We analyze the time evolution of two kinds of coherent states for a particle in a Pöschl-Teller potential. We find a pair of canonically conjugate operators and compare the behavior of their time evolution for both coherent states. The nonlinear ones are more localized. The trajectory in the phase space of the mean values of these two operators is a kind of generalization of the Rose algebraic curves. The new pair of canonically conjugate variables leads to a fourth-order Schrödinger equation which has the same energy spectrum as the Pöschl-Teller system.

Quantum mechanics presents peculiar properties that, on the one hand, have been the subject of several theoretical and experimental studies about its very foundations and, on the other hand, provide tools for developing new technologies, the so-called quantum technologies. The nonclassicality pointed out by Leggett-Garg inequalities has represented, with Bell inequalities, one of the most investigated subjects. In this article we study the connection of Leggett-Garg inequalities with a new emerging field of quantum measurement, the weak values in the case of a series of sequential measurements on a single object. In detail, we perform an experimental study of the four-time-correlator Leggett-Garg test, by exploiting single and sequential weak measurements performed on heralded single photons.

We study the breaking of the discrete time-translation symmetry in small periodically driven quantum systems. These systems are intermediate between large closed systems and small dissipative systems, which both display such symmetry breaking but have qualitatively different dynamics. As a nontrivial example, strongly different from the familiar case of parametric resonance, we consider period tripling in a quantum nonlinear oscillator. We develop theoretical methods of the analysis of period tripling, including the theory of multiple-state resonant tunneling in phase space with the account taken of the involved geometric phase. For moderately strong driving, the period tripling persists for a time, which is exponentially long compared with all dynamical times. This time is further extended by an even weak decoherence.

An exact reduced dynamical map along with its operator sum representation is derived for a central spin interacting with a thermal spin environment. The dynamics of the central spin shows high sustainability of quantum traits such as coherence and entanglement in the low-temperature regime. However, for sufficiently high temperature and when the number of bath particles approaches the thermodynamic limit, this feature vanishes and the dynamics closely mimics Markovian evolution. The properties of the long-time-averaged state and the trapped information of the initial state for the central qubit are also investigated in detail, confirming that the nonergodicity of the dynamics can be attributed to the finite temperature and finite size of the bath. It is shown that if a certain stringent resonance condition is satisfied, the long-time-averaged state retains quantum coherence, which can have far reaching technological implications in engineering quantum devices. An exact time-local master equation of the canonical form is derived. With the help of this master equation, the nonequilibrium properties of the central spin system are studied by investigating the detailed balance condition and irreversible entropy production rate. The result reveals that the central qubit thermalizes only in the limit of very high temperature and large number of bath spins.

Born's rule, which postulates the probability of a measurement outcome in a quantum state, is pivotal to interpretations and applications of quantum mechanics. By exploiting the departure of the product of two Hermitian operators in Born's rule from Hermiticity, we prescribe an intrinsic and natural scheme to decompose Born's probability into a classical part and a quantum part, which have significant implications in quantum information theory. The classical part constitutes the information compatible with the associated measurement operator, while the quantum part represents the quantum coherence of the state with respect to the measurement operator. Fundamental properties of the decomposition are revealed. As applications, we establish several trade-off relations for the classicality and quantumness in Born's probability, which may be interpreted as alternative realizations of Heisenberg's uncertainty principle. The results shed physical lights on related issues concerning quantification of complementarity, coherence, and uncertainty, as well as the classical-quantum interplay.

We investigate the validity of two common assumptions in the modeling of superconducting circuits: first, that the superconducting qubits are pointlike and, second, that the UV behavior of the transmission line is not relevant to the qubit dynamics. We show that in the experimentally accessible ultrastrong-coupling regime and for short (but attainable) times, the use of an inaccurate cutoff model (such as a sharp cutoff or none at all) could introduce very significant inaccuracies in the model's predictions.

We consider the uncertainty bound on the sum of variances of two incompatible observables in order to derive a corresponding steering inequality. Our steering criterion, when applied to discrete variables, yields the optimum steering range for two-qubit Werner states in the two-measurement and two-outcome scenario. We further employ the derived steering relation for several classes of continuous-variable systems. We show that non-Gaussian entangled states such as the photon-subtracted squeezed vacuum state and the two-dimensional harmonic-oscillator state furnish greater violation of the sum steering relation compared to the Reid criterion as well as the entropic steering criterion. The sum steering inequality provides a tighter steering condition to reveal the steerability of continuous-variable states.

The problem studied in this paper is, if the number of queries to unitary operations is fixed, say $k$, then when do local operations and classical communication (LOCC) suffice for optimally distinguishing bipartite unitary operations? We consider the above problem for two-qubit unitary operations in the case of $k=1$, showing that for two two-qubit entangling unitary operations without local parties, LOCC achieves the same distinguishability as the global operations. Specifically, we obtain the following: (i) if such two unitary operations are perfectly distinguishable by global operations, then they are perfectly distinguishable by LOCC also, and (ii) if they are not perfectly distinguishable by global operations, then LOCC can achieve the same optimal discrimination probability as the global operations.

Angle-differential elastic electron-scattering cross section, $\frac{d\sigma }{d\mathrm{\Omega }}$, for a 20-eV electron collision with a half-filled-subshell $\mathrm{Mn}(...3d^{5}4s^2,{}^{6}S)$ atom is studied using a semiempirical static polarization potential of the atom in the calculations. The study is in order, primarily due to noticeable discrepancies between results of the only two existing experimental measurements of the differential cross section, as well as discrepancies between the experimental results and available theoretical data. The calculation of $\frac{d\sigma }{d\mathrm{\Omega }}$ is performed in the framework of the spin-polarized Hartree-Fock approximation modified by the addition of the Bates static polarization potential $V_{\mathrm{pol}}\left(r\right)$ into the equations. An element of the study is the utilization of individual static dipole polarizabilities, ${\alpha }_{4s\uparrow }$ and ${\alpha }_{4s\downarrow }$, of the $4s$ electrons with opposite spin orientations ($4s\uparrow$ and $4s\downarrow$ electrons) from the atomic $4s^2$ subshell. They are calculated and used for the subsequent calculation of $V_{\mathrm{pol}}\left(r\right)$ and, finally, $\frac{d\sigma }{d\mathrm{\Omega }}$. The utility of the model is proven by a good agreement between the results of a trial calculation of $\frac{d\sigma }{d\mathrm{\Omega }}$ and corresponding trial calculated results obtained in the framework of a sophisticated random phase approximation with exchange. The results of the subsequent final calculation of $\frac{d\sigma }{d\mathrm{\Omega }}$ are compared with the experimental data along with the available theoretical results obtained in the framework of a spin-polarized local density approximation. Renewed theoretical and experimental studies of the 20-eV $\frac{d\sigma }{d\mathrm{\Omega }}$ of Mn are urged.

The nonmonotonic energy dependence of the $\mathrm{L}{\mathrm{i}}^0$ fraction on high-work-function surfaces has not been understood so far. To further study this phenomenon, in this work, efficient neutralization of $\mathrm{N}{\mathrm{a}}^{+}$ ions has been reported on various surfaces, instead of $\mathrm{L}{\mathrm{i}}^{+}$ ions. The nonmonotonic energy dependence of the $\mathrm{N}{\mathrm{a}}^0$ fraction becomes more and more obvious with the increase of the surface work function. For Cu(111) and Cu(110) at the scattering angle of 7°, the energy dependence of the neutral fraction is still nonmonotonic as compared to the scattering angles of 135° and 53°. For the scattering angle of 53°, the nonmonotonic angle dependence has been observed for these surfaces. The essences of the nonmonotonic angle and energy dependences are the same. The quantum-mechanical calculations reveal that the width and position of the atomic level below the Fermi level at short ion-surface distances are responsible for high neutral fractions at large exit energies, and that the neutral fraction at much smaller exit energies is probably related to the neutralization at large distances. For the exit angle dependence, the competition between neutralization at short and large distances strongly depends on the surface work function. In particular, the neutralization is enhanced by the relatively large parallel velocity.

High-harmonic generation by a laser-driven solid slab is simulated using time-dependent density functional theory. Multiple harmonic plateaus up to very high harmonic orders are observed already at surprisingly low field strengths. The full all-electron harmonic spectra are, in general, very different from those of any individual Kohn-Sham orbital. Freezing the Kohn-Sham potential instead is found to be a good approximation for the laser intensities and harmonic orders considered. The origins of the plateau cutoffs are explained in terms of band gaps that can be reached by Kohn-Sham electrons and holes moving through the band structure.

We introduce the optimal fingerprinting process which is aimed at accurately identifying the parameters which characterize the dynamics of a physical system. A database is first built from the time evolution of an ensemble of dynamical systems driven by a specific field, which is designed by optimal control theory to maximize the efficiency of the recognition process. Curve fitting is then applied to enhance the precision of the identification. As an illustrative example, we consider the estimation of the relaxation parameters of a spin-1/2 particle. The experimental results are in good accord with the theoretical computations. We show on this example a physical limit of the estimation process.

An attosecond XUV or x-ray pump-control scheme for the electron-spectral-line profiles of Fano and Auger resonances is proposed and studied. A weak pump resonantly excites the atom and creates the resonance, and then a second strong attosecond control pulse resonantly coupling the resonance to an valance excited state is applied at different time delays ($\mathrm{\Delta }{t}_{21}$). Resonance with lifetimes ($1/\mathrm{\Gamma }$) much longer than the pulse duration ($\tau$) is studied. It is found that the dynamic variations of the electron spectra can be partitioned into two or three regions with respect to the time delays and pulse area of the control pulse: explicitly, the overlap region ($\mathrm{\Delta }{t}_{21}<\sim 4\tau$) and analysis region ($\mathrm{\Delta }{t}_{21}>\sim 4\tau$) in the case with a sub-$\pi$-control pulse; and the overlap region ($\mathrm{\Delta }{t}_{21}<\sim 4\tau$), reverse region ($\sim 4\tau <\mathrm{\Delta }{t}_{21}<\sim 2/\mathrm{\Gamma }$), and analysis region ($\mathrm{\Delta }{t}_{21}>\sim 2/\mathrm{\Gamma }$) in the case with a sub-$2\pi$-control pulse. In the case with a sub-$\pi$-control pulse, the electron spectral line profiles do not change too much and only the degrees of asymmetries of the spectra are reduced in the overlap region, while in the analysis region, the main profiles of the electron spectra are maintained but with modulation structures. In the case with a sub-$2\pi$-control pulse, the electron spectral line profiles totally reverse the asymmetries in the overlap region, while in the reverse region, the electron spectra keep the reversed asymmetries but with modulation structures, and the electron spectra pertain the modulation structures in the analysis region but with the main profiles reversed. All these dynamic features of the electron spectra can be fully understood with the help of an analytic theory, which is also fully presented based on the time-dependent perturbation theory.

We perform the experimental demonstration of the method proposed earlier [F. P. Dos Santos, Phys. Rev. A 91, 063615 (2015)] to extract the differential phase in dual atom interferometers. From a single magneto-optical trap, we generate two atomic sources, vertically separated and free falling synchronously, with the help of an accelerated lattice. We drive simultaneous Raman interferometers onto the two sources and use the correlation with the vibration signal measured by a seismometer to extract the phase of each interferometer. We demonstrate an optimal sensitivity of the extracted differential phase between the two interferometers, free from vibration noise and limited by detection noise, when the two interferometers are in phase.

We theoretically investigate a two-dimensional harmonically trapped gas of identical atoms with Rashba spin-orbit coupling and no interatomic interactions. In analogy with the spin Hall effect in uniform space, the gas exhibits a spin Hall mode. In particular, in response to a displacement of the center of mass of the system, spin-dipole moment oscillations occur. We determine the properties of these oscillations exactly and find that their amplitude strongly depends on the spin-orbit-coupling strength and the quantum statistics of the particles.

An absolute optical instrument is a region of space, typically defined by a spatially varying index of refraction, in which bound ray trajectories are closed. Traditional examples of such devices include Maxwell's fisheye and the Eaton and Luneburg lenses. In this paper we employ the close analogy between classical mechanics and geometrical optics to develop a general theory of absolute instruments based on the Hamilton-Jacobi equation. Based on this theory, we derive many general properties of absolute instruments, and design a number of previously unknown examples. We also show how absolute optical instruments are related to superintegrable systems in mechanics and that the optical case is much less restrictive, which leads to an immense design space of absolute optical instruments.

The energy absorption and energy extinction cross sections of an object in uniform translational motion in free space are Lorentz invariant, but the total energy scattering cross section is not. Indeed, the forward-scattering theorem holds true for comoving observers but not for other inertial observers. If a pulsed plane wave with finite energy density is incident upon an object, the energies scattered, absorbed, and removed from the incident signal by the object are finite. The difference between the energy extinction cross section and the sum of the total energy scattering and energy absorption cross sections for a non-comoving inertial observer can be either negative or positive, depending on the object's velocity, shape, size, and composition. Calculations for a uniformly translating, solid, homogeneous sphere show that all three cross sections go to zero as the sphere recedes directly from the source of the incident signal at speeds approaching $c$, whether the material is a plasmonic metal (e.g., silver) or simply a dissipative dielectric material (e.g., silicon carbide).

We demonstrate the importance of considering correlations between degenerate Zeeman sublevels that develop in dense atomic ensembles. In order to do this, we develop a set of equations capable of simulating large numbers of atoms while still incorporating correlations between degenerate Zeeman sublevels. This set of equations is exact in the single-photon limit and may be interpreted as a generalization of the frequently used coupled-harmonic-oscillator equations. Using these equations, we demonstrate that in sufficiently dense systems, correlations between Zeeman sublevels can cause nontrivial differences in the photon-scattering line shape in arrays and clouds of atoms.

We study Bragg-induced power oscillations in Fourier space between a pair of optical resonant transverse modes propagating through a periodic $\mathcal{PT}$-symmetric lattice, represented by a refractive index that includes gain and loss in a balanced way. Our results imply that the $\mathcal{PT}$-symmetric system shows exceptionally rich phenomena absent in its Hermitian counterpart. It is demonstrated that the resonant modes exhibit unique characteristics, such as Bragg power oscillations controlled via the $\mathcal{PT}$ symmetry, severe asymmetry in mode dynamics, and trapped enhanced transmission. We have also performed numerical simulations in (1+1) and (2+1) dimensions of propagating Gaussian beams to compare with analytical calculations developed under a two-waves model.

Optical quantum protocols are reliant on the production of highly pure single photons. However, most parametric heralded single-photon sources possess spectral correlations, limiting the purity of the produced photon. The most common method for restoring the purity is with narrowband spectral filtering, which comes at the cost of reducing the rate of heralding detection. Here, we characterize this trade-off analytically for a large class of parametric sources. It is possible to achieve up to 20% heralding success probabilities with 90% heralded photon purities.