Chip-scale cavity optomechanics in lithium niobate

We develop a chip-scale cavity optomechanical system in single-crystal lithium niobate that exhibits high optical quality factors and a large frequency-quality product as high as $3.6\times 10^{12}$ Hz at room temperature and atmosphere. The excellent optical and mechanical properties together with the strong optomechanical coupling allow us to efficiently excite the coherent regenerative optomechanical oscillation operating at 375.8 MHz with a threshold power of 174 ${\rm \mu W}$ in the air. The demonstrated lithium niobate optomechanical device enables great potential for achieving electro-optic-mechanical hybrid systems for broad applications in sensing, metrology, and quantum physics

Quantum correlations from dynamically modulated optical nonlinear interactions

We investigate optical nonlinear interactions in a dynamic environment by studying generation of photons in spontaneous parametric down conversion inside a nonlinear cavity where the optical path length is periodically modulated in time. We show that the temporal dynamics of the cavity modify the nonlinear interaction and the generated continuous variable time-frequency entangled bi-photon state evolves into a tunable discrete higher dimensional state in the non-adiabatic modulation regime where the modulation time scales are much faster than the photon lifetime. In this regime, the system mimics effects of a quantum random walk in a photonic lattice with many associated effects including localized and delocalized wavefunctions of the generated photons. We also propose generation of time-frequency hyper-entangled states in the adiabatic limit. Our analysis shows that the proposed system is promising for applications in quantum simulation and information processing in the time-frequency domain.Comment: 10 pages, 6 figures (including appendix

The direction of the dd-vector in a nematic triplet superconductor

We investigate the states of triplet pairing in a candidate nematic superconductor versus typical material parameters, using the mean field theory for two- and three-dimensional tight-binding models with local triplet pairing in the $E_u$ representation. In the two-dimensional model, the system favors the fully gapped chiral state for weaker warping or lower filling level, while a nodal and nematic $\Delta_{4x}$ state is favorable for stronger warping or higher filling, with the $d$-vector aligned along the principle axis. In the presence of lattice distortion, relative elongation along one of the principle axes, ${\bf a}$, tends to rotate the nematic $d$-vector orthogonal to ${\bf a}$, resulting in the nematic $\Delta_{4y}$ state at sufficient elongation. Three-dimensionality is seen to suppress the chiral state in favor of the nematic ones. Our results may explain the variety in the probed direction of the $d$-vector in existing experiments.Comment: 5 pages, 4 color figure

The Deviation of the Vacuum Refractive Index Induced by a Static Gravitational Field

We analyzed the influence of static gravitational field on the vacuum and proposed the concept of inhomogeneous vacuum. According to the observational result of the light deflection in solar gravitational field as well as the corresponding Fermat's principle in the general relativity, we derived an analytical expression of the refractive index of vacuum in a static gravitational field. We found that the deviation of the vacuum refractive index is composed of two parts: one is caused by the time dilation effect, the other is caused by the length contraction effect. As an application, we simulated the effect of the gravitational lensing through computer programming and found that the missing central imaging could be interpreted in a reasonable way.Comment: 5 pages, 6 figure

Self-Frequency Shift of Cavity Soliton in Kerr Frequency Comb

We show that the ultrashort cavity soliton in octave-spanning Kerr frequency comb generation exhibits striking self-adaptiveness and robustness to external perturbations, resulting in a novel frequency shifting/cancellation mechanism and gigantic dispersive wave generation in response to the strong frequency dependence of Kerr nonlinearity, Raman scattering, chromatic dispersion, and cavity Q. These observations open up a great avenue towards versatile manipulation of nonlinear soliton dynamics, flexible spectrum engineering of mode-locked Kerr frequency combs, and highly efficient frequency translation of optical waves

Partial classification of cuspidal simple modules for Virasoro-like algebra

Let $\mathfrak P$ be the Lie algebra of Hamiltonian vector fields on the torus, which is also known as the Virasoro-like algebra, a special kind of the so-called Block type Lie algebra. And let $\mathfrak A$ be the Laurent polynomial algebra in two variables. In this paper, by following S.E. Rao's strategy of "backward induction", we prove that any quasi-finite simple $(\mathfrak A,\mathfrak P)$-module has to come from Larsson-Shen's construction.Comment: 14 page

Multicolor Bound Soliton Molecule

We show a new class of bound soliton molecule that exists in a parametrically driven nonlinear optical cavity with appropriate dispersion characteristics. The composed solitons exhibit distinctive colors but coincide in time and share a common phase, bound together via strong inter-soliton four-wave mixing and Cherenkov radiation. The multicolor bound soliton molecule shows intriguing spectral locking characteristics and remarkable capability of spectrum management to tailor soliton frequencies, which may open up a great avenue towards versatile generation and manipulation of multi-octave spanning phase-locked Kerr frequency combs, with great potential for applications in frequency metrology, optical frequency synthesis, and spectroscopy.Comment: 5 pages, 6 figure

High-frequency and high-quality silicon carbide optomechanical microresonators

Silicon carbide (SiC) exhibits excellent material properties attractive for broad applications. We demonstrate the first SiC optomechanical microresonators that integrate high mechanical frequency, high mechanical quality, and high optical quality into a single device. The radial-breathing mechanical mode has a mechanical frequency up to 1.69 GHz with a mechanical Q around 5500 in atmosphere, which corresponds to a mechanical f-Q product as high as 9.47x10^12 Hz. The strong optomechanical coupling allows us to efficiently excite and probe the coherent mechanical oscillation by optical waves. The demonstrated devices, in combination with the superior thermal property, chemical inertness, and defect characteristics of SiC, show great potential for applications in metrology, sensing, and quantum photonics, particularly in harsh environments that are challenging for other device platforms.Comment: 18 pages, 5 figure

Further results on complete permutation monomials over finite fields

In this paper, we construct some new classes of complete permutation monomials with exponent $d=\frac{q^n-1}{q-1}$ using AGW criterion (a special case). This proves two recent conjectures in [Wuetal2] and extends some of these recent results to more general $n$'s

Novel polymer nanocomposite composed of organic nanoparticles via self-assembly

We report a novel class of polymer nanocomposite composed of organic nanoparticles dispersed in polymer matrix, with the particle sizes of 30-120 nm in radius. The organic nanoparticles were formed by the self-assembly of protonated poly(4-vinyl-pyridine)-r-poly(acrylonitrile) and amphiphilic metanil yellow dye molecules through electrostatic interactions in aqueous solution. A strongly broadened Raman shift band was probed, suggesting the presence of enhanced optoelectronic property from the polymer nanocomposite. Here, using random-copolymer polyelectrolytes and mesogenic amphiphiles as the designed building blocks for self-assembly, a new approach is acutally provided to fabricate organic nanoparticles.Comment: 12 pages, 5 figures