A versatile and numerically inexpensive method is presented allowing the accurate calculation of phase diagrams for bosonic lattice models. By treating clusters within the Gutzwiller theory, a surprisingly good description of quantum fluctuations beyond the mean-field theory is achieved approaching quantum Monte Carlo predictions for large clusters. Applying this powerful method to the Bose-Hubbard model, we demonstrate that it yields precise results for the superfluid to Mott-insulator transition in square, honeycomb, and cubic lattices. Due to the exact treatment within a cluster, the method can be effortlessly adapted to more complicated Hamiltonians in the fast progressing field of optical lattice experiments. This includes state- and site-dependent superlattices, large confined atomic systems, and disordered potentials, as well as various types of extended Hubbard models. Furthermore, the approach allows an excellent treatment of systems with arbitrary filling factors. We discuss the perspectives that allow for the computation of large, spatially varying lattices, low-lying excitations, and time evolution.

The results are shown to be incorrect by means of a counterexample, an explicit preparation for the probe is given that yields an arbitrary amplification, and the source of the error is pointed out.

It is pointed out that the “counterexample” presented in the Comment is a family of probe wave functions which are increasingly broad as the shift becomes large. Furthermore, the author's variational calculation is not correct in the sense that we have to gauge fix the freedom of the phase translation. It is shown that there are two kinds of solutions, normalizable and un-normalizable. The former is our optimal solution, and the latter is what he found. It seems only the former is relevant from a practical point of view.

We present theoretical investigations of high-order-harmonic generation (HHG) resulting from the interaction of noble gases with localized surface plasmons. These plasmonic near-fields are produced when a metal nanoparticle is subject to a few-cycle laser pulse. The enhanced field, which largely depends on the geometrical shape of the metallic nanostructure, has a strong spatial dependency. We demonstrate that the strong nonhomogeneity of this laser field plays an important role in the HHG process and leads to a significant increase of the harmonic-cutoff energy. In order to understand and characterize this feature, we include the functional form of the laser electric field obtained from recent attosecond streaking experiments [F. Süßmann and M. F. Kling, Proc. SPIE 8096, 80961C (2011)] in the time-dependent Schrödinger equation. By performing classical simulations of the HHG process we show consistency between them and the quantum-mechanical predictions. These allow us to understand the origin of the extended harmonic spectra as a selection of particular trajectory sets. The use of metal nanoparticles is an alternate way of generating coherent XUV light with a laser field whose characteristics can be synthesized locally.

The pairing and superfluid phenomena in a two-component Fermi gas can be strongly affected by the population and mass imbalances. Here we present phase diagrams of an atomic Fermi-Fermi mixture as they undergo BCS–Bose-Einstein condensation (BEC) crossover using a pairing fluctuation theory. We focus on the finite temperature and trap effects, with an emphasis on the mixture of ${}^6$Li and ${}^{40}$K. We show that there exist exotic types of phase separation in the (near-)BEC regime, associated with a pseudogap effect. Moreover, in the BCS and unitary regimes, the spatial density and gap profiles exhibit sandwichlike shell structures with superfluid or pseudogapped normal state in the middle shell. Such a sandwichlike shell structure appears when the mass imbalance increases beyond a certain threshold. Our result is relevant to future experiments on the ${}^6$Li-${}^{40}$K and other possible Fermi-Fermi mixtures.

We consider a pair of atoms in an arbitrary trapping potential in the presence of a magnetically tunable Feshbach resonance. We find the energy levels and occupation of the bound molecular states, taking into account possible coupling between center of mass and relative motion induced by the trap. As a specific example, we discuss the case of different atomic species in a harmonic potential, where each atom feels a different trapping frequency.

The nuclear $(n;t)$ reaction of the three-electron ${}^6$Li atom with thermal or slow neutrons is considered. An effective method has been developed for determining the probabilities of the formation of various atoms and ions in different bound states. We discuss a number of fundamental questions directly related to numerical computations of the final-state atomic probabilities. A few appropriate variational expansions for atomic wave functions of the incident lithium atom and final helium atom and/or tritium negatively charged ion are discussed. It appears that the final ${}^4$He atom arising during the nuclear $(n,{}^6$Li; ${}^4$He$,t)$ reaction in the three-electron Li atom can also be created in its triplet states. The formation of the quasistable three-electron $e_3^{-}$ during the nuclear $(n;t)$ reaction at the Li atom is briefly discussed. Bremsstrahlung emitted by atomic electrons accelerated by the rapidly moving nuclear fragments from this reaction is analyzed. The frequency spectrum of the emitted radiation is investigated.

We present an ab initio theoretical investigation of the coherent control and significant enhancement of multiphoton ionization (MPI) and high-order-harmonic generation (HHG) of atoms and molecules by means of intense frequency-comb laser fields. We show that the nonperiodically or quasiperiodically time-dependent Schrödinger equation for the frequency-comb laser excitation problem can be transformed exactly into a time-independent non-Hermitian generalized Floquet matrix eigenvalue problem by means of the many-mode Floquet theory and the complex-scaling transformation. The generalized Floquet Hamiltonian can be optimally discretized and the complex quasienergy eigenvalues and eigenfunctions can be solved accurately and efficiently by means of the generalized pseudospectral method. The procedure is applied to a case study of the resonance-enhanced MPI and HHG of atomic hydrogen driven by an intense frequency-comb laser field. Our study shows that both the MPI and HHG rates can be coherently controlled by tuning the laser parameters such as the pulse-to-pulse carrier-envelope-phase (CEP) shift. In particular, both the MPI and HHG rates exhibit dramatic enhancement by tuning the CEP shift, due to the phenomenon of multiphoton resonances.

This paper treats theoretically the spontaneous resonant inelastic scattering of Laguerre-Gauss (LG) beams from the vibrations of complex polyatomic molecules within the semiclassical framework. We develop an interaction Hamiltonian that accounts for the position of the molecule within the excitation beam to derive the effective differential scattering cross section of a classical LG beam from a molecule using the frequency-domain third-order nonlinear optical response function. To gain physical insight, we utilize a model vibronic molecule to study the changes to this scattering process. For specific molecular parameters including vibrational frequency and relative displacement of the involved electronic states, this investigation shows that an incident LG beam asymmetrically enhances one of two participating excitation transitions causing modulation of the interference present in the scattering process. This modulation allows a pathway to coherent control of resonant inelastic scattering from complex, polyatomic molecules. We discuss the possible application of this control to the resonant x-ray inelastic scattering (RIXS) of small polyatomic molecules central to applications ranging from single-molecule electronics to solar energy science.

Single-photon ionization leading to two vacancies in the $2p$ subshell of argon is investigated experimentally using the photoelectron time-of-flight magnetic bottle coincidence technique. Three peaks corresponding to the ${}^{3}P$, ${}^{1}D$, and ${}^{1}S$ states of the dication are found in the ionization energy range 535 to 562 eV. Multiconfigurational Dirac-Fock calculations were performed to estimate the single-photon double-ionization cross sections. Reasonable agreement between the measured and simulated spectra is found if single and double excitations are taken into account in the wave-function expansion.

We experimentally observed optical precursors in optically pumped crystals using polarization-based interference. By switching the user-programmable medium among the fast light, slow light, and no-dispersion regimes, we observed an unchanged polarization state for the wave fronts. The robust polarization-encoded information carried by wave fronts suggests that precursors are the preferred carriers for both quantum and classical information in communication networks.

The generalized Breit-Wheeler process, i.e., the emission of $e^{+}{e}^{-}$ pairs off a probe photon propagating through a polarized short-pulsed electromagnetic (e.g., laser) wave field, is analyzed. We show that the production probability is determined by the interplay of two dynamical effects. The first one is related to the shape and duration of the pulse and the second one is the nonlinear dynamics of the interaction of $e^{\pm }$ with the strong electromagnetic field. The first effect manifests itself most clearly in the weak-field regime, where the small field intensity is compensated by the rapid variation of the electromagnetic field in a limited space-time region, which intensifies the few-photon events and can enhance the production probability by orders of magnitude compared to an infinitely long pulse. Therefore, short pulses may be considered as a powerful amplifier. The nonlinear dynamics in the multiphoton Breit-Wheeler regime plays a decisive role at large field intensities, where effects of the pulse shape and duration are less important. In the transition regime, both effects must be taken into account simultaneously. We provide suitable expressions for the $e^{+}{e}^{-}$ production probability for kinematic regions which can be used in transport codes.

We present a technique based upon two-pathway coherent control for the measurement of a weak transition moment. In our approach, we use two coherent optical beams, one the second harmonic of the other, to drive a transition by means of three distinct optical interactions. The interference between these interactions allows a determination of one moment relative to another. In this work, we demonstrate the approach by applying it to an experimental determination of the magnetic dipole moment for the $6s{}^2{S}_{1/2}\to 7s{}^2{S}_{1/2}$ transition in atomic cesium. Our results are in excellent agreement with previous single-beam measurements. We also discuss prospects for extending this measurement technique to a new determination of the weak-force induced parity-nonconserving moment on this same transition.

We present the results of our numerical simulation on the photoelectron spectra of hydrogen atoms ionized by the single-photon process of intense XUV laser pulses. The dynamic interference structure in the photoelectron spectra is investigated with respect to the dynamic Stark effect, XUV laser parameters, and properties of the ionization continuum states. The research outcome is that plane waves can be readily deployed to study photoelectron spectroscopy, which is crucial to the wave-function ansatz for generic systems of atoms and molecules. The dynamic Stark effect is prominently demonstrated above certain carrier frequencies of the XUV laser pulse, which mandates a photon energy threshold for the dynamic Stark effect to be discerned in the photoelectron spectra. A one-dimensional model for the hydrogen atom is feasible, which is of fundamental significance in modeling atoms and molecules with reduced dimensionality models. We also point out that detailed characterization of the interference fringes in the photoelectron spectra will facilitate more quantitative investigations of the Stark effect contained in the photoelectron spectra created by single XUV photons.

We theoretically investigate the quantum paths of the high-order harmonic generation (HHG) by using a left and a right circularly polarized Gaussian laser pulse with a proper time delay. When the carrier phase of the two pulses is ${\phi }_1=0$, ${\phi }_2=0.5\pi$, the “gating” structure of the combined laser field disappears. The numerical results indicate that no “gating”-structure-combined laser pulse can control the quantum path. The HHG process is investigated by the semiclassical three-step model that makes use of a finite initial transverse velocity in the elliptically polarized field. For the case of ${\lambda }_1=800$ nm, ${\lambda }_2=1600$ nm, only a short quantum path contributes to the HHG, and an isolated attosecond pulse would be obtained. For the case of ${\lambda }_2=1600$, ${\phi }_2=0.5\pi$, a supercontinuum spectrum plateau from 180 to 570 eV which includes the water window region is obtained, and attosecond pulses with the duration of about 75 as and a tunable central wavelength could be generated by superposing a bandwidth of 50 eV in the plateau area.

We derive ab initio local Hubbard models for several optical-lattice potentials of current interest, including the honeycomb and kagome lattices, verifying their accuracy on each occasion by comparing the interpolated band structures against the originals. To achieve this, we calculate the maximally localized generalized Wannier basis by implementing the steepest-descent algorithm of Marzari and Vanderbilt [Phys. Rev. B 56, 12847 (1997)] directly in one and two dimensions. To avoid local minima we develop an initialization procedure that is both robust and requires no prior knowledge of the optimal Wannier basis.

We systematically develop a density functional description for the equilibrium properties of a two-dimensional, harmonically trapped, spin-polarized dipolar Fermi gas based on the Thomas–Fermi–von Weizsäcker approximation. We pay particular attention to the construction of the two-dimensional kinetic energy functional, where corrections beyond the local density approximation must be motivated with care. We also present an intuitive derivation of the interaction energy functional associated with the dipolar interactions and provide physical insight into why it can be represented as a local functional. Finally, a simple and highly efficient self-consistent numerical procedure is developed to determine the equilibrium density of the system for a range of dipole interaction strengths.

Motivated by the ongoing controversy over the origin of the nonlinear index saturation and subsequent intensity clamping in femtosecond filaments, we study the atomic nonlinear polarization induced by high-intensity ultrashort laser pulses in hydrogen by numerically solving the time-dependent Schrödinger equation. Special emphasis is given to the efficient modeling of the nonlinear polarization at a central laser frequency corresponding to a wavelength of 800 nm. Here, the recently proposed model of the higher-order Kerr effect (HOKE) and two versions of the standard model for femtosecond filamentation, including either a multiphoton or tunnel ionization rate, are compared. We find that around the clamping intensity the instantaneous HOKE model does not reproduce the temporal structure of the nonlinear response obtained from the quantum-mechanical results. In contrast, the noninstantaneous charge contributions included in the standard models ensure a reasonable quantitative agreement. Therefore, the physical origin for the observed saturation of the overall electron response is confirmed to mainly result from contributions of free or nearly-free electrons.

A large class of exact analytical traveling solitary wave solutions in a variety of inhomogeneous structures consisting of linear and nonlinear layers is obtained. The solutions are related to a spatial resonance condition and describe reflectionless and radiationless beam propagation for arbitrary angles and spatial widths in the nonparaxial regime.

We investigate electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in an open V-type molecular system. Through detailed analytical calculations of the absorption spectrum of a probe laser field using the residue theorem and spectrum decomposition, we find that EIT may occur and a crossover from EIT to ATS exists for hot molecules. However, there is no EIT and hence no EIT-ATS crossover for cold molecules. Furthermore, we prove that for hot molecules EIT is allowed even for a counter-propagating configuration. We provide explicit formulas of EIT conditions and widths of EIT transparency windows of the probe field when hot molecules work in copropagating and counter-propagating configurations, respectively. Our theoretical result agrees well with the recent experimental ones reported by Lazoudis et al. [Phys. Rev. A 83, 063419 (2011)].