Optical binding in nanoparticle assembly: Potential energy landscapes

Optical binding is an optomechanical effect exhibited by systems of micro- and nanoparticles, suitably irradiated with off-resonance laser light. Physically distinct from standing-wave and other forms of holographic optical traps, the phenomenon arises as a result of an interparticle coupling with individual radiation modes, leading to optically induced modifications to Casmir-Polder interactions. To better understand how this mechanism leads to the observed assemblies and formation of patterns in nanoparticles, we develop a theory in terms of optically induced energy landscapes exhibiting the three-dimensional form of the potential energy field. It is shown in detail that the positioning and magnitude of local energy maxima and minima depend on the configuration of each particle pair, with regards to the polarization and wave vector of the laser light. The analysis reveals how the positioning of local minima determines the energetically most favorable locations for the addition of a third particle to each equilibrium pair. It is also demonstrated how the result of such an addition subtly modifies the energy landscape that will, in turn, determine the optimum location for further particle additions. As such, this development represents a rigorous and general formulation of the theory, paving the way toward full comprehension of nanoparticle assembly based on optical binding

Multiple light scattering and optomechanical forces

When off-resonant light travels through a transparent medium, light scattering is the primary optical process to occur. Multiple-particle events are relatively rare in optically dilute systems: scattering generally takes place at individual atomic or molecular centers. Several well-known phenomena result from such single-center interactions, including Rayleigh and Raman scattering, and the optomechanical forces responsible for optical tweezers. Other, less familiar effects may arise in circumstances where throughput radiation is able to simultaneously engage with two or more scattering sites in close, nanoscale, proximity. Exhibiting the distinctive near-field electromagnetic character, inter-particle interactions such as optical binding and a variety of inelastic bimolecular processes can then occur. Although the theory for each two-center process is well established, the connectivity of their mechanisms has not received sufficient attention. To address this deficiency, and to consider the issues that ensue, it is expedient to represent the various forms of multi-particle light scattering in terms of transitions between different radiation states. The corresponding quantum amplitudes, registering the evolution of photon trajectories through the material system, can be calculated using the tools of quantum electrodynamics. Each of the potential outcomes for multi-particle scattering generates a set of amplitudes corresponding to different orderings of the constituent photon-matter interactions. Performing the necessary sums over quantum pathways between radiation states is expedited by a state-sequence development, this formalism also enabling the identification of intermediate states held in common by different paths. The results reveal the origin and consequences of linear momentum conservation, and they also offer new insights into the behavior of light between closely neighboring scattering events. © 2010 Society of Photo-Optical Instrumentation Engineers

A retarded coupling approach to intermolecular interactions

A wide range of physical phenomena such as optical binding and resonance energy transfer involve electronic coupling between adjacent molecules. A quantum electrodynamical description of these intermolecular interactions reveals the presence of retardation effects. The clarity of the procedure associated with the construction of the quantum amplitudes and the precision of the ensuing results for observable energies and rates are widely acknowledged. However, the length and complexity of the derivations involved in such quantum electrodynamical descriptions increase rapidly with the order of the process under study. Whether through the use of time-ordering approaches, or the more expedient state-sequence method, time-consuming calculations cannot usually be bypassed. A simple and succinct method is now presented, which provides for a direct and still entirely rigorous determination of the quantum electrodynamical amplitudes for processes of arbitrarily high order. Using the approach, new results for optical binding in two- and three-particle systems are secured and discussed

Chiral discrimination in optical binding

The laser-induced intermolecular force that exists between two or more particles in the presence of an electromagnetic field is commonly termed “optical binding.” Distinct from the single-particle forces that are at play in optical trapping at the molecular level, the phenomenon of optical binding is a manifestation of the coupling between optically induced dipole moments in neutral particles. In other, more widely known areas of optics, there are many examples of chiral discrimination—signifying the different response a chiral material has to the handedness of an optical input. In the present analysis, extending previous work on chiral discrimination in optical binding, a mechanism is identified using a quantum electrodynamical approach. It is shown that the optical binding force between a pair of chiral molecules can be significantly discriminatory in nature, depending upon both the handedness of the interacting particles and the polarization of the incident light, and it is typically several orders of magnitude larger than previously reported

A Study of Cool White Dwarfs in the Sloan Digital Sky Survey Data Release 12

In this work we study white dwarfs where $30\,000\,\text{K} {>} \mathrm{T}_{\rm{eff}} {>} 5\,000\,\text{K}$ to compare the differences in the cooling of DAs and non-DAs and their formation channels. Our final sample is composed by nearly $13\,000$ DAs and more than $3\,000$ non-DAs that are simultaneously in the SDSS DR12 spectroscopic database and in the \textit{Gaia} survey DR2. We present the mass distribution for DAs, DBs and DCs, where it is found that the DCs are ${\sim}0.15\,\mathrm{M}_\odot$ more massive than DAs and DBs on average. Also we present the photometric effective temperature distribution for each spectral type and the distance distribution for DAs and non-DAs. In addition, we study the ratio of non-DAs to DAs as a function of effective temperature. We find that this ratio is around ${\sim}0.075$ for effective temperature above ${\sim}22\,000\,\text{K}$ and increases by a factor of five for effective temperature cooler than $15\,000\,\text{K}$. If we assume that the increase of non-DA stars between ${\sim}22\,000\,\text{K}$ to ${\sim}15\,000\,\text{K}$ is due to convective dilution, $14{\pm}3$ per cent of the DAs should turn into non-DAs to explain the observed ratio. Our determination of the mass distribution of DCs also agrees with the theory that convective dilution and mixing are more likely to occur in massive white dwarfs, which supports evolutionary models and observations suggesting that higher mass white dwarfs have thinner hydrogen layers.Comment: 9 pages, 10 figures, accepted by MNRA

Non-Abelian Chern-Simons-Higgs vortices with a quartic potential

We have constructed numerically non-Abelian vortices in an SU(2) Chern-Simons-Higgs theory with a quartic Higgs potential. We have analyzed these solutions in detail by means of improved numerical codes and found some unexpected features we did not find when a sixth-order Higgs potential was used. The generic non-Abelian solutions have been generated by using their corresponding Abelian counterparts as initial guess. Typically, the energy of the non-Abelian solutions is lower than that of the corresponding Abelian one (except in certain regions of the parameter space). Regarding the angular momentum, the Abelian solutions possess the maximal value, although there exist non-Abelian solutions which reach that maximal value too. In order to classify the solutions it is useful to consider the non-Abelian solutions with asymptotically vanishing $A_t$ component of the gauge potential, which may be labelled by an integer number $m$. For vortex number $n=3$ and above, we have found uniqueness violation: two different non-Abelian solutions with all the global charges equal. Finally, we have investigated the limit of infinity Higgs self-coupling parameter and found a piecewise Regge-like relation between the energy and the angular momentum.Comment: 9 pages, 13 figure

Asteroseismological study of massive ZZ Ceti stars with fully evolutionary models

We present the first asteroseismological study for 42 massive ZZ Ceti stars based on a large set of fully evolutionary carbon$-$oxygen core DA white dwarf models characterized by a detailed and consistent chemical inner profile for the core and the envelope. Our sample comprise all the ZZ Ceti stars with spectroscopic stellar masses between 0.72 and $1.05M_{\odot}$ known to date. The asteroseismological analysis of a set of 42 stars gives the possibility to study the ensemble properties of the massive pulsating white dwarf stars with carbon$-$oxygen cores, in particular the thickness of the hydrogen envelope and the stellar mass. A significant fraction of stars in our sample have stellar mass high enough as to crystallize at the effective temperatures of the ZZ Ceti instability strip, which enables us to study the effects of crystallization on the pulsation properties of these stars. Our results show that the phase diagram presented in Horowitz et al. (2010) seems to be a good representation of the crystallization process inside white dwarf stars, in agreement with the results from white dwarf luminosity function in globular clusters.Comment: 58 pages, 11 figures, accepted in Ap