A formal proof is given that for $N$-boson systems in which two-body interaction potentials are described by a single Gaussian the ratio of higher-order to the lowest-order hyper-radial potentials decreases at $N\to \infty$ as $N^{-1/2}$ or faster. As a result, for such potentials, the convergence of binding energies for ground and several lowest excited states, obtained in expansion of the $N$-body wave function over the hyperspherical-harmonics basis, improves with increasing number of bosons. For a phenomenological three-body repulsive potential, introduced to account for the missing hard core, the ratio of higher-order to lowest-order hyper-radial potential, corresponding to this three-body potential, also decreases as $N^{-1/2}$ or faster when $N\to \infty$. Although adding the three-body contributions leads to increased influence from the total nondiagonal couplings around the node of the lowest hyper-radial potential, the arguments are given that this should not dramatically deteriorate the convergence if the range of repulsion is properly chosen. This means that the hyperspherical-harmonics expansion with soft two-body and repulsive three-body effective forces may become an attractive tool for studying the spectra of many-body systems. It is suggested that fine tuning of the three-body repulsion to reproduce the binding energies over a large region of $N$ is possible. In particular, it has been shown that an $N$-independent choice for the three-body repulsion exists for which the ground-state binding energies of $N\le 112$ atoms of helium, obtained in the lowest-order approximation of the hyperspherical-harmonics expansion, are close to the prediction of the Green's function Monte Carlo method with a hard-core He-He potential.

The Husimi distribution is proposed for a phase-space analysis of quantum phase transitions in the two-dimensional U(3) vibron model for $N$-size molecules. We show that the inverse participation ratio and Wehrl's entropy of the Husimi distribution give sharp signatures of the quantum (shape) phase transition from linear to bent. Numerical results are complemented with a variational approach using parity-symmetry-adapted U(3) coherent states, which reach the minimum Wehrl entropy $\frac{N(3+2N)}{(N+1)(N+2)}$, in the rigidly linear phase, according to a generalized Wehrl-Lieb conjecture. We also propose a characterization of the vibron-model quantum phase transition by means of the zeros of the Husimi distribution.

Nuclear quadrupole moments ($Q$'s) in three isotopes of the potassium atom (K) with mass numbers 39, 40, and 41 are evaluated more precisely in this work. The $Q$ value of ${}^{39}$K is determined to be 0.0614(6) $b$ by combining the available experimental result of the electric quadrupole hyperfine structure constant ($B$) with our calculated $B/Q$ result of its $4P_{3/2}$ state. Furthermore, combining this $Q$ value with the measured ratios $Q$(${}^{40}$K)$/Q$(${}^{39}$K) and $Q$(${}^{41}$K)$/Q$(${}^{39}$K), we obtain $Q$(${}^{40}$K)$=-0.0764\left(8\right)b$ and $Q$(${}^{41}$K)$=0.0747\left(7\right)b$, respectively. These results disagree with the sub-1$\%$ accuracy standard values recently quoted by Pyykkö [Mol. Phys. 106, 1965 (2008)]. The calculations were carried out by employing the relativistic coupled-cluster theory at the single, double, and involving important valence triple approximation. The accuracies of the calculated $B/Q$ results can be viewed on the basis of comparison between our calculated magnetic dipole hyperfine structure constants ($A$'s) with their corresponding measurements for many low-lying states. Both $A$ and $B$ results in a few more excited states are presented. Also, we find that the latest reported experimental hyperfine structure constant results for the $4P$ states in ${}^{39}$K are inconsistent with our calculations.

The $P$-wave hybrid theory of electron-hydrogen elastic scattering [Bhatia, Phys. Rev. A 85, 052708 (2012)] is applied to the $P$-wave scattering from He ion. In this method, both short-range and long-range correlations are included in the Schrödinger equation at the same time, by using a combination of a modified method of polarized orbitals and the optical potential formalism. The short-range-correlation functions are of Hylleraas type. It is found that the phase shifts are not significantly affected by the modification of the target function by a method similar to the method of polarized orbitals and they are close to the phase shifts calculated earlier by Bhatia [Phys. Rev. A 69, 032714 (2004)]. This indicates that the correlation function is general enough to include the target distortion (polarization) in the presence of the incident electron. The important fact is that in the present calculation, to obtain similar results only a 20-term correlation function is needed in the wave function compared to the 220-term wave function required in the above-mentioned calculation. Results for the phase shifts, obtained in the present hybrid formalism, are rigorous lower bounds to the exact phase shifts. The lowest $P$-wave resonances in He atom and hydrogen ion have also been calculated and compared with the results obtained using the Feshbach projection operator formalism [Bhatia and Temkin, Phys. Rev. A 11, 2018 (1975)] and also with the results of other calculations. It is concluded that accurate resonance parameters can be obtained by the present method, which has the advantage of including corrections due to neighboring resonances, bound states, and the continuum in which these resonances are embedded.

We theoretically investigated the generation progress of high-order harmonics utilizing Bohmian trajectories, which are calculated from the accurate numerical wave function. It is found that the harmonic emission spectrum from atoms in an intense laser field calculated by Bohmian trajectories agrees well with that found by numerically solving the time-dependent Schrödinger equation. Through the analysis of the dynamic behavior of Bohmian trajectories, we investigated the ionization process, the acceleration of the ionized electron in the laser field, and its recollision with the parent ion in the progress. Furthermore, the individual behavior and the coherent contribution of these trajectories to the harmonic emission are discussed.

Experiments on the triatomic hydrogen molecular ion in intense ultrashort laser pulses are important for understanding the fundamentals of polyatomic molecular dynamics and for providing a benchmark for theory. Here we extend our earlier measurements [Phys. Rev. Lett. 103, 103004 (2009)] to provide a comprehensive picture of D${}_3$${}^{+}$ fragmentation in 7- and 40-fs, 790-nm laser pulses at intensities up to 10${}^{16}$ W/cm${}^2$. Our measurements incorporate two- and three-body coincidence three-dimensional momentum imaging involving a crossed-beam setup. We provide details of the relative fragmentation rates of all the possible breakup channels as a function of intensity, as well as kinetic energy release and angular distributions.

We examine density-ordered and superfluid phases of fermionic dipoles in a two-dimensional square lattice at nonzero temperature. The critical temperature of the density-ordered phases is determined and is shown to be proportional to the coupling strength for strong coupling. We calculate the superfluid fraction and the Berezinskii-Kosterlitz-Thouless transition temperature of the superfluid phase. We finally analyze the effects of an external harmonic trapping potential.

We study a Bose-Einstein condensate (BEC) in a double-well potential subject to an unsharp continuous measurement of the atom number in one of the two wells. We investigate the backaction of the measurement on the quantum dynamics and the viability to monitor the ensuing time evolution. For vanishing interatomic interactions, mainly the expectation values of the measured local observable can be inferred from the measurement record. Conversely, in the presence of moderate interatomic interactions, the entire many-body state—modified by the measurement—is monitored with unit fidelity and, at the same time, the measurement effects a transition from quantum to mean-field (classical) behavior of the BEC. We show that this perfect state estimation is possible because the interatomic interactions enhance the information gained via the measurement.

In this paper, by treating the hopping parameter in the Bose-Hubbard model as a perturbation, with the help of the resummed Green's function method and cumulant expansion, the momentum distribution function of an ultracold Bose system in a triangular optical lattice is calculated analytically. By its use, the time-of-flight absorption picture is plotted and the corresponding visibility is determined. A comparison between our analytical results and the experimental data of Becker et al. [New J. Phys. 12, 065025 (2010)] exhibits a qualitative agreement.

We analyze the two-body momentum correlation function for a uniform, weakly interacting, one-dimensional Bose gas. We show that the strong positive correlation between opposite momenta, expected in a Bose-Einstein condensate with a true long-range order, almost vanishes in a phase-fluctuating quasicondensate where the long-range order is destroyed. Using the Luttinger liquid approach, we derive an analytic expression for the momentum correlation function in the quasicondensate regime, showing (i) the reduction and broadening of the opposite-momentum correlations (compared to the singular behavior in a true condensate) and (ii) an emergence of anticorrelations at small momenta. We also numerically investigate the momentum correlations in the crossover between the quasicondensate and the ideal Bose-gas regimes using a classical field approach and show how the anticorrelations gradually disappear in the ideal-gas limit.

We study two-species Bose-Einstein condensates in quasi-two-dimensional optical lattices of varying geometry and potential depth. Based on the numerically exact Bloch and Wannier functions obtained using the plane-wave expansion method, we quantify the drag (entrainment coupling) between the condensate components. This drag originates from the (short-range) interspecies interaction and increases with the kinetic energy. As a result of the interplay between interaction and kinetic energy effects, the superfluid-drag coefficient shows a nonmonotonic dependence on the lattice depth. To make contact with future experiments, we quantitatively investigate the drag for mass ratios corresponding to relevant atomic species.

We demonstrate that there exist globally convergent infinite tanh power series with which the spinless light-bullet solutions in the (3+1)D cubic-quintic complex Ginzburg-Landau equation can be exactly expressed. It is found that as these fixed-point bullet solutions exist, the series coefficients asymptotically approach certain nonzero constants; otherwise they oscillate and eventually decay to nil. In terms of the specific Padé approximants, the analytical solutions obtained for either the conventional bullets or the composite ones are in excellent agreement with numerical simulations.

There is a well-known mathematical similarity between two-dimensional classical polarization optics and two-level quantum systems, where the Poincaré and Bloch spheres are identical mathematical structures. This analogy implies that the classical degree of polarization and quantum purity are in fact the same quantity. We make extensive use of this analogy to analyze various measures of polarization for higher dimensions proposed in the literature, in particular the $N=3$ case, illustrating interesting relationships that emerge as well as the advantages of each measure. We also propose a different class of measures of entanglement based on the purity of subsystems.

We report an experimental proof and full characterization of laser generation in molecular nitrogen in an argon-nitrogen gas mixture remotely excited at a distance above 2 m in a femtosecond laser filament. Filamentation experiments performed with near-infrared, 1-μm-wavelength and midinfrared, 4-μm-wavelength short-pulse laser sources show that mid-IR laser pulses enable radical enhancement of filamentation-assisted lasing by N${}_2$ molecules. Energies as high as 3.5 μJ are achieved for the 337- and 357-nm laser pulses generated through the second-positive-band transitions of N${}_2$, corresponding to a 0.5$\%$ total conversion efficiency from midinfrared laser energy to the energy of UV lasing.

We present an experimental and theoretical investigation of two-photon direct frequency-comb spectroscopy performed through velocity-selective excitation. In particular, we explore the effect of repetition rate on the $5S_{1/2}\to 5D_{3/2,5/2}$ two-photon transitions excited in a rubidium atomic vapor cell. The transitions occur via stepwise excitation through the $5P_{1/2,3/2}$ states by use of the direct output of an optical frequency comb. Experiments were performed with two different frequency combs, one with a repetition rate of $\approx 925$ MHz and one with a repetition rate of $\approx 250$ MHz. The experimental spectra are compared to each other and to a theoretical model.

We introduce a method to test if a given velocity definition corresponds to an actual physical flow in a dispersive medium. We utilize the equivalence of the pulse dynamics in the real-$\omega$ and real-$k$ Fourier expansion approaches as a test tool. To demonstrate our method, we take the definition introduced by Peatross et al. [Phys. Rev. Lett. 84, 2370 (2000)] and calculate the velocity in two different ways. We calculate (i) the mean arrival time between two positions in space, using the real-$\omega$ Fourier expansion for the fields and (ii) the mean spatial displacement between two points in time, using the Fourier expansion in real-$k$ space. We compare the velocities calculated in the two approaches. If the velocity definition truly corresponds to an actual flow, the two velocities must be the same. However, we show that the two velocities differ significantly (3$\%$) in the region of superluminal propagation even for the successful definition of Peatross et al.

A sequence of femtosecond laser pulses propagating through atmosphere and delayed near the rotational recurrence period of N${}_2$ can resonantly drive molecular alignment. Through the polarization density, the molecular alignment provides an index of refraction contribution that acts as a lens copropagating with each laser pulse. Each pulse enhances this contribution to the index, modifying the propagation of subsequent pulses. Here we present propagation simulations of femtosecond pulse sequences in which we have implemented a self-consistent calculation of the rotational polarization density using linearized density matrix theory. We find that a femtosecond pulse sequence can enhance pulse compression or collimation in atmosphere. In particular, when the pulses are delayed by exactly the rotational recurrence period, each subsequent pulse is increasingly compressed due to a combination of spectral broadening and negative dispersion. Alternatively, when the intensity peak of each pulse is centered on the maximum index generated by the preceding pulses, each pulse is increasingly collimated.

The existence and stability of spatial solitons in one-dimensional binary photonic lattices with alternating spacing and a saturable defocusing type of nonlinearity are investigated. Five types of nonlinear localized structures are found to exist: two in the mini-gap in the energy spectrum and others in the regular gap. It is proved that some of them are stable in certain ranges of the system parameters. Interactions between two identical localized structures propagating parallel to each other are investigated, too. It is shown that this interaction leads to formation of different localized patterns, such as solitons, breather-like modes, and breather complexes. The interaction output depends on the power and type of interacting identical solitons, the separation between them, the width of the mini-gap, and the phase relation between the tails of interacting solitons.

The quantum-mechanical convergent close-coupling approach has been used to calculate the fully differential cross section for the single ionization of helium by C${}^{6+}$ ions at 100 MeV/amu. This allows one to test the quality of approximations used in standard approaches to the problem, particularly in geometries that are out of the scattering plane, where there is a strong disagreement between calculations and measurements. The obtained results show that the fully quantum-mechanical treatment of the internuclear motion does not enable one to get any better agreement with experimental data. In addition, we have performed calculations for the precise geometry where experimental data were collected, i.e., in the plane perpendicular to the momentum-transfer direction. We conclude that this rotation also has a minor effect on the shape of the cross section.

We present a method for the experimental measurement of nonclassicality witnesses and demonstrate its application. Our proposal requires only the coherent displacement of the initial state, which can be achieved by overlapping the latter with a coherent state at a beam splitter, and subsequent photon-number-resolved detection. This setup allows a complete test of nonclassicality of an arbitrary quantum state. The role of the quantum efficiency as well as statistical and systematic uncertainties are discussed. Finally, the scheme is demonstrated for a realistic example.