Fully Quantized Theory of Six-Wave Mixing with Matter Waves

We show that Wu-Yang theory of fully quantized four-wave mixing can be generalized to the six-wave mixing and derive the analytical solution of the coupled equations describing the quantum dynamics of six-wave mixing.

Weak Nonlinear Matter Waves in a Trapped Spin-1 Condensates

The dynamics of the weak non//near matter sofitary waves in a spin-1 condensates with harmonic external potential are investigated analytically by a perturbation method. It is shown that, in the small amplitude limit, the dynamics of the solitary waves are governed by a variable-coetficient Korteweg-de Vries （KdV） equation. The reduction to the （KdV） equation may be useful to understand the dynamics of nonlinear matter waves in spinor BECs. The analytical expressions for the evolution of soliton show that the small-amplitude vector solitons of the mixed types perform harmonic oscillations in the presence of the trap. Furthermore, the emitted radiation profiles and the soliton oscillation frequency are also obtained.

Determination of Solar Radius and Earth’s Radius by Relativistic Matter Wave

In recent years, relativistic matter waves have been applied to the solar system to explain some quantum gravity effects. This paper shows that the solar size and Earth’s size are the consequences of Bode’s rule in terms of the relativistic matter wave. The solar radius is determined as 7e+8 (m) with a relative error of 0.72%;the Earth’s radius is determined as 6.4328e+6 (m) with a relative error of 0.86%. The Earth’s atmospheric circulation is also investigated in terms of the relativistic matter wave, the wind fields on the Earth’s surface are calculated, and the results agree well with experimental observation. These findings indicate that the solar system is under the control of the planetary relativistic matter waves.

On the Existence of a Minimum Universal Speed of Physical Transmissions Associated with Matter Wave in Special Relativity

In this work, we show that it is possible to establish coordinate transformations between inertial reference frames in the theory of special relativity with a minimum universal speed of physical transmissions. The established coordinate transformations, referred to as modified Lorentz transformations because they have almost identical form to the Lorentz transformations, also comply with the requirement of invariance of the Minkowski line element. Particularly, the minimum universal speed can be associated with the phase speed of de Broglie matter wave. As application, we also discuss the possibility to formulate relativistic classical and quantum mechanics for the special relativity associated with the modified Lorentz transformations, which describes physical processes that represent an expansion or a collapsing of massive quantum particles.

Optical frequency comb technology: from ground to space

Optical frequency combs,as powerful tools for precision spectroscopy and research into optical frequency standards,have driven continuous progress and significant breakthroughs in applications such as time-frequency transfer,measurement of fundamental physical constants,and high-precision ranging,achieving a series of milestone results in ground-based environments.With the continuous maturation and evolution of femtosecond lasers and related technologies,optical frequency combs are moving from ground-based applications to astronomical and space-based applications,playing an increasingly important role in atomic clocks,exoplanet observations,gravitational wave measurements,and other areas.This paper,focusing on astronomical and space-based applications,reviews research progress on astronomical frequency combs,optical clock time-frequency networks,gravitational waves,dark matter measurement,dual-comb large-scale absolute ranging,and high-resolution atmospheric spectroscopy.With enhanced performance and their gradual application in the field of space-based research,optical frequency combs will undoubtedly provide more powerful support for astronomical science and cosmic exploration in the future.

Why Energy and Mass Can Be Converted between Each Other? A New Perspective Based on a Matter Wave Model

It was predicted by Einstein that energy and mass can be converted between each other. But why? Energy and mass are two very different physical concepts. How can they be exchanged with each other? We think the key to answer this question is to recall that a particle can behave like a wave. Particle properties like energy and momentum are known to be related to their corresponding wave properties (frequency and wave vector). Mass is clearly a particle property;is it also related to a wave property? This study suggests that it is. We found that mass and energy appear to share similar physical nature in the wave perspective. Both of them are related to the curvature of bending the vacuum medium during the propagation of the excitation wave. This similarity explains why they are convertible.

Remarkable Findings in Fundamental Theory of Quantum Mechanics—Matter Wave and Discrete Time in Physics

The relation of matter wave, which is well-known as a hypothesis proposed by de Broglie in 1923, gave basis for establishing the quantum mechanics. After that, experimental results revealed that a micro particle has a wave nature. However, the theoretical validity of the relation itself has never been revealed since his proposal. Theoretical basis that a micro particle has a wave nature has been thus disregarded in the unsolved state. The diffusion equation having been accepted as Fick’s second law was derived from the theory of Markov process in mathematics. It was then revealed that the diffusivity D depends on an angular momentum of a micro particle in a local space. The fact being unable to discriminate between micro particles in a local space resulted in having to accept the existence of minimum time t0 (>0) in the quantum mechanics. Based on t0 and D obtained here, the theoretical validity of relation of matter wave was confirmed. Denying the density theorem in mathematics for time in physics indicates that the probabilistic interpretation is essentially indispensable for understanding the quantum mechanics. The logical necessity of quantum theory itself is thus understandable through introducing t0 into the Newton mechanics. It is remarkable that the value of t0 between 1.14×10-17 s ≤ t0 ≤1.76×10-14 s obtained here is extremely larger than that of the well-known Planck time tp=5.396×10-44 s.

Oscillation properties of matter–wave bright solitons in harmonic potentials

We investigate the oscillation periods of bright soliton pair or vector bright soliton pair in harmonic potentials. We demonstrate that periods of low-speed solitons are greatly affected by the position shift during their collisions. The modified oscillation periods are described by defining a characterized speed, with the aid of asymptotic analysis on related exact analytic soliton solutions in integrable cases. The oscillation period can be used to distinguish the inter-and intra-species interactions between solitons. However, a bright soliton cannot oscillate in a harmonic trap, when it is coupled with a dark soliton(without any trapping potentials). Interestingly, it can oscillate in an anti-harmonic potential, and the oscillation behavior is explained by a quasi-particle theory. The modified period of two dark-bright solitons can be also described well by the characterized speed. These results address well the effects of position shift during soliton collision, which provides an important supplement for previous studies without considering phase shift effects.

High efficient Raman sideband cooling and strong three-body recombination of atoms

We report a highly efficient three-dimensional degenerated Raman sideband cooling(3D dRSC)that enhances the loading of a magnetically levitated optical dipole trap,and observe the strong atom loss due to the three-body recombination.The 3D dRSC is implemented to obtain 5×10^(7)Cs atoms with the temperature of~480 nK.The cold temperature enables 1.8×10^(7)atoms loaded into a crossed dipole trap with an optimized excessive levitation magnetic gradient.Compared to the loading of atoms from a bare magneto-optical trap or the gray-molasses cooling,there is a significant increase in the number of atoms loaded into the optical dipole trap.We derive for the three-body recombination coefficient of L_(3)=7.73×10^(-25)cm^(6)/s by analyzing the strong atom loss at a large scattering length of 1418 Bohr radius,and discover the transition from the strong three-body loss to the dominant one-body loss.Our result indicates that the lifetime of atoms in the optical dipole trap is finally decided by the one-body loss after the initial strong three-body loss.

Dynamics of Bright/Dark Solitons in Bose-Einstein Condensates with Time-Dependent Scattering Length and External Potential

We present an analytical study on the dynamics of bright and dark solitons in Bose-Einstein condensates with time-varying atomic scattering length in a time-varying external parabolic potential. A set of exact soliton solutions of the one-dimensional Gross-Pitaevskii equation are obtained, including fundamental bright solitons, higher-order bright solitons, and dark solitons. The results show that the soliton＇s parameters （amplitude, width, and period） can be changed in a controllable manner by changing the scattering length and external potential. This may be helpful to design experiments.

Variational Approach for the Bose-Hubbard Model

The phase diagram of the one-dimensional Bose-Hubbard model describing interacting bosons in optical lattice is investigated with the variational approach. This method can also be generalized to the two-dimensional case.

Quasiparticle Spectrum of Quantum Degenerate Fermi Gas in the Presence of Self—Consistent Magnetization Field

In this paper, we develop a systematic and simple method to derive quasiparticle spectrum of the quantum degenerate Fermi gases within the framework of Hartree–Fock–Bogoliubov theory which turns a general nonlinear two-body interaction Hamiltonian into a bilinear Hamiltonian by introducing certain self-consistent mean fields. Applying the approach, we obtain the quasi-particle spectrum of the model describing the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas in the presence of the magnetization fields and . When the gap parameter Δ is smaller than one or both of the magnetization fields, the spectrum manifests roton-type structure dramatically different from the spectrum in the absence of the magnetization fields.

Primary Assumptions and Guidance Laws in Wave Mechanics

In an article written by Louis de Broglie in 1959 (30 years after the Nobel prize rewarding his foundation of Wave Mechanics), the most challenging problem raised by the Bohr, Heisenberg and Born Standard Quantum Mechanics (SQM) was pointed out in the renunciation to describe “a permanent localization in space, and therefore a well-defined trajectory” for any moving particle. This challenge is taken up in the present paper, showing that de Broglie’s Primary Assumption p=hk, predicting the wave-particle duality, does also allow to obtain from the energy-dependent form of the Schrödinger and/or Klein-Gordon equations the Guidance Laws piloting particles along well-defined trajectories. The energy-independent equations, on the other hand, may only give rise—both in SQM and in the Bohmian approach—to probabilistic descriptions, overshadowing the role of de Broglie’s matter waves in physical space.

The Dynamics of Wave-Particle Duality

Both classical and wave-mechanical monochromatic waves may be treated in terms of exact ray-trajectories (encoded in the structure itself of Helmholtz-like equations) whose mutual coupling is the one and only cause of any diffraction and interference process. In the case of Wave Mechanics, de Broglie’s merging of Maupertuis’s and Fermat’s principles (see Section 3) provides, without resorting to the probability-based guidance-laws and flow-lines of the Bohmian theory, the simple law addressing particles along the Helmholtz rays of the relevant matter waves. The purpose of the present research was to derive the exact Hamiltonian ray-trajectory systems concerning, respectively, classical electromagnetic waves, non-relativistic matter waves and relativistic matter waves. We faced then, as a typical example, the numerical solution of non-relativistic wave-mechanical equation systems in a number of numerical applications, showing that each particle turns out to “dances a wave-mechanical dance” around its classical trajectory, to which it reduces when the ray-coupling is neglected. Our approach reaches the double goal of a clear insight into the mechanism of wave-particle duality and of a reasonably simple computability. We finally compared our exact dynamical approach, running as close as possible to Classical Mechanics, with the hydrodynamic Bohmian theory, based on fluid-like “guidance laws”.

The Basic Idea behind the Relativistic and the Quantum Concepts

A new aspect of unification is presented in this paper. This aspect depends on two postulates of our recent theory concerning light propagation in a specific medium. The special theory of relativity is demonstrated as a reflection of our first postulate, regarding the existence of multiple, equivalent rest frames in our medium. The second postulate is concerned with energy forms in nature, and it deals with the quantum behavior of light and wave behavior of matter. By using this postulate, we are able to justify the existence of these two phenomena. As a consequence of this, gravity as described by general relativity is unified as a background-independent interaction under the same postulate.

Generating Real Random Numbers with Uncertainty Principle

The real random number generation is a critical problem in computer science.The current generation methods are either too dangerous or too expensive,such as using decays of some radioactive elements.They are also hard to control.By the declaration of uncertainty principles in quantum mechanics,real probabilistic events can be substituted by easier and safer processes,such as electron diffraction,photon diffraction and qubits.The key to solve the problem of Schr?dinger’s cat is to identify that the atom stays in different states after and before the decay,and the result of the decay is probabilistic according to the wave packet co llapse hypothesis.Same matter is able to possess different kinds of properties such as wave-particle duality due to that it can stay in various states,and which state will the matter stay is determined by the chosen set of physical quantities(or mechanical quantities).One eigenstate of a set of physical quantities can be a superpos ition of other eigenstates of different sets of physical quantities,and the collapse from a superposition to an eigenstate it contains is really random.Using this randomness,real random number can be generated more easily.

Gravitational wave radiation from a double white dwarf system inside our galaxy: a potential method for seeking strange dwarfs

Like the investigation of double white dwarf （DWD） systems, strange dwarf （SD） - white dwarf （WD） system evolution in Laser Interferometer Space Antenna （LISA）＇s absolute amplitude-frequency diagram is investigated. Since there is a strange quark core inside an SD, SDs＇ radii are significantly smaller than the value predicted by the standard WD model, which may strongly affect the gravitational wave （GW） signal in the mass-transferring phases of binary systems. We study how an SD-WD binary evolves across LISA＇s absolute amplitude-frequency diagram. In principle, we provide an executable way to detect SDs in the Galaxy＇s DWD systems by radically new windows offered by GW detectors.

Two-parameter estimation in a matter-wave Sagnac interferometer

We explore the general characteristics of a matter-wave Sagnac interferometer in a two-parameter estimation scheme. We find that the measurement precisions of both parameters cannot reach the Heisenberg limit(HL) simultaneously when the input state is maximally entangled. Only one of the parameters' uncertainties can approach the HL while the other is scaled by the standard quantum limit.We provide the conditions with which the measurement precision of the specific parameter can reach the HL. We also discuss and figure out the concrete expressions of the constraint conditions for saturating the quantum Cramér–Rao bound. To satisfy these constraint conditions, the evolution time has to be a series of discrete values. Additionally, we calculate the variances of the parameters through some examples under these constraint conditions. The results provided in our work show some intrinsic features of the matter-wave Sagnac interferometer for the two-parameter estimation, which can be valuable in actual experiments.

Matter Effects on Neutrino Oscillations in Different Supernova Models

In recent years,with the development of simulations about supernova explosion,we have a better understanding about the density profiles and the shock waves in supernovae than before.There might be a reverse shock wave,another sudden change of density except the forward shock wave,or even no shock wave,emerging in the supernova.Instead of using the expression of the crossing probability at the high resonance,PH,we have studied the matter effects on neutrino oscillations in different supernova models.In detail,we have calculated the survival probability of νe(P_s)and the conversion probability of ν_x(P_c) in the Schrodinger equation within a simplified two-flavor framework for a certain case,in which the neutrino transfers through the supernova matter from an initial flavor eigenstate located at the core of the supernova.Our calculations was based on the data of density in three different supernova models obtained from simulations.In our work,we do not steepen the density gradient around the border of the shock wave,which differs to what was done in most of the other simulations.It is found that the mass and the density distribution of the supernova do make a difference on the behavior of P_s and P_c.With the results of P_s and P_c,we can estimate the number of νe(and ν_x) remained in the beam after they go through the matter in the supernova.

Superballistic wavepacket spreading in double kicked rotor

We investigate possible ways in which a quantum wavepacket spreads. We show that in a general class of double kicked rotor system, a wavepacket may undergo superballistic spreading; i.e., its variance increases as the cubic of time. The conditions for the observed superballistic spreading and two related characteristic time scales are studied. Our results suggest that the symmetry of the studied model and whether it is a Kolmogorov-Arnold-Moser system are crucial to its wavepacket spreading behavior. Our study also sheds new light on the exponential wavepacket spreading phenomenon previously observed in the double kicked rotor system.