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Physical Chemistry Chemical Physics

Quantum stochastic resonance in parity violating chiral molecules

Pedro Bargueño, Salvador Miret-Artés, Isabel Gonzalo

Published Nov 10, 2010• 5 citations
Publisher

Abstract

In order to explore parity violating effects in chiral molecules, of interest in some models of evolution towards homochirality, quantum stochastic resonance (QSR) is studied for the population difference between the two enantiomers of a chiral molecule (hence for the optical activity of the sample), under low viscous friction and in the deep quantum regime. The molecule is described by a two-state model in an asymmetric double well potential where the asymmetry is given by the known predicted parity violating energy difference (PVED) between enantiomers. In the linear response to an external driving field that lowers and rises alternatively each one of the minima of the well, a signal of QSR is predicted only in the case that the PVED is different from zero, the resonance condition being independent on tunneling between the two enantiomers. It is shown that, at resonance, the fluctuations of the first order contribution to the internal energy are zero. Due to the small value of the PVED, the resonance would occur in the ultracold regime. Some proposals concerning the external driving field are suggested.

DOI
10.1039/c0cp01319f

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In order to explore parity violating effects in chiral molecules, of interest in some models of evolution towards homochirality, quantum stochastic resonance (QSR) is studied for the population difference between the two enantiomers of a chiral molecule (hence for the optical activity of the sample), under low viscous friction and in the deep quantum regime. The molecule is described by a two-state model in an asymmetric double well potential where the asymmetry is given by the known predicted parity violating energy difference (PVED) between enantiomers. In the linear response to an external driving field that lowers and rises alternatively each one of the minima of the well, a signal of QSR is predicted only in the case that the PVED is different from zero, the resonance condition being independent on tunneling between the two enantiomers. It is shown that, at resonance, the fluctuations of the first order contribution to the internal energy are zero. Due to the small value of the PVED, the resonance would occur in the ultracold regime. Some proposals concerning the external driving field are suggested.
A Langevin canonical framework for a chiral two-level system coupled to a bath of harmonic oscillators is used within a coupling scheme different from the well-known spin-boson model to study the quantum stochastic resonance for chiral molecules. This process refers to the amplification of the response to an external periodic signal at a certain value of the noise strength, being a cooperative effect of friction, noise, and periodic driving occurring in a bistable system. Furthermore, from this stochastic dynamics within the Markovian regime and Ohmic friction, the competing process between tunneling and the parity violating energy difference present in this type of chiral systems plays a fundamental role. This mechanism is finally proposed to observe the so-far elusive parity-violating energy difference in chiral molecules.
We propose a theoretical mechanism to indirectly detect the small parity-violating energy difference (PVED) between chiral enantiomers through a macroscopic enantiomeric excess observed in an ultracold gas. We consider that chiral molecules are formed resonantly via ultracold collisions of achiral diatomic molecules, with PVED inducing a slight asymmetry in the resonance energies of right- and left-handed configurations. After formation, chiral molecules evolve within a Bose-Einstein condensate (BEC), incorporating nonlinear interactions, tunneling between enantiomeric states, intrinsic PVED, and thermal conversion rates. These collective dynamics enable amplification of the microscopic bias into a global population imbalance. Using coupled rate equations, we show that, under realistic regimes, a complete enantiomeric excess can be achieved even for extremely small intrinsic asymmetries. We illustrate the model with concrete examples (HSOH, H2_22​Se2_22​, H2_22​Te2_22​), predicting observable enantiomeric excesses under plausible experimental conditions. We also consider non-PVED effects that could be amplified under the proposed mechanism, including electric and magnetic fields as well as thermal fluctuations, the latter being illustrated through the aforementioned molecular examples. Overall, our results suggest that ultracold physics could provide a new pathway to probe molecular parity violation, a fundamental weak effect that remains experimentally undetected.
In this review, the concepts of quantum tunneling and parity violation are introduced in the context of chiral molecules. A particle moving in a double well potential provides a good model to study the behavior of chiral molecules, where the left well and right well represent the L and R enantiomers, respectively. If the model considers the quantum behavior of matter, the concept of quantum tunneling emerges, giving place to stereomutation dynamics between left- and right-handed chiral molecules. Parity-violating interactions, like the electroweak one, can be also considered, making possible the existence of an energy difference between the L and R enantiomers, the so-called parity-violating energy difference (PVED). Here we provide a brief account of some theoretical methods usually employed to calculate this PVED, also commenting on relevant experiments devoted to experimentally detect the aforementioned PVED in chiral molecules. Finally, we comment on some ways of solving the so-called Hund’s paradox, with emphasis on mean-field theory and decoherence.
Interactions which do not conserve parity might influence chiral compounds giving rise to a parity violating energy difference (PVED) that might have affected the evolution towards homochirality. However, this tiny effect predicted by electroweak-quantum chemistry calculations is easily masked by thermal effects, making it desirable to reach cold regimes in the laboratory. As an alternative route to the detection of the PVED, we study a simplified model of Bose-Einstein condensation of a sample of non-interacting chiral molecules, showing that it leads to a nonzero optical activity of the condensate and also to a subcritical temperature in the heat capacity, due to the internal structure of the molecule characterized by tunneling and parity violation. This predicted singular behavior found for the specific heat, below the condensation temperature, might shed some light on the existence of the thus far elusive PVED between enantiomers.
A study of (aperiodic) quantum stochastic resonance (QSR) in parallel is put forward. By doing so, a generally stochastic input signal is fed into an array of parallel dissipative quantum two-level systems (TLS) and its integral response is studied against increasing temperature. The response is quantified by means of an information-theoretic measure provided by the rate of mutual information per element and, in addition, by the cross-correlation between the information-carrying input signal and the output response. For ohmic-like quantum dissipation, both measures exhibit QSR for biased two-level systems. Our prime focus here, however, is on the case with zero asymmetry between the two localized stable states. We then find that the mutual information measure exhibits QSR only for sufficiently strong dissipation ( > 3/2), as measured by the dimensionless ohmic friction strength . Moreover, the mutual information measure relates QSR within quantum linear response theory to the signal-to-noise-ratio (SNR) , being independent of the input driving frequencies in this limit. In contrast, the cross correlation measure connects QSR to a genuine synchronization phenomenon . For a single symmetric TLS, aperiodic QSR is exhibited in the cross-correlation measure for a Gaussian exponentially correlated input signal for > 1 already. Upon feeding the aperiodic input signal into a parallel array of unbiased TLS's, QSR successively emerges above the critical ohmic dissipation strength > 1/2 with increasing number n of parallel units. Thus, QSR can occur in parallel despite the fact that it does not occur in each individual, unbiased, TLS for < 1. This paradoxical phenomenon - which can be tested with an array of bistable superconducting quantum interference devices - constitutes a true quantum effect: it is due to the power-law dependence on temperature of the tunnelling rate and the stochastic linearization of quantum fluctuations with increasing number of parallel units.
With the creation of ultracold atoms and molecules, a new type of chemistry---``resonance'' chemistry---emerges: chemical reactions can occur when the energy of colliding atoms and molecules matches a bound state of the combined molecule (Feshbach resonance). This chemistry is rather similar to reactions that take place in nuclei at low energies. In this paper we suggest some problems for future experimental and theoretical work related to the resonance chemistry of ultracold molecules. Molecular Bose-Einstein condensates are particularly interesting because in this system collisions and chemical reactions are extremely sensitive to weak fields; also, a preferred reaction channel may be enhanced due to a finite number of final states. The sensitivity to weak fields arises due to the high density of narrow compound resonances and the macroscopic number of molecules with kinetic energy E=0E=0E=0 (in the ground state of a mean-field potential). The high sensitivity to the magnetic field may be used to measure the distribution of energy intervals, widths, and magnetic moments of compound resonances and study the onset of quantum chaos. A difference in the production rate of right-handed and left-handed chiral molecules may be produced by external electric E\mathbf{E}E and magnetic B\mathbf{B}B fields and the finite width $\ensuremath{\Gamma}$ of the resonance (correlation $\ensuremath{\Gamma}\mathbf{E}∙\mathbf{B}$). The same effect may be produced by the parity-violating energy difference in chiral molecules.