Solitonic characteristics are revealed in the diffusion process of a hump or a notch wave packet in a one-dimensional Bose–Einstein condensate. By numerically solving the time-dependent Gross–Pitaevskii equation, we find completely different spreading behavior for attractive or repulsive condensates. For the attractive condensate, a series of bright solitons are continuously generated one after another at the wave front and they nearly stay at the positions where they are generated in the whole diffusion process. In contrast, for the repulsive condensate, the initial wave packet splits at the beginning into a series of grey solitons that travel at different velocities. The moving velocity of the grey soliton depends on nonlinear interaction strength, as well as the shape of a particular grey soliton.

We propose a new exponential shape function in wormhole geometry within modified gravity. The energy conditions and the equation-of-state parameter are obtained. The radial and tangential null energy conditions, and also the weak energy condition are validated, which indicates the absence of exotic matter due to modified gravity allied with such a new proposal.

Soliton molecules were first discovered in optical systems and are currently a hot topic of research. We obtain soliton molecules of the (2+1)-dimensional fifth-order KdV system under a new resonance condition called velocity resonance in theory. On the basis of soliton molecules, asymmetric solitons can be obtained by selecting appropriate parameters. Based on the $N$-soliton solution, we obtain hybrid solutions consisting of soliton molecules, lump waves and breather waves by partial velocity resonance and partial long wave limits. Soliton molecules, and some types of special soliton resonance solutions, are stable under the meaning that the interactions among soliton molecules are elastic. Both soliton molecules and asymmetric solitons obtained may be observed in fluid systems because the fifth-order KdV equation describes the ion-acoustic waves in plasmas, shallow water waves in channels and oceans.

We report the realization of quantum logic spectroscopy on the $^1\!S_0\rightarrow {}^3\!P_0$ clock transition of a single $^{27}$Al$^+$ ion. This ion is trapped together with a $^{40}$Ca$^+$ ion in a linear Paul trap, coupled by Coulomb repulsion, which provides sympathetic Doppler laser cooling and also the means for internal state detection of the clock state of the $^{27}$Al$^+$ ion. A repetitive quantum nondemolition measurement is performed to improve the fidelity of state detection. These techniques are applied to obtain clock spectroscopy at approximately 45 Hz. We also perform the preliminary locking on the $^1\!S_0\rightarrow {}^3\!P_0$ clock transition. Our work is a fundamental step that is necessary toward obtaining an ultra-precision quantum logic clock based on $^{40}$Ca$^+$-$^{27}$Al$^+$ ions.

Boron carbide (B$_{4}$C) coatings have high reflectivity and are widely used as mirrors for free-electron lasers in the x-ray range. However, B$_{4}$C coatings fabricated by direct-current magnetron sputtering show a strong compressive stress of about $-3$ GPa. By changing the argon gas pressure and nitrogen-argon gas mixing ratio, we are able to reduce the intrinsic stress to less than $-1$ GPa for a 50-nm-thick B$_{4}$C coating. It is found that the stress in a coating deposited at 10 mTorr is $-0.69$ GPa, the rms roughness of the coating surface is 0.53 nm, and the coating reflectivity is 88%, which is lower than those of coatings produced at lower working pressures. When the working gas contains 8% nitrogen and 92% argon, the B$_{4}$C coating shows not only $-1.19$ GPa stress but also a low rms roughness of 0.16 nm, and the measured reflectivity is 93% at the wavelength of 0.154 nm.

A high-$Q$ quartz crystal microbalance (QCM) sensor with a fundamental resonance frequency of 210 MHz is developed based on inverted mesa technology. The mass sensitivity reaches $5.332\times 10^{17}$ Hz/kg at the center of the electrode, which is 5–7 orders of magnitude higher than the commonly used 5 MHz or 10 MHz QCMs (their mass sensitivity is $10^{10}$–$10^{12}$ Hz/kg). This mass sensitivity is confirmed by an experiment of plating 1-ng rigid aluminium films on the surface of the QCM sensor. By comparing the changes in QCM equivalent parameters before and after coating the aluminum films, it is found that the QCM sensor maintains the high-$Q$ characteristics of the quartz crystal while the mass sensitivity is significantly improved. Therefore, this QCM sensor may be used as a promising analytical tool for applications requiring high sensitivity detection.

This work aims to study the $N$-coupled Hirota equations in an optical fiber under the zero boundary condition at infinity. By analyzing the spectral problem, a matrix Riemann–Hilbert problem on the real axis is strictly established. Then, by solving the presented matrix Riemann–Hilbert problem under the constraint of no reflection, the bright multi-soliton solutions to the $N$-coupled Hirota equations are explicitly gained.

Direct ZnO x-ray detectors with tunable sensitivity are realized by delicately controlling the oxygen flux during the sputtering deposition process. The photocurrents induced by x-rays from a 40 kV x-ray tube with a Cu anode increase apparently as the oxygen flux decreases, which is attributed to the introduction of $V_{\rm o}$ detects. By introducing $V_{\rm o}$ defects, the annihilation rate of the photo-generated electron-hole pairs will be greatly slowed down, leading to a remarkable photoconductive gain. This finding informs a novel way to design the x-ray detectors based on abundant oxide materials.

Using the single-mode approximation, we study entanglement measures including two independent quantities; i.e., negativity and von Neumann entropy for a tripartite generalized Greenberger–Horne–Zeilinger (GHZ) state in noninertial frames. Based on the calculated negativity, we study the whole entanglement measures named as the algebraic average $\pi_{3}$-tangle and geometric average ${\it \Pi}_{3}$-tangle. We find that the difference between them is very small or disappears with the increase of the number of accelerated qubits. The entanglement properties are discussed from one accelerated observer and others remaining stationary to all three accelerated observers. The results show that there will always exist entanglement, even if acceleration $r$ arrives to infinity. The degree of entanglement for all 1–1 tangles are always equal to zero, but 1–2 tangles always decrease with the acceleration parameter $r$. We notice that the von Neumann entropy increases with the number of the accelerated observers and $S_{\kappa_{\rm I}\zeta_{\rm I}}$ ($\kappa, \zeta\in ({\rm A, B, C})$) first increases and then decreases with the acceleration parameter $r$. This implies that the subsystem $\rho_{\kappa_{\rm I}\zeta_{\rm I}}$ is first more disorder and then the disorder will be reduced as the acceleration parameter $r$ increases. Moreover, it is found that the von Neumann entropies $S_{\rm ABCI}$, $S_{\rm ABICI}$ and $S_{\rm AIBICI}$ always decrease with the controllable angle $\theta$, while the entropies of the bipartite subsystems $S_{2-2_{\rm non}}$ (two accelerated qubits), $S_{2-1_{\rm non}}$ (one accelerated qubit) and $S_{2-0_{\rm non}}$ (without accelerated qubit) first increase with the angle $\theta$ and then decrease with it.

We characterize a modified continuous-variable quantum key distribution (CV-QKD) protocol with four states in the middle of a quantum channel. In this protocol, two noiseless linear amplifiers (NLAs) are inserted before each detector of the two parts, Alice and Bob, with the purpose of increasing the secret key rate and the maximum transmission distance. We present the performance analysis of the new four-state CV-QKD protocol over a Gaussian lossy and noisy channel. The simulation results show that the NLAs with a reasonable gain $g$ can effectively enhance the secret key rate as well as the maximum transmission distance, which is generally satisfied in practice.

Learning the Hamiltonian of a quantum system is indispensable for prediction of the system dynamics and realization of high fidelity quantum gates. However, it is a significant challenge to efficiently characterize the Hamiltonian which has a Hilbert space dimension exponentially growing with the system size. Here, we develop and implement an adaptive method to learn the effective Hamiltonian of an 11-qubit quantum system consisting of one electron spin and ten nuclear spins associated with a single nitrogen-vacancy center in a diamond. We validate the estimated Hamiltonian by designing universal quantum gates based on the learnt Hamiltonian and implementing these gates in the experiment. Our experimental result demonstrates a well-characterized 11-qubit quantum spin register with the ability to test quantum algorithms, and shows our Hamiltonian learning method as a useful tool for characterizing the Hamiltonian of the nodes in a quantum network with solid-state spin qubits.

We present a method for derivation of the density matrix of an arbitrary multi-mode continuous variable Gaussian entangled state from its phase space representation. An explicit computer algorithm is given to reconstruct the density matrix from Gaussian covariance matrix and quadrature average values. As an example, we apply our method to the derivation of three-mode symmetric continuous variable entangled state. Our method can be used to analyze the entanglement and correlation in continuous variable quantum network with multi-mode quantum entanglement states.

The modulational instability of two-component Bose–Einstein condensates (BECs) under an external parabolic potential is discussed. Based on the trapped two-component Gross–Pitaevskill equations, a time-dependent dispersion relation is obtained analytically by means of the modified lens-type transformation and linear stability analysis. It is shown that a modulational unstable time scale exists for trapped two-component BECs. The modulational properties—which are determined by the wave number, external trapping parameter, intra- and inter-species atomic interactions—are modified significantly. The analytical results are confirmed by direct numerical simulation. Our results provide a criterion for judging the occurrence of instability of the trapped two-component BECs in experiment.

Recently, a report from Elite Readers suggested that a strange phenomenon of 'square-shaped waves' had occurred at the beaches of the Isle of Rhe in the Bay of Biscay. Based on the hydrological and geological data of the Bay of Biscay, we find that the special phenomenon is closely related to a solitary wave that can be described by the shallow water wave equation. We discuss the formation mechanisms of the square-shaped waves by the Kadomtsev–Petviashvili equation. The combination of exact solutions and actual condition provides the simulated initial state. We then reproduce a square-shaped structure by a numerical method and obtain the result consistent with the observed picture from media. Our work enriches public understanding of strange water waves and has great significance for tourism development and shipping transportation.

We demonstrate a long-coherent-time coupling between microwave and optical fields through cold atomic ensembles. The phase information of the microwave field is stored in a coherent superposition state of a cold atomic ensemble and is then read out by two optical fields after 12 ms. A similar operation of mapping the phase of optical fields into a cold atomic ensemble and then retrieving by microwave is also demonstrated. These studies demonstrate that long-coherent-time cold atomic ensembles could resonantly couple with microwave and optical fields simultaneously, which paves the way for realizing high-efficiency, high-bandwidth, and noiseless atomic quantum converters.

An elongated trap potential for cold atoms is designed based on a quadrupole-Ioffe configuration. Phase fluctuations in a Bose–Einstein condensate (BEC), which is confined by the trap, are studied. We simulate the atom density distribution induced by fluctuation after time of flight from this elongated trap potential and study the temperature measurement method related to the distribution. Furthermore, taking advantage of the tight confinement and radio frequency dressing technique, we propose a double well potential for splitting BECs. Our results are helpful for improving understanding of low-dimensional quantum gases and provide important guidance for atomic interferometry.

The definitions of strong superadditive deficit for relative entropy coherence and monogamy deficit of measurement-dependent global quantum discord are proposed. The equivalence between them is proved, which provides a useful criterion for the validity of the strong superadditive inequality of relative entropy coherence. In addition, the strong superadditive deficit of relative entropy coherence is proved to be greater than or equal to zero under the condition that bipartite measurement-dependent global quantum discord (GQD) does not increase under the discarding of subsystems. Using the Monte Carlo method, it is shown that both the strong superadditive inequality of relative entropy coherence and the monogamy inequality of measurement-dependent GQD are established under general circumstances. The bipartite measurement-dependent GQD does not increase under the discarding of subsystems. The multipartite situation is also discussed in detail.

Quantum contextuality is one kind of quantumness that distinguishes quantum mechanics from classical theory. As the simplest exclusivity graph, quantum contextuality of the $n$-cycle graph has been reviewed, while only for odd $n$ the quantumness can be revealed. Motivated by this, we propose the degree of non-commutativity and the degree of uncertainty to measure the quantumness in the $n$-cycle graphs. As desired, these two measures can detect the quantumness of any $n$-cycle graph when $n\ge 4$.

In the traditional random-conformational-search model, various hypotheses with a series of meta-stable intermediate states were proposed to resolve the Levinthal paradox in protein-folding time. Here we introduce a quantum strategy to formulate protein folding as a quantum walk on a definite graph, which provides us a general framework without making hypotheses. Evaluating it by the mean of first passage time, we find that the folding time via our quantum approach is much shorter than the one obtained via classical random walks. This idea is expected to evoke more insights for future studies.

An absorption-desorption model with long-ranged interaction is simulated by the dynamic Monte Carlo method. The dynamic process has an inert phase and an active phase that is controlled by the absorption rate. In the active phase, the number of vacancies increases with time exponentially, while in the inert phase the vacant sites will be occupied by adsorbates rapidly. At the critical absorption rate, both the number of vacancies and the time-depending active probability exhibit power-law behavior. We determine the critical absorption rate and the scaling exponents of the power-laws. The effect of the interaction range of desorption on the critical exponents is investigated. In the short-ranged interaction limit, the critical exponents of Schlögl's first model are recovered. The model may describe the stability of the inner Helmholtz layer, an essential component of the electrochemical double-layer capacitor at a nanowire.

The first digit law, also known as Benford's law or the significant digit law, is an empirical phenomenon that the leading digit of numbers from real world sources favors small ones in a form $\log(1+{1}/{d})$, where $d=1, 2,\ldots, 9$. Such a law has been elusive for over 100 years because it has been obscure whether this law is due to the logical consequence of the number system or some mysterious mechanism of nature. We provide a simple and elegant proof of this law from the application of the Laplace transform, which is an important tool of mathematical methods in physics. It is revealed that the first digit law originates from the basic property of the number system, thus it should be attributed as a basic mathematical knowledge for wide applications.

Measurement-device-independent quantum key distribution (MDI-QKD) offers a practical way to realize a star-type quantum network. Previous experiments on MDI-QKD networks can only support the point-to-point communication. We experimentally demonstrate a plug-and-play MDI-QKD network which can support the point-to-multipoint communication among three users. Benefiting from the plug-and-play MDI-QKD architecture, the whole network is automatically stabilized in spectrum, polarization, arrival time, and phase reference. The users only need the encoding devices, which means that the hardware requirements are greatly reduced. Our experiment shows that it is feasible to establish a point-to-multipoint MDI-QKD network.

The realization of controllable couplings between any two qubits and among any multiple qubits is the critical problem in building a programmable quantum processor (PQP). We present a design to implement these types of couplings in a double-dot molecule system, where all the qubits are connected directly with capacitors and the couplings between them are controlled via the voltage on the double-dot molecules. A general interaction Hamiltonian of $n$ qubits is presented, from which we can derive the Hamiltonians for performing operations needed in building a PQP, such as gate operations between arbitrary two qubits and parallel coupling operations for multigroup qubits. The scheme is realizable with current technology.

Due to the obvious deviations of the existing theoretical models from the experimental results of ferroelectric phase transition, a new model is proposed on the basis of the coupling between spontaneous polarization and spontaneous strain in ferroelectrics. The spontaneous polarization and specific heat of ferroelectric phase transition predicted by the model are in better agreement with the corresponding data of triglyceride sulfate, a typical ferroelectric. In addition, the model predicts a new type of ferroelectric in which a phase transition and a phase-like transition coexist.

We demonstrate a simple scheme of 6.835 GHz microwave source based on the sub-sampling phase lock loop (PLL). A dielectric resonant oscillator of 6.8 GHz is directly phase locked to an ultra-low phase noise 100 MHz oven controlled crystal oscillator (OCXO) utilizing the sub-sampling PLL. Then the 6.8 GHz is mixed with 35 MHz from an direct digital synthesizer (DDS) which is also referenced to the 100 MHZ OCXO to generate the final 6.835 GHz signal. Benefiting from the sub-sampling PLL, the processes of frequency multiplication, which are usually necessary in the development of a microwave source, are greatly simplified. The architecture of the microwave source is pretty simple. Correspondingly, its power consumption and cost are low. The absolute phase noises of the 6.835 GHz output signal are $-$47 dBc/Hz, $-$77 dBc/Hz, $-$104 dBc/Hz and $-$121 dBc/Hz at 1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, respectively. The frequency stability limited by the phase noise through the Dick effect is theoretically estimated to be better than $5.0 \times 10^{-14}\tau^{1/2}$ when it is used as the local oscillator of the Rb atomic clocks. This low phase noise microwave source can also be used in other experiments of precision measurement physics.

We analyze the effect of electrode diameter and thickness on the mass sensitivity. Through the theoretical approximate calculation, we find that the mass sensitivity does not change monotonically with electrode diameter and there is a maximum point. The optimum electrode diameter corresponding to the maximum mass sensitivity varies with the electrode thickness. For a particular electrode diameter, a quartz crystal microbalance (QCM) with thick electrode has a higher mass sensitivity. A proper plating experiment using 35 QCMs with different electrode diameters and thicknesses verifies this finding. The present study further reveals how electrode size affects mass sensitivity and is helpful for QCM design.

With the development of quantum information processing, multipartite entanglement measures are needed in many cases. However, there are still no complete orthogonal genuine multipartite entanglement (GME) bases available as Bell states to bipartite systems. To achieve this goal, we find a method to construct complete orthogonal GME states, and we exclude many equivalent states by leveraging the group theory. We also provide the case of a $3$-order $3$-dimensional Hilbert space as an example and study the application of general results in the dense coding scheme as an application. Moreover, we discuss some open questions and believe that this work will enlighten extensive studies in this field.

We propose a model for a three-terminal quantum well heat engine with heat leakage. According to the Landauer formula, the expressions for the charge current, the heat current, the power output and the efficiency are derived in the linear-response regime. The curves of the power output and the efficiency versus the positions of energy levels and the bias voltage are plotted by numerical calculation. Moreover, we obtain the maximum power output and the corresponding efficiency, and analyze the influence of the heat leakage factor, the positions of energy levels and the bias voltage on these performance parameters.