Classically, the spatial resolution of the image of an object is usually determined by the Rayleigh criterion. However, quantum properties of light have been exploited to form images with resolutions exceeding this criterion and beating the standard quantum limit, which allow high measurement sensitivity. We found that it is possible to super-resolve a distributed object made of two parts that are spatially separated but when superposed over each other form an object. A coincidence interference pattern of a nonlocal two-photon system with periodicity proportional to $\lambda /2$ was measured even when each photon, with wavelength of $\lambda$, has been scattered by different parts of an object, none of them being the object itself.

We present a theoretical approach to the study of second- and third-harmonic generation from metallic structures and nanocavities filled with a nonlinear material in the ultrashort pulse regime. We model the metal as a two-component medium, using the hydrodynamic model to describe free electrons and Lorentz oscillators to account for core electron contributions to both the linear dielectric constant and harmonic generation. The active nonlinear medium that may fill a metallic nanocavity, or be positioned between metallic layers in a stack, is also modeled using Lorentz oscillators and surface phenomena due to symmetry breaking are taken into account. We study the effects of incident TE- and TM-polarized fields and show that a simple reexamination of the basic equations reveals additional, exploitable dynamical features of nonlinear frequency conversion in plasmonic nanostructures.

A recent experiment [Phys. Rev. Lett. 102, 073902 (2009)] has demonstrated that elliptically polarized high-order harmonic generation can be produced from linearly polarized driving fields for aligned molecular systems. In order to reveal the underlying physical mechanisms of elliptical harmonics, we present fully ab initio and high-precision calculations and analyses of the amplitude, phase, and polarization state of the harmonic radiation from molecular hydrogen ions with arbitrary orientation. We find that high ellipticity arises from molecular orbital symmetry and two-center interference effects. Our ab initio exploration and findings lead to a general rule that the ellipticity becomes high for molecular orbitals represented by a symmetric combination of atomic orbitals, whereas it becomes low for molecular orbitals represented by an antisymmetric combination. This finding also applies to the general case of aligned linear molecules.

The linear transient response of a two-level system coupled with an environmental system is studied under correlated and factorized initial conditions. We find that the transient responses in these cases differ significantly from each other, especially for strong system-environment interaction at intermediate temperatures. This means that it is necessary to pay attention to the initial conditions chosen when analyzing experiments on transient linear response, because the conventional factorized initial condition results in an incorrect response, in which the quantum correlation between the relevant system and the environmental system is disregarded.

The new generation of planar Penning traps promises to be a flexible and versatile tool for quantum-information studies. Here, we propose a fully controllable and reversible way to change the typical trapping harmonic potential into a double-well potential, in the axial direction. In this configuration a trapped particle can perform coherent oscillations between the two wells. The tunneling rate, which depends on the barrier height and width, can be adjusted at will by varying the potential difference applied to the trap electrodes. Most notably, tunneling rates in the range of kHz are achievable even with a trap size of the order of $100$ $\mu$m.

Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task when the pair of possible states is not a priori known but instead the two possible states are provided through two respective program ports. We study optimal programmable discrimination machines for general qubit states when several copies of states are available in the data or program ports. Two scenarios are considered: One in which the purity of the possible states is a priori known, and the fully universal one where the machine operates over generic mixed states of unknown purity. We find analytical results for both the unambiguous and minimum error discrimination strategies. This allows us to calculate the asymptotic performance of programmable discrimination machines when a large number of copies are provided and to recover the standard state discrimination and state comparison values as different limiting cases.

We study the conditions for obtaining maximally multipartite-entangled states (MMESs) as nondegenerate eigenstates of Hamiltonians that involve only short-range interactions. We investigate small-size systems (with a number of qubits ranging from $3$ to $5$) and show some example Hamiltonians with MMESs as eigenstates.

In this study, we investigate the structure of the polar alkali-metal-atom–strontium diatomic molecules as possible candidates for the realization of samples of ultracold polar molecular species not yet investigated experimentally. Using a quantum chemistry approach based on effective core potentials and core polarization potentials, we model these systems as effective three-valence-electron systems, allowing for calculation of electronic properties with full configuration interaction. The potential curve and the permanent dipole moment of the ${}^2{\Sigma }^{+}$ ground state are determined as functions of the internuclear distance for LiSr, NaSr, KSr, RbSr, and CsSr molecules. These molecules are found to exhibit a significant permanent dipole moment, though smaller than those of the alkali-metal-atom–Rb molecules.

We analyze the importance of exchange, polarization, and electron-electron correlation in high-order harmonic generation in molecules interacting with intense laser fields. We find that electron exchange can become particularly important for harmonic emission associated with intermediate excitations in the molecular ion. In particular, for orbitals associated with two-hole one-particle excitations, exchange effects can eliminate structure-related minima and maxima in the harmonic spectra. Laser-induced polarization of the neutral molecule may also have major effects on orbital structure-related minima and maxima in the harmonic spectra. Finally, we show how exchange terms in recombination can be viewed as a shakedownlike process induced by sudden electronic excitation in the ion.

Here we present experimental results connecting field ionization to photoionization in Li Rydberg atoms obtained with 17- and 36-GHz microwave fields. At a low principal quantum number $n$, where the microwave frequency $\omega$ is much lower than the classical, or Kepler frequency, ${\omega }_K=1/n^3$, microwave ionization occurs by field ionization, at $E=1/9n^4$. When the microwave frequency exceeds the Kepler frequency, $\omega >1/n^3$, the field required for ionization is independent of $n$ and given by $E=2.4{\omega }^{5/3}$, in agreement with dynamic localization models, which cross over to a Fermi’s Golden Rule approach at the photoionization limit. A surprising aspect of our results is that when $\omega \approx 1/2n^2$, the one- and multiphoton ionization rates are similar, and even at the lowest microwave powers, all are 10 times lower than the perturbation theory rate calculated for single-photon ionization. Further, we show that when the Rydberg atoms are excited in the presence of the microwave field, the probability of an atom’s being bound at the end of the microwave pulse passes smoothly across the limit. This microwave stimulated recombination to bound Rydberg states can be well described by a simple classical model. More generally, these results suggest that the problem of a Rydberg atom coupled to a high-frequency microwave field is similar to the problem of interchannel internal coupling in multilimit atoms, a problem well described by quantum defect theory.

We investigate a dilute Bose gas confined in a tight one-dimensional (1D) optical lattice plus a superimposed random potential at zero temperature. Accordingly, the ground-state energy, quantum depletion, and superfluid density are calculated. The presence of the lattice introduces a crossover to the quasi-two-dimensional (2D) regime, where we analyze asymptotically the 2D behavior of the system, particularly the effects of disorder. We thereby offer an analytical expression for the ground-state energy of a purely 2D Bose gas in a random potential. The obtained disorder-induced normal fluid density $n_n$ and quantum depletion $n_d$ both exhibit a characteristic $1/\ln (1/n_{2\mathrm{D}}{a}_{2\mathrm{D}}^2)$ dependence. Their ratio $n_n/n_d$ increases to $2$ compared to the familiar $4/3$ in lattice-free three-dimensional (3D) geometry, signifying a more pronounced contrast between superfluidity and Bose-Einstein condensation in low dimensions. The conditions for possible experimental realization of our scenario are also proposed.

We consider a mixture of two-component Fermi and (one-component) Bose gases under the repulsive Bose-Fermi and attractive Fermi-Fermi interactions. We perform a systematic study of the finite-temperature phase diagrams in the chemical potential space, identifying, using the Landau-Ginzburg theory, the features generic to the phase diagrams within the validity of our model. We apply the theory to explore the physics of correlated BCS pairing among fermions in a tightly confined trap surrounded by a large Bose-Einstein condensate gas.

The hydrodynamics of quantized vortices and solitons in an atomic Bose-Einstein condensate excited by an oscillating potential are studied by numerically solving the two-dimensional Gross-Pitaevskii equation. The oscillating potential keeps nucleating vortex dipoles, whose impulses alternately change their direction synchronously with the oscillation of the potential. This leads to synergy dynamics of vortices and solitons in quantum fluids.

We report on a hard-x-ray imaging microscope consisting of a lens, a sample, and a transmission grating. After the theoretical framework of self-imaging phenomenon by the grating in the system is presented, equations for the electric field on the image plane are derived for ideal and real lenses and an equation for the intensity on the image plane for partially coherent illumination is derived. The equations are simple and similar to those applying to a projection microscope consisting of a transmission grating except that there is no defocusing effect, regardless of whether the grating is in front of or behind the lens. This means that x-ray phase-imaging microscopy can be done without the defocusing effect. It is also shown that, by resolving the self-image on the image plane, high-sensitive x-ray phase-imaging microscopy can be attained without degradation in the spatial resolution due to diffraction by the grating. Experimental results obtained using partially coherent illumination from a synchrotron x-ray source confirm that hard-x-ray phase-imaging microscopy can be quantitatively performed with high sensitivity and without the spatial resolution degradation.

A point source in a disordered scattering medium generates a speckle pattern with nonuniversal features, giving rise to the so-called $C_0$ correlation. We analyze theoretically the relationship between the $C_0$ correlation and the statistical fluctuations of the local density of states, based on simple arguments of energy conservation. This derivation leads to a clear physical interpretation of the $C_0$ correlation. Using exact numerical simulations, we show that $C_0$ is essentially a correlation resulting from near-field interactions. These interactions are responsible for the nonuniversality of $C_0$ that confers to this correlation a huge potential for sensing and imaging at the subwavelength scale in complex media.

A new-generation x-ray laser project is explained. It is based on the transitions in Pd-like ions in nanoplasmas. The gain coefficient is calculated for the $4d_{3/2}^{9}5d_{3/2}[J=0]-4d_{3/2}^{9}5p_{1/2}[J=1]$ transition ($\lambda \approx 10.8$ nm) in Pd-like tungsten. It is suggested that a cylindrical target made of nanostructured tungsten is pumped in the longitudinal direction by a laser pulse with energy 1–2 keV and duration $~500$ ps. For this pump pulse the target density and dimensions are calculated, as well as the temporal variations of the optimal plasma parameters for attaining $\mathit{gL}$ $~$ 14. The energy yield in the 10.8-nm line is more than ${10}^{20}$ eV.

A unification of the set of quasiprobability representations using the mathematical theory of frames was recently developed for quantum systems with finite-dimensional Hilbert spaces, in which it was proven that such representations require negative probability in either the states or the effects. In this article we extend those results to Hilbert spaces of infinite dimension, for which the celebrated Wigner function is a special case. Hence, this article presents a unified framework for describing the set of possible quasiprobability representations of quantum theory, and a proof that the presence of negativity is a necessary feature of such representations.

It is well-known that when searching one out of four, the original Grover’s search algorithm is exact; that is, it succeeds with certainty. It is natural to ask the inverse question: If we are not searching one out of four, is Grover’s algorithm definitely not exact? In this article we give a complete answer to this question through some rationality results of trigonometric functions.

In this article, we study an opposite problem of universal quantum state comparison, that is unambiguously determining whether multiple unknown quantum states from a Hilbert space are orthogonal or not. We show that no unambiguous quantum measurement can accomplish this task with a nonzero probability. Moreover, we extend the problem to a more general case, that is to compare how orthogonal multiple unknown quantum states are with a threshold, and it turns out that given any threshold this extended task is also impossible by any unambiguous quantum measurement except for a trivial case. It will be seen that the impossibility revealed in our problem is stronger than that in the universal quantum state comparison problem and distinct from those in the existing “no-go” theorems.