Abstract
We present an optomechanical model that describes the stochastic motion of an overdamped chiral nanoparticle diffusing in the optical bistable potential formed in the standing-wave of two counter-propagating Gaussian beams. We show how chiral optical environments can be induced in the standing-wave with no modification of the initial bistability by controlling the polarizations of each beam. Under this control, optical chiral densities and/or an optical chiral fluxes are generated, associated respectively with reactive vs. dissipative chiral optical forces exerted on the diffusing chiral nanoparticle. This optomechanical chiral coupling bias the thermodynamics of the thermal activation of the barrier crossing, in ways that depend on the nanoparticle enantiomer and on the optical field enantiomorph. We show that reactive chiral forces, being conservative, contribute to a global, enantiospecific, change of the Helmholtz free energy bistable landscape. In contrast, when the chiral nanoparticle is immersed in a dissipative chiral environment, the symmetry of the bistable potential is broken by non-conservative chiral optical forces. In this case, the chiral electromagnetic fields continuously transfer, through dissipation, mechanical energy to the chiral nanoparticle. For this chiral nonequilibrium steady-state, the thermodynamic changes of the barrier crossing take the form of heat transferred to the thermal bath and yield chiral deracemization schemes that can be explicitly calculated within the framework of our model. Three-dimensional stochastic simulations confirm and further illustrate the thermodynamic impact of chirality. Our results reveal how chiral degrees of freedom both of the nanoparticle and of the optical fields can be transformed into true thermodynamics control parameters, thereby demonstrating the significance of optomechanical chiral coupling in stochastic thermodynamics.
Highlights
When a chiral system is immersed within a chiral environment, specific interactions can be induced that combine the chirality of both the system and the environment
Within all the available states that lie below the level set by the temperature and the simulation time, these results perfectly reveal how the Brownian motion probes the chiral optical environment, where the chiral coupling modifies the diffusion driven by thermal fluctuations within the bistable potential
These modifications can be swapped by changing the enantiomer within a fixed chirality of the optical environment or the optical enantiomorph for a chosen nanoparticle enantiomer. (iv) The dissipative coupling yields nonconservative chiral forces that modify the thermal activation thermodynamics. In this nonequilibrium steady state of the system, the dissipation of heat to the thermal bath is responsible for lifting the degeneracy of the probability density function between the two local minima of the bistable potential. This breaking of the initial mirror symmetry of the bistable trap takes the form of an enantiospecific contribution to the thermodynamics. (v) The contribution of both types of coupling to the global thermodynamics is observed at the level of stochastic simulations of the Langevin equation for trajectory ensembles in the presence of external chiral forces
Summary
When a chiral system is immersed within a chiral environment, specific interactions can be induced that combine the chirality of both the system and the environment. Such coupling mechanisms can rely on fundamental asymmetries, such as the violation of parity [22,23] or can rely on the role of the environment (be it electromagnetic, chemical, geological, astronomical, and so forth) whose chirality determines the direction of the splitting in free energies [24] In all these examples, the thermodynamics involved in the variety of deracemization processes (by crystallization, chemistry, light, etc.) is not easy to resolve, and the precise role played by the chiral coupling engaged in each process is not easy to uncover. We address head-on the thermodynamic question by looking at one particular type of chiral coupling induced when a chiral scattering object is immersed within a chiral electromagnetic field This chiral coupling manifests itself by the emergence of chiral optical forces that have been recently discovered [25,26,27,28]. It provides the right settings to envision future experiments nurtured by theory in an exchange that has fertilized to date this newly born field of chiral optomechanics
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