In the “counterfactual quantum cryptography” scheme [T.-G. Noh, Phys. Rev. Lett. 103, 230501 (2009)], two legitimate distant peers may share secret-key bits even when the information carriers do not travel in the quantum channel. The security of this protocol with an ideal single-photon source has been proved by Yin et al. [Z.-Q. Yin, H. W. Li, W. Chen, Z. F. Han, and G. C. Guo, Phys. Rev. A 82, 042335 (2010)]. In this paper, we prove the security of the counterfactual-quantum-cryptography scheme based on a commonly used weak-coherent-laser source by considering a general collective attack. The basic assumption of this proof is that the efficiency and dark-counting rate of a single-photon detector are consistent for any $n$-photon Fock states. Then through randomizing the phases of the encoding weak coherent states, Eve's ancilla will be transformed into a classical mixture. Finally, the lower bound of the secret-key-bit rate and a performance analysis for the practical implementation are both given.

We study the effect of quenching on a discrete quantum random walk by removing a detector placed at a position $x_D$ abruptly at time $t_R$ from its path. The results show that this may lead to an enhancement of the occurrence probability at $x_D$ provided the time of removal $t_R<t_R^{\lim }$, where $t_R^{\lim }$ scales as $x_D{}^2$. The ratio of the occurrence probabilities for a quenched walker ($t_R\ne 0$) and free walker ($t_R=0$) shows that it scales as $1/t_R$ at large values of $t_R$ independent of $x_D$. On the other hand, if $t_R$ is fixed, this ratio varies as $x_D^2$ for small $x_D$. The results are compared to the classical case. We also calculate the correlations as functions of both time and position.

Developing control fields (pulse sequences) that can compensate for the dispersion in the parameters governing the evolution of a quantum system is an important problem in coherent spectroscopy and quantum information processing. The use of composite pulses for compensating for dispersion in system dynamics is widely known and applied. In this paper, we introduce pulse elements for correcting pulse errors. These design methods are analytical and can be used to prove arbitrarily good robust performance. Furthermore, the time to compensation is superior to existing Fourier synthesis methods, which is critical for minimizing errors due to relaxation effects.

We classify vortex-core structures according to the topology of the order parameter space. We develop a method to characterize how the order parameter changes inside the vortex core. We apply it to spin-1 Bose-Einstein condensates and show that the vortex-core structures are classified by winding numbers that are locally defined in the core region. We also show that a vortex-core structure with a nontrivial winding number can be stabilized under a negative quadratic Zeeman effect.

We study echoes and what we call “revival echoes” for a collection of atoms that are described by a single quantum wave function and are confined in a weakly anharmonic trap. The echoes and revival echoes are induced by applying two successive temporally localized potential perturbations to the confining potential, one at time $t=0$, and a smaller one at time $t=\tau$. Pulselike responses in the expectation value of position $\langle x\left(t\right)\rangle$ are predicted at $t\approx n\tau$ ($n=2,3,...$) and are particularly evident at $t\approx 2\tau$. While such echoes are familiar from previous work, a result of our study is the finding of revival echoes. Revivals (but not echoes) occur even if the second perturbation is absent. In particular, in the absence of the second perturbation, the response to the first perturbation dies away but then reassembles, producing a response at revival times $m{T}_x$ ($m=1,2,...$). The existence of such revivals is due to the discreteness of the quantum levels in a weakly anharmonic potential, and has been well studied previously. If we now include the second perturbation at $t=\tau$, we find temporally localized responses, revival echoes, both before and after $t\approx m{T}_x$ [e.g., at $t\approx m{T}_x-n\tau$ (prerevival echoes) and at $t\approx m{T}_x+n\tau$, (postrevival echoes)] where $m$ and $n$ are $1,2,...$. One notable point is that, depending on the form of the perturbations, the “principal” revival echoes at $t\approx T_x\pm \tau$ can be much larger than the echo at $t\approx 2\tau$. We develop a perturbative model for these phenomena, and compare its predictions to the numerical solutions of the time-dependent Schrödinger equation. The scaling of the size of the various echoes and revival echoes as a function of the symmetry of the perturbations applied at $t=0$ and $t=\tau$, and of the size of the external perturbations is investigated. The quantum recurrence and revival echoes are also present in higher moments of position, $\langle x^p\left(t\right)\rangle$, $p>1$. Recurrences are present at $t\approx m{T}_x/j$, and dominant prerevival and postrevival echoes occur at fractional shifts of $\tau$ [i.e. $t\approx (m{T}_x\pm \tau )/j$] where the $m=1,2,...$ and the integer values of $j$ are determined by $p$. Additionally, we use the Gross-Pitaevskii equation to study the effect of atom-atom interactions on these phenomena. We find that echoes and revival echoes become more difficult to discern as the size of the second perturbation is increased and/or as the atom-atom interactions become stronger.

We study the parametric resonance of capillary waves on the interface between two immiscible Bose-Einstein condensates pushed towards each other by an oscillating force. Guided by analytical models, we solve numerically the coupled Gross-Pitaevskii equations for a two-component Bose-Einstein condensate at zero temperature. We show that, at moderate amplitudes of the driving force, the instability is stabilized due to nonlinear modifications of the oscillation frequency. When the amplitude of the driving force is large enough, we observe a detachment of droplets from the Bose-Einstein condensates, resulting in the generation of quantum vortices (skyrmions). We analytically investigate the vortex dynamics, and conditions of quantized vortex generation.

We analyze the nonquadratic in time Zeno effect which arises when a few-atom state initially trapped between two high laser-induced barriers is briefly released to free evolution. We identify the Zeno time, analyze the energy distributions of those atoms which have escaped and those that remained inside the trap, and obtain a simple relation between the survival and nonescape probabilities. The relevant time scales are such that the effect would be observable for the atomic species used in current laser experiments.

The Landé $g$ factor describes the response of an atomic energy level to an external perturbation by a uniform and constant magnetic field. In the case of many-electron systems, the leading term is given by the interaction ${\mu }_B(\vec{L}+2\vec{S})·\vec{B}$, where $\vec{L}$ and $\vec{S}$ are the orbital and spin angular momentum operators, respectively, summed over all electrons. For helium, a long-standing experimental-theoretical discrepancy for $P$ states motivates a re-evaluation of the higher order terms which follow from relativistic quantum theory and quantum electrodynamics (QED). The tensor structure of relativistic corrections involves scalar, vector, and symmetric and antisymmetric tensor components. We perform a tensorial reduction of these operators in a Cartesian basis, using an approach which allows us to separate the internal atomic from the external degrees of freedom (magnetic field) right from the start of the calculation. The evaluation proceeds in a Cartesian basis of helium eigenstates, using a weighted sum over the magnetic projections. For the relativistic corrections, this leads to a verification of previous results obtained using the Wigner-Eckhart theorem. The same method, applied to the radiative correction (Bethe logarithm term) leads to a spin-dependent correction, which is different for singlet versus triplet $P$ states. Theoretical predictions are given for singlet and triplet $2P$ and triplet $3P$ states and compared to experimental results where available.

State-resolved squared form factors of the electric monopolar excitations to $3p^{5}4p{[1/2]}_0$ and $3p^{5}4p^{\prime }{[1/2]}_0$, the electric dipolar excitations to $3p^{5}4s{[3/2]}_1$ and $3p^{5}4s^{\prime }{[1/2]}_1$, and the electric quadrupolar excitations to $3p^{5}4p{[5/2]}_2$, $3p^{5}4p{[3/2]}_2$, and $3p^{5}4p^{\prime }{[3/2]}_2$ of argon are determined by inelastic x-ray scattering with a high resolution of 70 meV. Good agreement is observed between the present results and the calculations of the random phase approximation with exchange except that the present results of $3p^{5}4s^{\prime }{[1/2]}_1$ in $q^2>$ 3 a.u. are smaller and $3p^{5}4p{[1/2]}_0$ in $q^2<$ 1.5 a.u. are larger than the theoretical results. The difference may be due to the difficulty of obtaining accurate wave functions or dealing with the electronic correlations for a heavier atom such as argon. The disagreements between the present squared form factors and the ones measured by electron energy loss spectroscopy indicate that the first Born approximation is not satisfied, even at an incident electron energy of 2500 eV.

The angular distributions of Ne${}^{7+}$ ions transmitted at various kinetic energies of 7–70 keV through muscovite mica nanocapillaries of rhombic cross section are measured. It is found that the transmitted ion beams form a rectangular shape at tilt angles that are small compared to those given by the aspect ratio, i.e., the capillary geometrical opening angle. This shape is retained for all ion energies, but its size changes. The time evolution of the transmitted angular distributions shows that the characteristic profile occurs instantaneously and remains in the stationary state of the transmission, whereas it shifts with the increase of the accumulated incident charge. At tilt angles of the capillaries larger than their aspect ratio, the shape in the transmission profile gets distorted from the rectangle by the deposited charge. Combined with trajectory simulations we show the observed shaping effect is due to the image force seen by the ions, interplaying with a deflection by the deposited charge on the capillary walls.

We present angular distributions for two-photon double ionization of lithium at photon energies of 50 eV ($\lambda$ $=$ 25 nm) and 59 eV ($\lambda$ $=$ 21 nm). The results are obtained from full-dimensional solution of the two-active-electron time-dependent Schrödinger equation using the time-dependent close-coupling method. We investigate two different double ionization mechanisms. First, we consider direct double ionization of the Li ground state following the absorption of two photons. Secondly, we consider an initial photoexcitation of the $1s2s2p$ doubly excited state, followed by photoionization of the $2s$ and $2p$ electrons. We find significant differences between the angular distributions obtained for these two distinct processes. We also compare the characteristics of the angular distributions for Li with those of other two-electron atoms.

We perform a detailed analysis of high-order harmonic generation (HHG) in atoms within the strong field approximation (SFA) by considering spatially inhomogeneous monochromatic laser fields. We investigate how the individual pairs of quantum orbits contribute to the harmonic spectra. We show that in the case of inhomogeneous fields the electron tunnels with two different canonical momenta. One of these momenta leads to a higher cutoff and the other one develops a lower cutoff. Furthermore, we demonstrate that the quantum orbits have a very different behavior in comparison to the homogeneous field. We also conclude that in the case of the inhomogeneous fields both odd and even harmonics are present in the HHG spectra. Within our model, we show that the HHG cutoff extends far beyond the standard semiclassical cutoff in spatially homogeneous fields. Our findings are in good agreement both with quantum-mechanical and classical models.

We study interacting bosons in a two-dimensional square bipartite optical lattice. By focusing on the regime where the first three excited bands are nearly degenerate (i.e., the first-excited $p$ bands in one sublattice are nearly degenerate with the $s$ band of the other sublattice), we derive a multi-orbital tight-binding model which captures the most relevant features of the band structure. In addition, we also derive a corresponding generalized Bose-Hubbard model and solve it numerically under different situations, both with and without a confining trap. It is especially found that the hybridization between sublattices can strongly influence the phase diagrams and, in a trap, enable even appearances of condensed phases intersecting the same Mott insulating plateaus.

We present single-molecule and macroscopic calculations showing that laser-induced Stark shifts contribute significantly to the phase of high-order harmonics from polar molecules. This is important for orbital tomography, where phases of field-free dipole matrix elements are needed in order to reconstruct molecular orbitals. We derive an analytical expression that allows the first-order Stark phase to be subtracted from experimental measurements.

We analyze nonlinear surface modes supported by a metal-dielectric nanostructured metamaterial with a nonlinear surface layer. We demonstrate that such a semi-infinite structure can support both TE and TM polarized surface modes with the subwavelength localization, which can be regarded as an optical analog of the electronic Tamm states. Such nonlinear Tamm states may appear even in the cases when linear surface modes do not exist.

Uncertainty relations are fundamental in quantum mechanics. Here I propose state-independent variance-based uncertainty relations for two or more arbitrary observables in finite dimensional spaces. The uncertainty relations provide near-optimal lower bounds in some typical examples, and are useful for entanglement detection.

We study strongly correlated phases of a pseudo-spin-$\frac{1}{2}$ Bose gas in an artificial gauge field using the exact diagonalization method. The atoms are confined in two dimensions and interact via a two-body contact potential. In Abelian gauge fields, pseudospin singlets are favored by pseudo-spin-independent interactions. We find a series of incompressible phases at fillings $\nu =2k/3$. By comparison with the non-Abelian spin singlet (NASS) states, constructed as zero-energy eigenstates of a $(k+1)$-body contact interaction, we classify the nontrivial topology of the states. An additional spin-orbit coupling is shown to switch between NASS-like states and spin-polarized phases from the Read-Rezayi series.

Helicity transfer in electron-positron pair production by a relativistic proton colliding with an intense laser beam of circular polarization is studied. The pairs are produced nonlinearly via absorption of few laser photons. Our approach relies on the laser-dressed description of the leptons by relativistic Volkov states and the spin-projection formalism. We calculate spin-resolved production rates, differential in the energy and emission angle of one of the created leptons. The degree of longitudinal polarization is shown to depend on the number of laser photons involved, even when the total energy and momentum absorbed from the laser field is kept constant.

We investigate correlations among complementary observables. In particular, we show how to take advantage of mutually unbiased bases for the efficient detection of entanglement in arbitrarily high-dimensional, multipartite, and continuous-variable quantum systems. The introduced entanglement criteria are relatively easy to implement experimentally since they require only a few local measurement settings. In addition, we establish a link between the separability problem and the maximum number of mutually unbiased bases—opening an additional avenue in this long-standing open problem.