Recently, dynamical characterization of bulk topology has been experimentally realized under nonadiabatic sudden quench dynamics. However, it has been shown that only the topology of final phase can be characterized when the system is quenched from initial topologically trivial phase. In this paper, we make a thorough investigation of different types of quenching processes under nonadiabatic slow quench dynamics, and study not only the processes between nontrivial phase and trivial phase, but also between the phases with different topological invariants. We find that, under slow quench dynamics, both the initial and final topological phase can be characterized and the topological invariant can be captured by time-averaged spin polarization. Moreover, different types of processes can be distinguished from the special regions where the time-averaged spin polarization vanishes. Our findings are not only restricted to two-dimensional Chern insulators, but also are valid for three-dimensional chiral topological insulators. All the dynamical characterization schemes are entirely based on the experimentally measurable quantity time-averaged spin polarization, and thus one can expect our findings may provide reference for future experiments.

The completely symmetric states play an essential role in quantum physics. In this paper, we calculate the reduced density matrix (RDM) for a single particle of the completely symmetric system coupled by $N$ spin-$\frac{1}{2}$ particles, because it helps to investigate the evolution of expectation value for the observable and to calculate the entanglement between the subsystems. Furthermore, we use Majorana's stellar representation (MSR) to represent the results because it provides an intuitive geometric perspective to comprehend the quantum states in the high-dimensional Hilbert space with distributions and trajectories of the Majorana stars on a Bloch sphere. With the operation properties of the generalized many-body anticommutator, we get the general MSR form of a single-qubit RDM. As the application and verification, we calculate the single-qubit RDM for the Dicke states with the results. Similarly, we further solve the RDM of the spin-$\frac{N}{2}$ state in a uniform magnetic field and study the systems with symmetric structures on the Bloch sphere. The results exhibit the relations between the composite systems and the subsystems, and provide a new idea for the numerical solution of multiqubit systems.

Time continues to be an intriguing physical property in the modern era. On the one hand, we have the classical and relativistic notions of time, where space and time have the same hierarchy, which is essential in describing events in spacetime. On the other hand, in quantum mechanics time appears as a classical parameter, meaning that it does not have an uncertainty relation with its canonical conjugate. In this work, we use a recent spacetime-symmetric proposal [Phys. Rev. A 95, 032133 (2017)] that tries to solve the unbalance in nonrelativistic quantum mechanics by extending the usual Hilbert space, having the time parameter $t$ and the position operator $\widehat{X}$ in one subspace and the position parameter $x$ and time operator $\mathbb{T}$ in the other subspace. Time as an operator is better suitable for describing tunneling processes. We then solve the $1/2$-fractional integrodifferential equation for a particle subjected to strong and weak potential limits and obtain an analytical expression for the tunneling time through a rectangular barrier. Using a Gaussian energy distribution, we demonstrate that, for wavepackets well resolved in time, the expectation value of the operator $\mathbb{T}$ is the energy average of the classical time $T_{\text{class}}=\partial S/\partial E$, where $S$ is the classical action, which can be real or imaginary. For wavepackets not well resolved in time, the contribution of $T_{\text{class}}$ consistently vanishes, and solely properties of the energy distribution contribute to $\mathbb{T}$. We show that the time of travel for nontunneling particles is purely real. When tunneling is involved, complex arrival times emerge, becoming a signature of tunneling. Furthermore, we apply our results to a constant energy distribution, obtaining pure imaginary times for energies below the barrier while obtaining complex times for particles with a wavepacket spreading energies below and above the barrier, and show a comparison to previous works.

We propose a quantum algorithm that diagonalizes a Hamiltonian by implementing an ansatz that satisfies the generalized Rayleigh-Ritz variational principle. This algorithm uses a purification technique to target many quantum states in one quantum circuit and allows multiple eigenstates to be optimized and determined simultaneously. Moreover, it requires a reasonable circuit depth compared to existing algorithms and enables flexible postprocessing on the accurately determined eigensubspace. Using the transverse-field Ising model, we confirm that the eigenvalues obtained with the algorithm converge efficiently and uniformly with the iteration steps, tested by both simulations and IBM platform measurements. As limited quantum resources are needed, this algorithm is promising for noise resilience, better performances, and versatile applications.

We present the generalized state-dependent entropic uncertainty relations in a multiple measurements setting and the optimal lower bound is obtained by considering different measurement sequences. We then apply this uncertainty relation to witness entanglement and give the experimentally accessible lower bounds on both bipartite and tripartite entanglements. This method of detecting entanglement is applied to a physical system of two particles on a one-dimensional lattice and Greenberger-Horne-Zeilinger (GHZ)-Werner state. It is shown that, for measurements that are not in mutually unbiased bases, this generalized entropic uncertainty relation is superior to the previous state-independent one in entanglement detection. Furthermore, we conduct a demonstration of multipartite entanglement detection of GHZ states up to ten qubits on the Quafu cloud quantum computation platform. Our results might play important roles in detecting multipartite entanglement experimentally.

The three-body fragmentation dynamics of $\mathrm{BrC}{\mathrm{N}}^{q+} \left(q=3–6\right)$ produced by 1-keV electron impact has been investigated using the ion momentum imaging technique. Up to 11 three-body Coulomb explosion channels were identified and analyzed. The corresponding kinetic energy release (KER) distributions were obtained and compared with the predictions of the Coulomb explosion model. By means of the Dalitz plot, Newton diagram, and native frame method, we have studied the concerted and sequential fragmentation mechanisms for channels leading to ${\mathrm{Br}}^{l+}+{\mathrm{C}}^{+}+{\mathrm{N}}^{+} \left(l=1–3\right)$. The KER for the intermediate dications $\mathrm{Br}{\mathrm{C}}^{2+}$ and $\mathrm{C}{\mathrm{N}}^{2+}$ from the sequential mechanism were determined and the electronic states of the intermediate molecular ion $\mathrm{C}{\mathrm{N}}^{2+}$ were discussed. For the channels leading to higher charge states of the carbon and nitrogen ions, only the concerted fragmentation mechanism was observed.

Motivated by recent measurements for several alkali-metal atoms and alkali-metal-like ions, we perform a detailed study of electric dipole ($E1$) transition amplitudes in K, $\mathrm{Ca}{}^{+}$, Rb, $\mathrm{Sr}{}^{+}$, Cs, $\mathrm{Ba}{}^{+}$, Fr, and $\mathrm{Ra}{}^{+}$, which are of interest for studies of atomic parity violation, electric dipole moments, and polarizabilities. Using the all-orders correlation potential method, we perform high-precision calculations of $E1$ transition amplitudes between low-lying $s, p$, and $d$ states. We perform a robust error analysis, and compare our calculations to many amplitudes for which there are high-precision experimental determinations. We find excellent agreement, with deviations at the level of $\sim 0.1$%. We also compare our results to other theoretical evaluations, and discuss the implications for uncertainty analyses. Further, combining calculations of branching ratios with recent measurements, we extract high-precision values for several $E1$ amplitudes of $\mathrm{Ca}{}^{+}, \mathrm{Sr}{}^{+}$, Cs, Fr, and $\mathrm{Ra}{}^{+}$.

The formation of antihydrogen atoms from three-body collisions between positronium atoms and antiprotons plays a crucial role in the gravitational behavior of antihydrogen at rest (GBAR) experiment devoted to the measure of the action of gravity on antimatter. One of the main challenges facing this experiment is to find the means for increasing the production of antihydrogens which are produced by the reaction $\overline{p}+\text{Ps}\to \overline{\text{H}}+e^{-}$ with an extremely low rate. Along these lines, we investigate here the possibility to influence the collision process by using a laser field. A perturbative approach combining the Coulomb-Born approximation for modeling the charged-particle collision and a first-order perturbation theory for describing laser-atom interactions is employed to estimate laser-mediated charge-exchange cross sections. By carefully considering the laser specifications compatible with the experimental constraints, we present an extensive study of the influence of the laser parameters (laser wavelength and intensity) on the cross sections in the energy range of interest for GBAR. We show that under special irradiation conditions the rate of antihydrogen production may be significantly increased by the presence of the laser field.

The adiabatic theory of strong-field ionization is extended to the specific configuration in which ionization occurs from a vortex orbital in an axially symmetric target by an elliptically polarized pulse with small ellipticity and the major axis of the polarization ellipse directed along the vortex axis of the initial state. Generation of vortex electrons in the continuum, their propagation in the laser field, and subsequent rescattering on the parent ion are described. Adiabatic asymptotics of the rescattering parts of the solution to the time-dependent Schrödinger equation and the ionization amplitude are obtained. On the basis of these results, the factorization formula giving the photoelectron momentum distribution (PEMD) in the vicinity of a backward rescattering caustic is derived. Our interest in the present configuration stems from the fact that, because of the nonzero ellipticity of the field, liberated vortex electrons arrive for rescattering with a nonzero impact parameter. The corresponding scattering amplitude generalizes the recently introduced vortex scattering amplitude characterizing head-on vortex-target rescattering in the linear polarization case [O. I. Tolstikhin and T. Morishita, Phys. Rev. A 99, 063415 (2019)]. Using the factorization formula, one can extract the absolute value of this generalized scattering amplitude from the observable PEMD, which opens a new window for target structure imaging in strong-field physics. The theory is illustrated by calculations for two atomic targets, ${\mathrm{He}}^{+}(2p,m=1)$ and $\mathrm{Xe}(5p,m=1)$. We show that in the case of the initial $\pi$ orbital and nonzero ellipticity not only the absolute values of two head-on scattering amplitudes with $m=0$ and 1, but also their phase difference as functions of the scattering angle can be extracted from the PEMD.

For relativistic spinless particles, the standard equation with Lorentz covariance is the Klein-Gordon equation, while the square-root Klein-Gordon equation, which is usually referred to be semirelativistic since it lacks Lorentz covariance, is another frequently used equation. We numerically solve these two equations coupled with time-dependent electromagnetic fields using the non-Hermitian Arnoldi and the Hermitian Lanczos propagator, respectively, in the three-dimensional real space. The non-Hermitian Arnoldi method is shown to be ideally suited for the Klein-Gordon equation. A different method to treat the nonlocal operator in the square-root Klein-Gordon equation is developed, allowing the calculation of the propagator to be more efficient. Furthermore, some strong-field problems such as the photoionization, high harmonic generation, and the pair production are studied using our methods. The results of both equations are compared with those of the nonrelativistic Schrödinger equation, which demonstrates the relativistic effects in various regimes. We show that observables of the Klein-Gordon equation and the square-root Klein-Gordon equation are identical up to the first order of relativistic corrections and confirm it numerically.

The novel application of a piezoelectric quartz resonator for the detection of trapped ions has enabled the observation of the quartz-ions interaction under nonequilibrium conditions, opening new perspectives for high-sensitive motional frequency measurements of radioactive particles. Energized quartz crystals have (long) decay-time constants in the order of milliseconds, permitting the coherent detection of charged particles within short time scales. In this paper we develop a detailed model governing the interaction between trapped ${}^{40}\mathrm{Ca}^{+}$ ions and a quartz resonator connected to a low-noise amplifier. We apply this model to experimental data and extract the ions' reduced-cyclotron frequency in our 7-T Penning trap setup. We also obtain an upper limit for the coupling constant $g$ with the present quartz-amplifier-trap (QAT) configuration. The study of the reduced-cyclotron frequency is especially important for the use of this resonator in precision Penning-trap mass spectrometry. The improvement in sensitivity can be accomplished by increasing the quality factor of the QAT configuration, which in turn will improve the performance of the system towards the strong-coupling regime.

We present an ab initio study of the nonsequential strong-field ionization dynamics of a model two-electron atom with helium character. Single- and double-ionization events are characterized and displayed using detector signals extracted at different points in the two-electron two-dimensional space. The double photoelectron momentum distribution is calculated via coherent path-summation over virtual-particle trajectories. A comparison is made between the momentum distributions obtained with the virtual-detector method, the Schrödinger wave function, and the time-dependent surface flux method developed by Tao and Scrinzi [New J. Phys. 14, 013021 (2012)]. Insights into different ionization and electron recollision pathways are gained from detailed virtual-particle tracking and energy-time readouts. This study demonstrates the extension of virtual-detector theory to strong-field multielectron quantum dynamics and highlights the importance of the evolving quantum phase in quasiclassical electron propagation.

We study dipole-mode and scissors-mode oscillations of a harmonically trapped dipolar supersolid, composed of dipolar droplets arranged on a one-dimensional (1D) or a 2D lattice, to establish the robustness of its crystalline structure under translation and rotation, using a beyond-mean-field model including a Lee-Huang-Yang interaction. The dipolar atoms are polarized in the $z$ direction with the supersolid crystalline structure lying in the $x\text{−}y$ plane. A stable dipole-mode oscillation is possible in the case of both quasi-1D and quasi-2D dipolar supersolids, whereas a sustained angular scissors-mode oscillation is possible only in the case of a quasi-1D dipolar supersolid between a maximum and a minimum of trap anisotropy in the $x\text{−}y$ plane. In both cases there is no visible deformation of the crystalline structure of the dipolar supersolid during the oscillation. The theoretical estimate of the scissors-mode-oscillation frequency is in good agreement with the present results and the agreement improves with an increase in the number of droplets in the supersolid and also with an increase in the confining trap frequencies. The results of this study can be tested experimentally with present knowhow.

We study the effect of atomic interaction on the localization and the associated dynamics of Bose-Einstein condensates in a one-dimensional quasiperiodic optical lattice and random disordered potentials. When the interactions are absent, the condensates exhibit localization, which weakens as we increase the interaction strength beyond a threshold value for both potential types. We inspect the localized and delocalized states by perturbing the system via quenching the interaction strength instantaneously to zero and studying the dynamics of the condensate, which we further corroborate using the out-of-time-order correlator. The temporal behavior of the time correlator displays regular dynamics for the localized state, while it shows temporal chaos for the delocalized state. We confirm this dynamical behavior by analyzing the power spectral density of the time correlator. We further identify that the condensate admits a quasiperiodic route to chaotic dynamics for both the potentials. Finally, we present the variation of the maximal Lyapunov exponents for different nonlinearity and disorder strengths that have a positive value in the regime where the time-correlator function shows chaotic behavior. Through this, we establish the strong connection between the spatially delocalized state of the condensate and its temporal chaos.

We propose an adaptive phase technique for the parametric cooling of mechanical oscillators. Our scheme calls for a sequence of periodic adjustments of the phase of a parametric modulation of the mechanical oscillator that is conditioned on measurements of its two quadratures. The technique indicates an exponential loss of thermal energy at initial high occupancies, similar in performance to other optomechanical techniques such as cold-damping or cavity self-cooling. As the quantum ground state is approached, the phase adaptive scheme leads to residual occupancies at the level of a few phonons owing to the competition between parametric amplification of quantum fluctuations and the feedback action.

We explore the effects of quantum mechanical squeezing on the nonequilibrium thermodynamics of a coherent heat engine with squeezed reservoirs coupled to a squeezed cavity. We observe that the standard known phenomenon of flux optimization beyond the classical limit with respect to quantum coherence is destroyed as the cavity is squeezed. This loss is independent of reservoir squeezing. Under biased conditions, the squeezing-dependent flux is always higher than the classical limit. The efficiency at maximum power (EMP) in the presence of cavity-squeezing is greater than what was predicted by Curzon and Ahlborn even in the absence of reservoir squeezing. The EMP with respect to either reservoir's squeezing parameters is surprisingly equal and linear in ${\eta }_C$ with a slope unequal to the universally accepted slope, $1/2$. The slope is found to be proportional to the dissipation into the cavity mode with an intercept proportional to a specific numerical value of the engine's efficiency.