General scientific summaries

We investigate finite-size scaling of genuine multisite entanglement in the ground state of quantum spin-1/2 Heisenberg ladders. We obtain the ground states of odd- and even-legged Heisenberg ladder Hamiltonians and compute genuine multisite entanglement, the generalized geometric measure (GGM), which shows that for even rungs, GGM increases for odd-legged ladder while it decreases for even ones. Interestingly, the ground state obtained by short-range dimer coverings, under the resonating valence bond ansatz, encapsulates the qualitative features of GGM for both the ladders. We find that while the quantity converges to a single value for higher legged odd- and even-ladders, in the asymptotic limit of a large number of rungs, the finite-size scaling exponents of the same tend to diverge. The scaling exponent of GGM is therefore capable to distinguish the odd–even dichotomy in Heisenberg ladders, even when the corresponding multisite entanglements merge.

General Scientific Summary

Introduction and background. The sequences of odd and even numbers mathematically reach the same infinity. The question is whether limits of functions of odd/even numbers reach the same limiting function as the respective sequences tend to infinity. In many-body physics, the dichotomy between physical properties of odd and even quantum ladders is known, and a typical result is exemplified by the seminal work of White, Noack, and Scalapino (PRL 73,886 (1994)), wherein the spin gap was shown to exhibit different behaviors in odd and even ladders. The values of the spin gaps were shown as converging to a single value with the increase in the number of legs, irrespective of whether we are with odd or even ladders. It may now be asked whether one can identify a physical quantity that would have different limiting values depending on whether odd or even legged ladders are followed to reach the infinite 2D square lattice. We answer this query in the affirmative by identifying the scaling of multisite entanglement as the physical quantity that is capable of doing the job.

Main results. We evaluate the asymptotic genuine multisite entanglement of states of quantum spin models on ladder lattices with odd and even legs, and perform finite size scaling analysis of the same. We find that scaling exponents of the multisite entanglement for large lattices tend to diverge for odd and even ladders, as the number of legs are increased, even though the amount of the multisite entanglement converges in the asymptotic limit.

Wider implications. We believe that the results presented in the manuscript will be of interest to the broad physics community working on stronglycorrelated systems, quantum information in many-body physics, and related quantum technologies. The methodology presented in the manuscript will, we believe, also appeal to the general theoretical physics community.

Thresholds of stimulated Brillouin scattering (SBS) in solid-state whispering gallery mode (WGM) microresonators are analyzed. It is shown that the SBS interaction is substantially different here from that known in the bulk case and in the case of water droplet resonators. The reason is the absence of pure longitudinal acoustic WGMs owing to strong coupling of the longitudinal (l) and transverse (t) acoustic displacements at the surface of the resonator. As a result, a considerable increase of the SBS thresholds takes place, and the lowest thresholds correspond to the hybrid tl-modes with very large radial indices. Nevertheless, the thresholds lie in the μW range of the pump power. Dependence of the SBS power thresholds on the modal numbers and the possibility of self-tuning to the SBS resonance are analyzed.

GENERAL SCIENTIFIC SUMMARY

Introduction and background. There is much research interest in optical research interest in optical whispering gallery mode (WGM) resonators, combining huge quality factors with small mode volumes. They provide a huge intensity enhancement leading to numerous nonlinear effects even at very low cw input powers. Low-threshold Brillouin lasing with acoustic WGMs has been reported. Its interpretation was based on the presumption of the longitudinal (l) acoustic WGMs. Recently, we have shown that such modes are absent in actual solid-state resonators, where the acoustic WGMs are either transverse (t) or hybrid (tl) with strong t-parts.

Main results. We provide a rigorous theory of stimulated Brillouin scattering (SBS) thresholds in optical WGM resonators made of isotropic solid-state materials. Our theory predicts substantially higher power thresholds than previously expected, because of the absence of pure longitudinal acoustic WGMs. These thresholds lie roughly in the μW range and correspond to the excitation of the acoustic tl modes with very large radial numbers. Quasi-continuity of the acoustic WGM spectrum strongly facilitates fulfillment of SBS phase matching despite the pronounced discreteness of the optical WGM spectrum. Our theoretical model predicts the values and the wavelength and size dependencies of the SBS thresholds. It is in good agreement with the literature data on the SBS-WGM lasing.

Wider implications. The theoretical model presented here provides a firm basis for comparison with experiments and for prediction of new experimental features. By varying the pump wavelength and the WGM resonator size, the SBS lasing can be deliberately activated or suppressed.

At optical frequencies metals behave as an electron plasma and conventional antenna designs need modifications when transferred to this regime. In contrast to antenna theory and to the effective wavelength picture, the position and width of the dipolar resonance of a rectangular cuboidal plasmonic nanoantenna scales nonlinearly with its length, width and height, as shown in this paper directly by analytical formulae. Moreover we show that the quality factor calculated for different sizes varies significantly with size, in contrast to the quasi-static approximation which predicts invariance. We present analytical expressions that provide a tool for direct and precise calculation of the dipolar plasmon resonance which can be applied to the antenna design process. These expressions enable both physical insight and the quick exploration of a wide range of parameters to tailor the plasmon resonance response or scattering by nanoparticles, for either metals or dielectrics, for numerous promising applications in optical sensor, photovoltaic and light emitting device design.

We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner function and thus provides an intuitive framework for discussing quantum effects and semiclassical approximations in the rotational motion. Examples illustrating the viability of this quasi-probability distribution include the phase space description of a molecular alignment effect.