rayleigh scattering can dominate the ecoherence process even at large detunings from the excited state levels. We find excellent agreement between a masters theory approach and experimental measurements. Figure 1: Comparison of decoherence rates as a function of detuning from the Be cycling transition. Squares experiment, Blue/Red line full masters equation theory, Cyan line incomplete model sometimes used in literature. 2. References [1] D.J. Wineland, et al., Phil. Trans. R. Soc. Lond. A 361, 1349 (2003). [2] R. Ozeri, et al., Phys. Rev. A 75, 042329 (2007). [3] R. Ozeri, et al., Phys. Rev. Lett. 95, 030402 (2005).
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.