Interference-induced suppression of particle emission from a Bose-Einstein condensate in lattice with time-periodic modulations

Emission of matter-wave jets from a parametrically driven condensate has attracted significant experimental and theoretical attention due to the appealing visual effects and potential metrological applications.In this work,we investigate the collective particle emission from a Bose-Einstein condensate confined in a one-dimensional lattice with periodically modulated interparticle interactions.We give the regimes for discrete modes,and find that the emission can be distinctly suppressed.The configuration induces a broad band,but few particles are ejected due to the interference of the matter waves.We further qualitatively model the emission process and demonstrate the short-time behaviors.This engineering provides a way to manipulate the propagation of particles and the corresponding dynamics of condensates in lattices,and may find application in the dynamical excitation control of other nonequilibrium problems with time-periodic driving.

Structural Foundation and Geometry of the Material Singularity (and Its Quantum Entanglement)

In this paper we develop and study, as the second part of one more general development, the energy transmutation equation for the material singularity, previously obtained through the symmetrisation of a wave packet, that is, we develop the correlation between the terms of this equation, which accounts for the formation of matter from a previous vibrational state, and the different possible energy species. These energetic species are ascribed, in a simplified form, to the equation E¯ω=E¯k+E¯f, which allows us, through its associated phase factor, to gain an insight into the wave character of the kinetic energy and thus to attain the basis of the matter-wave, and all sorts of related phenomenologies, including that concerning quantum entanglement. The formation of the matter was previously identified as an energetic process, analogous to the kinetic one, in which finally the inertial mass is consolidated as a mass in a different phase, now, in addition, the mass of the material singularity is identified as a volumetric density of waves of toroidal geometry created in the process of singularisation or energy transfer between species, which makes it possible to establish the real relation or correspondence between the corpuscular and photonic energy equation (E=mc2=hν), i.e. to explain through m the intimate sense of the first equivalence, which explains what νis in the second one.

Matter-wave interference in an axial triple-well optical dipole trap

This paper proposes a scheme of axial triple-well optical dipole trap by employing a simple optical system composed of a circular cosine grating and a lens. Three optical wells separated averagely by -37 μm were created when illuminating by a YAG laser with power 1 mW. These wells with average trapping depth -0.5 μK and volume -74 μm^3 are suitable to trap and manipulate an atomic Bose-Einstein condensation （BEC）. Due to a controllable grating implemented by a spatial light modulator, an evolution between a triple-well trap and a single-well one is achievable by adjusting the height of potential barrier between adjacent wells. Based on this novel triple-well potentials, the loading and splitting of BEC, as well as the interference between three freely expanding BECs, are also numerically stimulated within the framework of mean-field treatment. By fitting three cosine functions with three Gaussian envelopes to interference fringe, the information of relative phases among three condensates is extracted.

Dynamic stability and manipulation of bright matter-wave solitons by optical lattices in Bose-Einstein condensates

An extended variation approach to describing the dynamic evolution of self-attractive Bose-Einstein condensates is developed. We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a timespace periodic optical lattice. The dynamics of condensates is shown to be well approximated by four coupled nonlinear differential equations. A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the condensate. We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites. In this case, the analytical predictions of Bose-Einstein condensates variational dynamics are found to be in good agreement with numerical simulations. We then find a stable region for successful manipulating matter-wave solitons without collapse, which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice.

Moving Matter-Wave Solitons in Spin-Orbit Coupled Bose-Einstein Condensates

We investigate the moving matter-wave solitons in spin-orbit coupled Bose Einstein condensates （BECs） by a perturbation method. Starting with the one-dimensional Gross Pitaevskii equations, we derive a new KdV-like equation to which an approximate solution is obtained by assuming weak Raman coupling and strong spin orbit coupling. The derivation of the KdV-like equation may be useful to understand the properties of solitons excitation in spin-orbit coupled BECs. We find different types of moving solitons： dark-bright, bright bright and dark dark solitons. Interestingly, moving dark-dark soliton for attractive intra- and inter-species interactions is found, which depends on the Raman coupling. The amplitude and velocity of the moving solitons strongly depend on the Raman coupling and spin orbit coupling.

Collision Dynamics of Dissipative Matter-Wave Solitons in a Perturbed Optical Lattice

We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-one- dimensional Bose-Einstein condensate with linear gain and three-body recombination loss perturbed by a weak optical lattice. It is shown that the linear gain can modify the stability of the single dissipative soliton moving in the optical lattice. The collision dynamics of two individual dissipative matter-wave solitons explicitly depend on the linear gain parameter, and they display different dynamical behaviors in both the in-phase and out-of-phase interaction regimes.

Matter-Wave Solitons in Two-Component Bose—Einstein Condensates with Tunable Interactions and Time Varying Potential

We present three families of exact matter-wave soliton solutions for an effective one-dimension twocomponent Bose-Einstein condensates(BECs) with tunable interactions,harmonic potential and gain or loss term. We investigate the dynamics of bright-bright solitons,bright-dark solitons and dark-dark solitons for the time-dependent expulsive harmonic trap potential,periodically modulated harmonic trap potential,and kinklike modulated harmonic trap potential.Through the Feshbach resonance,these dynamics can be realized in experiments by suitable control of time-dependent trap parameters,atomic interactions,and interaction with thermal cloud.

Matter-Wave Solitons in Two-Dimensional Bose—Einstein Condensates with Time-Dependent Scattering Length in a Harmonic Trap

We present three families of one-soliton solutions for （2＋1）-dimensional Gross-Pitaevskii equation with both time-dependent scattering length and gain or loss in a harmonic trap. Then we investigate the dynamics of these solitons in Bose-Einstein condensate8 （BECs） by some selected control functions. Our results show that the intensities of these solitons first increase rapidly to the condensation peak, then decay very slowly to the background; thus the lifetime of a bright soliton, a train of bright solitons and a dark soliton in BECs can be all greatly extended. Our results offer a useful method for observing matter-wave solitons in BECs in future experiments.

The Difference in Mass between Relativity and Quantum Mechanics, Also Novel Effects of the Axial Doppler Shift

If a particle has a wave function or is in other ways a moving wave, it should have an axial Doppler shift. Writers on relativity do not give moving particles that. The classic equation of quantum mechanics requires that frequency and mass have the same distortion from velocity (Doppler shift). But in the common writings on relativity mass always goes up with increases of velocity, and the transverse shift of frequency always goes down with increases of velocity [1] [2] [3] [4]. Most of this is due to simplifications and errors in the Lorentz transformation, some came from being in the aether wind era originally and because accelerators are noisy. It is not valid to say because the aether axial wind averages to zero between reflections so does axial Doppler shifts. After the first reflection in the Lorentz transformation, the light from the Sun is in Earth’s reference frame and there are no more Doppler shifts. Also the Michelson-Morley experiment is not all cases, and light is not the only thing deformed by velocity. The axial shift’s formula has the cosine of the observation angle in it. The implications are not just quantitative but also qualitative because anything with an axial Doppler shift has different values in different directions from an observer. That is the defining property of a vector and that changes its dimensions and the dimensions of the differential relations it is in. This happens with other scalar qualities as well. That means scalars such as mass and charge are now vectors and have additional dimensions. Therefore differential equations with them have additional dimensions. This includes Faraday-Max- well’s equations and Schrodinger’s equations. Also the Doppler blue shift seems to imply additional dimensions of time another way. That is the first Lorentz transformation error;the second is assumption of non-existent symmetry.

Reciprocity as an Ever-Present Dual Property of Everything

Reciprocity may be understood as relation of action and reaction in the sense of Hegel’s philosophical definition. Quoting Kant, freedom and ethical necessities are reciprocally limited. In this contribution, a more mathematical than philosophical reflection about reciprocity as an ever-present dual property of everything was given. As a crystallographer, the author is familiar with the action of Fourier transforms and the relation between a crystal lattice and its reciprocal lattice, already pointing to the duality between particles and waves. A generalization of the reciprocity term was stimulated by results of the famous Information Relativity (IR) theory of Suleiman with its proven physical manifestation of matter-wave duality, compared to the set-theoretical E-Infinity theory developed by El Naschie, where the zero set represents the pre-quantum particle, and the pre-quantum wave is assigned to the empty set boundary surrounding the pre-particle. Expectedly, the most irrational number of the golden mean is involved in these thoughts, because this number is intimately connected with its inverse. An important role plays further Hardy’s maximum quantum entanglement probability as the fifth power of φand its connection to the dark matter. Remembering, the eleven dimensions in Witten’s M-theory may be decomposed into the Lucas number L5 = 11 = φ−5 – φ5. Reciprocity is indeed omnipresent in our world as piloting waves that accompany all observable earthen and cosmic matter. As a side effect of the IR theory some fundamental constants such as the gyromagnetic factor of the electron, Sommerfeld’s fine-structure constant as well as the charge of the electron must be marginally changed caused by altered relativistic corrections. Consequences also arise for our vision about the evolution of life and consciousness.

Describe Quantum Mechanics in Dual 4 d Complex Space-Time and the Ontological Basis of Wave Function

Micro-object is both particle and wave, so the traditional Particle Model (mass point model) is actually not applicable for it. Here to describe its motion, we expand the definition of time and space and pick up the spatial degrees of freedom hidden by particle model. We say that micro-object is like a rolling field-matter-ball, which has four degrees of freedom including one surface curvature degree and three mapping degrees in the three-dimensional phenomenal space. All the degrees are described by four curvature coordinate components, namely “k1, k2, k3, k4”, which form the imaginary part of a complex phase space, respectively. While as to the real part, we use “x1, x2, x3, x4” to describe the micro object’s position in our real space. Consequently, we build a Dual 4-dimensional complex phase space whose imaginary part is 4-dimension k space and real part is 4-dimension x space to describe the micro-object’s motion. Furthermore, we say that wave function can describe the information of a field-matter-ball’s rotation & motion and also matter-wave can spread the information of micro-object’s spatial structure & density distribution. Matter-wave and probability-wave can transform to each other though matter-wave is a physical wave. The non-point property is the foundational source of the probability in Quantum Mechanics.

Theoretical Evidence for Wave Nature of Micro Particle and New Theory of Its Collective Motion in Material

Since a material is composed of micro particles, investigating behavior of those particles is essentially dominant for materials science. The diffusivity of diffusion equation is relevant to not only a collective motion of micro particles but also a motion of single particle. An elementary process of diffusion was thus theoretically investigated in a local space and time. As a result, the investigation concluded that the wave nature of micro particle results from denying the mathematical density theorem of a real time in the Newton mechanics. In other words, the basic theory of quantum mechanics is established in accordance with the cause-and-effect relationship in the Newton mechanics, for the first time, regardless of the de Broglie hypothesis. In relation to the collective motion of micro particles, the new diffusion theory was also reasonably established using the universal expression of diffusivity obtained here. In the present paper, the new findings indispensable for the fundamental knowledge in physics are thus systematically discussed in accordance with the theoretical frame in physics.

Quadrupolar matter-wave soliton in two-dimensional free space

We study two-dimensional （2D） matter-wave solitons in the mean-field models formed by electric quadrupole particles with long-range quadrupoleluadrupole interaction （QQI） in 2D free space. The existence of 2D matter-wave solitons in the free space was predicted using the 2D Gross Pitaevskii Equation （GPE）. We find that the QQI solitoms have a higher mass （smaller size and higher intensity） and stronger anisotropy than the dipol^dipole interaction （DDI） solitons under the same environmental parameters. Anisotropic solitomsoliton interaction between two identical QQI solitons in 2D free space is studied. Moreover, stable anisotropic dipole solitons are observed, to our knowledge, for the first time in 2D free space under anisotropic nonlocal cubic nonlinearity.

Cross-symmetry breaking of two-component discrete dipolar matter-wave solitons

We study the spontaneous symmetry breaking of dipolar Bose-Einstein condensates trapped in stacks of two-well systems, which may be effectively built as one-dimensional trapping lattices sliced by a repelling laser sheet. If the potential wells are sufficiently deep, the system is modeled by coupled discrete Gross-Pitaevskii equations with nonlocal self- and cross-interaction terms representing dipole-dipole interactions. When the dipoles are not polarized perpendicular or parallel to the lattice, the cross- interaction is asymmetric, replacing the familiar symmetric two-component solitons with a new species of cross-symmetric or -asymmetric ones. The orientation of the dipole moments and the interwell hopping rate strongly affect the shapes of the discrete two-component solitons as well as the characteristics of the cross-symmetry breaking and the associated phase transition. The sub- and super-critical types of cross-symmetry breaking can be controlled by either the hopping rate between the components or the total norm of the solitons. The effect of the interplay between the contact nonlinearity and the dipole angle on the cross-symmetry breaking is also discussed.

Dynamics of Analytical Matter-Wave Solutions in Three-Dimensional Bose–Einstein Condensates with Two- and Three-Body Interactions

Using the F-expansion method we present analytical matter-wave solutions to Bose-Einstein condensates with two- and three-body interactions through the generalized three-dimensional Gross-Pitaevskii equation with time- dependent coefficients, for the periodically time-varying interactions and quadratic potential strength. Such solutions exist under certain conditions, and impose constraints on the functions describing potential strength, nonlinearities, and gain （loss）. Various shapes of analytical matter-wave solutions which have important applications of physical interest are s^udied in details.