Optomechanical force gradient sensing with levitated nanosphere pair

Guided by recent progress in ground state cooling and ultraweak force sensing in the optomechanical systems with optically levitated particles,we propose a novel quantum sensing protocol that can detect the gradient of a force field directly with extremely high sensitivity.The system consists of a pair of nanospheres levitated in the high vacuum environment with optical tweezers and an optical resonator.By positioning the two spheres suitably relative to the cavity,only the collective breathing mode of the sphere pair couples to the cavity field.This optomechanical coupling will transfer the information of force difference acting on the two sensors to cavity photons,which can then be detected directly at the output of the cavity.Given the optimal control of various technical noise sources,the sensitivity could reach 10^(-15)N m^(-1)/√HZ with a high spatial resolution of micron scale on a state-of-the-art experimental setup.The potential application of this protocol in searching for short range“new force”is analyzed.Compared with conventional searching protocols with a single levitated sphere,the method proposed here can increase the signal-to-noise ratio by more than one magnitude in a large searching parameter space.

Shape gradient and classical gradient of curvatures:driving forces on micro/nano curved surfaces

Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a gen- eral theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived： （a） Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. （b） On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. （c） Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradi- ents form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. （d） The direction of the driving force induced by the hard curved surface is independent of the hydrophilieity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.

Simulation of Influence of Partially Coherent Gaussian Laser Beam on Gradient Force Acting on Dielectric Nanoparticle inside Random Medium

The partially coherent beams propagating through random media have been used in the past to enhance effect of nonlinear optical interaction. Moreover, after propagation through a random （or turbulent） medium the coherent beam becomes a partially coherent one. In this research, the analytical formula for the average intensity of Gaussian beam propagating through random medium is derived and the influence of coherent partiality on optical gradient force acting on dielectric particle rounded by a random media is investigated.

A vectorial model for the nonlinear gradient force exerted on metallic Rayleigh nanoparticles

Optical tweezers have proved to be a powerful tool with a wide range of applications.The gradient force plays a vital role in the stable optical trapping of nano-objects.The scalar method is convenient and effective for analyzing the gradient force in traditional optical trapping.However,when the third-order nonlinear effect of the nano-object is stimulated,the scalar method cannot adequately present the optical response of the metal nanoparticle to the external optical field.Here,we propose a theoretical model to interpret the nonlinear gradient force using the vector method.By combining the optical Kerr effect,the polarizability vector of the metallic nanoparticle is derived.A quantitative analysis is obtained for the gradient force as well as for the optical potential well.The vector method yields better agreement with reported experimental observations.We suggest that this method could lead to a deeper understanding of the physics relevant to nonlinear optical trapping and binding phenomena.

Theoretical study of the trapping efficiency of an optical tweezers array system

Optical tweezers have been a valuable research tool since their invention in the 1980s. One of the most important developments in optical tweezers in recent years is the creation of two-dimensional arrays of optical traps. In this paper, a method based on interference is discussed to form gradient laser fields, which may cause the spatial modulation of particle concentration. The parameters related to the optical tweezers array are discussed in detail and simulated by the Matlab software to show the influence of important parameters on the distribution of particle concentration. The spatial redistribution of particles in a laser interference field can also be predicted according to the theoretical analysis.

б-sharpen immersed boundary method(б-SIBM)—New method for solving the horizontal pressure-gradient force(PGF) problem of б-coordinate

Although G-coordinate is one of the most popular methods used in marine and estuarine modeling, it has long suffered from the so-called ＂steep boundary problem＂, namely, the PGF problem. In this paper, a new method called the ＂σ-sharpen immersed boundary method＂ （σ-SIBM） is put forward. In this method, the virtual flat bottom boundary is creatively introduced in regions with the steep boundary and is taken as the boundary of numerical domain. By this, OH/Ox of numerical domain changes to be a controllable value and the steep bottom problem is then transformed to the non-conforming boundary problem, which is, in turn, solved by the SIBM. The accuracy and efficiency of the σ-sharpen immersed boundary method （σ-SIBM） has been showed by both comparative theoretical analysis and classical numerical tests. First, it is shown that the σ-SIBM is more effective than the z-level method, in that σ-SIBM needs special treatment only in the steep section, but the z-level method needs the special treatment in each grid note. Second, it is superior to the p-method in that it is not restricted by the density distribution. This paper revisits the classical seamount numerical test used in numerous studies to prove the sigma errors of the pressure gradient force （PGFE） and their long-term effects on circulation. It can be seen that, as for the maximum erroneous velocity and kinetic energy, the value of σ-SIBM is much less than that of the z-level method and the traditional σ-method.

Resonant gradient force on atom interacting with laser field

The gradient force, as a function of position and velocity, is derived for a two-level atom interacting with a standing-wave laser field. Basing on optical Bloch equations, the numerical solutions for the gradient force f⊥,n (n = 0,1, 2,3,4, …) pointing in the direction of the transverse of the laser beam are given. It is shown the higher order gradient force plays important role at strong intensity (G = 64), the contribution of them can not be neglected.

Conditions for formation and trapping of the two-ion Coulomb cluster in the dissipative optical superlattice

Conditions have been studied under which a polychromatic optical superlattice can form and trap the Coulomb cluster of two strongly interacting ions. In our previous work （Krasnov I V and Kamenshchikov L P 2014 Opt. Comm. 312 192） this new all-optical method of obtaining and confining the Coulomb clusters was demonstrated by numerical simulations for special values of the optical superlattice parameters and in the case of Yb ions. In the present paper the conditions are explicitly formulated, under which the long-lived two-ion cluster in the superlattice cell is formed. The peculiarity of these conditions is the renormalization of the ion-ion Coulomb interaction. Notably, the renormalized Coulomb force is determined by the effective charge which depends on the light field parameters and can strongly differ from the ＂bare＂ ion charge. This result can be accounted for by the combined manifestation of the quantum fluctuations of optical forces, nonlinear dependence of these forces on the velocity, and non-Maxwellian （Tsallis type） velocity distribution of the ions in the optical superlattice. Explicit analytical formulas are also obtained for the parameters of the optical two-ion cluster.

IMPACT STUDY ON THE CALCULATION OF VERTICAL VELOCITY IN DIFFERENT VERTICAL COORDINATE SYSTEMS

With the development of high-resolution and multi-scale unified numerical model, some of techniques about non-hydrostatic meso-scale numerical weather prediction are addressed. The impact of the vertical coordinate system is one of them. In this paper, based on a WRF (Weather Research and Forecast) model, the impact on the calculation of vertical velocity was studied with different vertical coordinates. The simulation results showed that the calculation of vertical velocity is sensitive to vertical coordinates. It is especially more evident when the resolution increased. Due to the close relationships between vertical velocity and precipitation, the difference of vertical velocity inevitably influences model’s description of precipitation. An ideal experiment exhibits that pressure gradient force computations in the pressure terrain- following coordinate are sensitive to surface pressure.

Guided motion of short carbon nanotube driven by non-uniform electric field

The molecular dynamics simulations are performed to show that in aque- ous environments, a short single-walled carbon nanotube （SWCNT） guided by a long SWCNT, either inside or outside the longer tube, is capable of moving along the nanotube axis unidirectionally in an electric field perpendicular to the carbon nanotube （CNT） axis with the linear gradient. The design suggests a new way of molecule transportation or mass delivery. To reveal the mechanism behind this phenomenon, the free energy profiles of the system are calculated by the method of the potential of mean force （PMF）.

Integrated unified phase-field modeling(UPFM)

For a long time,the phase-field method has been considered a mesoscale phenomenological method that lacks physical accuracy and is unable to be closely linked to the mechanical or functional properties of materials.Some misunderstandings existing in these viewpoints need to be clarified.Therefore,it is necessary to propose or adopt the perspective of“unified phase-field modeling(UPFM)”to address these issues,which means that phase-field modeling has multiple unified characteristics.Specifically,the phase-field method is the perfect unity of thermodynamics and kinetics,the unity of multi-scale models from microto meso and then to macro,the unity of internal or/and external driving energy with order parameters as field variables,the unity of multiple physical fields,and thus the unity of material composition design,process optimization,microstructure control,and performance prediction.It is precisely because the phase-field approach has these unified characteristics that,after more than 40 years of development,it has been increasingly widely applied in materials science and engineering.

Optimized Vertical Layers for the Hybrid Terrain-Following Coordinate Minimizing Numerical Errors in a 2D Rising Bubble Experiment near Steep Terrain

The basic terrain-following(BTF)coordinate simplifies the lower boundary conditions of a numerical model but leads to numerical error and instability on steep terrain.Hybrid terrain-following(HTF)coordinates with smooth slopes of vertical layers(slopeVL)generally overcome this difficulty.Therefore,the HTF coordinate becomes very desirable for atmospheric and oceanic numerical models.However,improper vertical layering in HTF coordinates may also increase the incidence of error.Except for the slopeVL of an HTF coordinate,this study further optimizes the HTF coordinate focusing on the thickness of vertical layers(thickVL).Four HTF coordinates(HTF1–HTF4)with similar slopeVL but different vertical transition methods of thickVL are designed,and the relationship between thickVL and numerical errors in each coordinate is compared in the classic idealized thermal convection[two-dimensional(2D)rising bubble]experiment over steep terrain.The errors of potential temperatureθand vertical velocity w are reduced most,by approximately 70%and 40%,respectively,in the HTF1 coordinate,with a monotonic increase in thickVL according to the increasing height;however,the errors ofθincreased in all the other HTF coordinates,with nonmonotonic thickVLs.Furthermore,analyses of the errors of vertical pressure gradient force(VPGF)show that due to the interpolation errors of thickVL,the inflection points in the vertical transition of thickVL induce the initial VPGF errors;therefore,the HTF1 coordinate with a monotonic increase in thickVL has the smallest errors among all the coordinates.More importantly,the temporal evolution of VPGF errors manifests top-type VPGF errors that propagate upward gradually during the time integration.Only the HTF1 and HTF4 coordinates with a monotonic increase in thickVL near the top of the terrain can suppress this propagation.This optimized HTF coordinate(i.e.,HTF1)can be a reference for designing a vertical thickVL in a numerical model.

A New Approach to Implement Sigma Coordinate in a Numerical Model

This study shows a new way to implement terrain-following s-coordinate in a numerical model,which does not lead to the well-known"pressure gradient force(PGF)"problem.First,the causes of the PGF problemare analyzedwith existing methods that are categorized into two different types based on the causes.Then,the new method that bypasses the PGF problem all together is proposed.By comparing these threemethods and analyzing the expression of the scalar gradient in a curvilinear coordinate system,this study finds out that only when using the covariant scalar equations of s-coordinate will the PGF computational form have one term in each momentum component equation,thereby avoiding the PGF problem completely.A convenient way of implementing the covariant scalar equations of s-coordinate in a numerical atmospheric model is illustrated,which is to set corresponding parameters in the scalar equations of the Cartesian coordinate.Finally,two idealized experimentsmanifest that the PGF calculated with the new method is more accurate than using the classic one.This method can be used for oceanic models as well,and needs to be tested in both the atmospheric and oceanic models.

Migration of Paramagnetic Ions in Glass Melts Under Influence of a Magnetic Field

Magnetic forces are widely used to influence the properties of materials.The main focus of recent investigations concerning oxide melts mainly was on the use of Lorentz forces either to mix glass melts to avoid an improved inhomogeneity or to measure the flow of these melts.In the last years also the use of magnetic gradient forces has become an object of research mainly in electrochemistry.On the basis of preliminary investigations the influence of these forces on paramagnetic ions such as Fe;in oxide melts is investigated to examine the potential of magnetic gradient forces as a tool to create defined gradient materials.

;heoretical analysis for optomechanical all-optical transistor

In this paper, we propose an on-chip all optical transistor driven by optical gradient force. The transistor consists of a single micro-ring resonator, half of which is suspended from the substrate, and a bus waveguide. The free-standing arc is bent by optical gradient force generated when the control light is coupled into the ring. The output power of the probe light is tuned continuously as the transmission spectrum red-shift due to the displacement of the free-standing arc. The transistor shows three working regions known as cutoff region, amplified region and saturate region, and the characteristic curve is tunable by changing the wavelength of the control light. Potential applications of the all optical transistor include waveform regeneration and other optical computing.