Rabi oscillations of quantum population are known to occur in two-level systems driven by spectrally narrow laser fields. In this work we study Rabi oscillations induced by shaped broadband femtosecond laser pulses. Due to the broad spectral width of the driving field, the oscillations are initiated between a ground state and a coherent superposition of excited states, or a “wave packet,” rather than a single excited state. Our experiments reveal an intricate dependence of the wave-packet phase on the intensity of the laser field. We confirm numerically that the effect is associated with the strong-field nature of the interaction and provide a qualitative picture by invoking a simple theoretical model.

We find the conditions under which the normal state of a spin-1 Bose gas is unstable toward condensation, ferromagnetism, liquid crystalline-like nematicity, and Bardeen-Cooper-Schrieffer-like pairing. When the spin-dependent interactions are much weaker than the density-density interaction there is direct transition from a featureless normal state to a fully ordered Bose-Einstein condensate with either ferromagnetic or nematic order. When the spin-independent and spin-dependent interactions are of comparable magnitude, we find several different symmetry breaking transitions at intermediate temperatures above the Bose-condensation transition temperature. We make predictions for the $T_c$ for these transitions, and assess the role of magnetic field and finite system size.

Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the statics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counterintuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright-soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscillations of solitons are found to be in good agreement with results obtained via a Bogoliubov–de Gennes analysis and direct numerical simulations.

We describe families of discrete solitons in quadratic waveguide arrays supported by competing cascaded nonlinear interactions between one fundamental and two second-harmonic modes. We characterize the existence, stability, and excitation dynamics of these solitons and show that their features may resemble those of solitons in saturable media. Our results also demonstrate that a power threshold may appear for soliton formation, leading to a suppression of beam self-focusing which explains recent experimental observations.

D. A. Long et al. [Phys. Rev. A 80, 042513 (2009)] recently reported accurate measurements on the ultraweak electric quadrupole (E2) transitions in the O${}_2$ $A$ band. They also presented elegant theoretical calculation of the line intensities based on Hund's case (b) formulation. However, their theoretical elucidation fails to relate to a highly relevant previous work by Balasubramanian and Narayanan [Acta Phys. Hung 74, 341 (1994)] in which closed-form expressions for the E2 branch line strengths for the eight possible rotational branches of the $b{}^1{\Sigma }_g^{+}-X{}^3{\Sigma }_g^{-}$ transition, in intermediate coupling, are derived. The complete equivalence of the two methods is proven through direct calculation. A second point of concern is that the magnetic dipole (M1) transition moment $M_1$ $=$ 0.0687 μ${}_{\mathrm{B}}$ deduced by Long et al. from the previously measured transition intensities is ∼2.7 times the ab initio value of 0.0255 μ${}_{\mathrm{B}}$ computed by Minaev et al. [Chem. Phys. 208, 299 (1996)]. Since the latter reproduces closely the measured Einstein's spontaneous emission coefficient of the $A$ band, this large discrepancy is intriguing.

We study the quantum phases of a three-color Hubbard model that arises in the dynamics of the $p$-band orbitals of spinless fermions in an optical lattice. Strong, color-dependent interactions are induced by an optical Feshbach resonance. Starting from the microscopic scattering properties of ultracold atoms, we derive the orbital exchange constants at 1/3 filling on the cubic optical lattice. Using this, we compute the phase diagram in a Gutzwiller ansatz. We find phases with “axial orbital order” in which $p_z$ and $p_x+i{p}_y$ (or $p_x-i{p}_y$) orbitals alternate.

We present a method of obtaining nonlinear integral equations characterizing the thermodynamics of one-dimensional multicomponent gases interacting via a $\delta$-function potential. In the case of the repulsive two-component Bose gas we obtain a simple system of two nonlinear integral equations, allowing for an efficient numerical implementation, in contrast with the infinite number of coupled equations obtained by employing the thermodynamic Bethe ansatz. Our technique makes use of the quantum transfer matrix and the fact that, in a certain continuum limit, multicomponent gases can be obtained from appropriate anisotropic spin chains.

We present observable lower and upper bounds for the entanglement of formation (EOF) and quantum discord (QD), which facilitates estimates of EOF and QD for arbitrary experimental unknown states in finite-dimensional bipartite systems. These bounds can be easily obtained by a few experimental measurements on a twofold copy $\varrho \otimes \varrho$ of the mixed states. Based on our results, we use the experimental measurement data of the real experiment given by Schmid et al. [Phys. Rev. Lett. 101, 260505 (2008)] to obtain the lower and upper bounds of EOF and QD for the experimental unknown state.

We generalize the recently developed “internal” density-functional theory (DFT) and Kohn-Sham scheme to multicomponent systems. We obtain a general formalism, applicable for the description of multicomponent self-bound systems (such as molecular systems where the nuclei are treated explicitly, atomic nuclei and mixtures of ${}^3$He and ${}^4$He droplets), where the fundamental translational symmetry has been treated correctly. The main difference with traditional DFT is the explicit inclusion of center-of-mass correlations in the functional. A large part of the paper is dedicated to the application to molecular systems, which permits us to clarify the approximations that underly traditional DFT.

The properties of the geometric phases between three quantum states are investigated in a high-dimensional Hilbert space using the Majorana representation of symmetric quantum states. We found that the geometric phases between the three quantum states in an $N$-state quantum system can be represented by $N-1$ spherical triangles on the Bloch sphere. The parameter dependence of the geometric phase was analyzed based on this picture. We found that the geometric phase exhibits rich nonlinear behavior in a high-dimensional Hilbert space.

Leggett-type nonlocal realistic inequalities that have been derived to date are all contingent upon suitable geometrical constraints to be strictly satisfied by the spatial arrangement of the relevant measurement settings. This undesirable restriction is removed in the present work by deriving appropriate forms of nonlocal realistic inequalities, one of which involves the fewest number of settings compared to all such inequalities derived earlier. The way such inequalities would provide a logically firmer basis for a clearer testing of a Leggett-type nonlocal realistic model vis-à-vis quantum mechanics is explained.

We study the time evolution of the amount of entanglement generated by one-dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribution obtained by a time-independent Hamiltonian can simulate the average and standard deviation of the typical entanglement, if the Hamiltonian contains suitable many-body interactions. We also show that the time required to achieve such a distribution is polynomial in the system size for certain types of Hamiltonians.

In the absence of quantum channels, local operations on subsystems and classical communication between parties (LOCC) constitute the most general protocols available on spatially separated quantum systems. Every LOCC protocol implements a separable quantum measurement, but it is known that there exist separable measurements that cannot be implemented by LOCC. A longstanding problem in quantum information theory is to understand the difference between LOCC and the full set of separable measurements. Toward this end, we show in this paper how to construct an LOCC protocol to implement an arbitrary separable measurement whenever such a protocol exists. In addition, given a measurement that cannot be implemented by LOCC within some fixed maximum number of rounds, the method shows explicitly that this is the case.

One of the unsolved problems in the characterization of the optimal entanglement witnesses is the existence of optimal witnesses acting on bipartite Hilbert spaces ${\mathcal{H}}_{m,n}={\mathbb{C}}^m\otimes {\mathbb{C}}^n$ such that the product vectors obeying $\langle e,f\left|W\right|e,f\rangle =0$ do not span ${\mathcal{H}}_{m,n}$. So far, the only known examples of such witnesses were found among indecomposable witnesses, one of them being the witness corresponding to the Choi map. However, it remains an open question whether decomposable witnesses exist without the property of spanning. Here we answer this question affirmatively, providing systematic examples of such witnesses. Then, we generalize some of the recently obtained results on the characterization of $2\otimes n$ optimal decomposable witnesses [R. Augusiak et al., J. Phys. A 44, 212001 (2011)] to finite-dimensional Hilbert spaces ${\mathcal{H}}_{m,n}$ with $m,n\ge 3$.

We present an investigation of the Lamb shift $(2P_{1/2}$-2$S_{1/2})$ in the muonic deuterium $(\mu$D) atom using the three-dimensional quasipotential method in quantum electrodynamics. The vacuum polarization, nuclear-structure, and recoil effects are calculated with the account of contributions of orders ${\alpha }^3$, ${\alpha }^4$, ${\alpha }^5$, and ${\alpha }^6$. The results are compared with earlier performed calculations. The obtained numerical value of the Lamb shift at $202.4139$ meV can be considered a reliable estimate for comparison with forthcoming experimental data.

Double-differential ionization cross sections (DDCSs) of vapor-phase adenine molecules (${\mathrm{C}}_5{\mathrm{H}}_5{\mathrm{N}}_5$) by 0.5- and 2.0-MeV proton impact have been measured by the electron spectroscopy method. Electrons ejected from adenine were analyzed by a 45${}^{\circ }$ parallel-plate electrostatic spectrometer over an energy range of 1.0–1000 eV at emission angles from 15${}^{\circ }$ to 165${}^{\circ }$. Single-differential cross sections (SDCSs) and total ionization cross sections (TICSs) were also deduced. It was found from the Platzman plot, defined as SDCSs divided by the classical Rutherford knock-on cross sections per target electron, that the SDCSs at higher electron energies are proportional to the total number of valence electrons (50) of adenine, while those at low-energy electrons are highly enhanced due to dipole and higher-order interactions. The present results of TICS are in fairly good agreement with recent classical trajectory Monte Carlo calculations, and moreover, a simple analytical formula gives nearly equivalent cross sections in magnitude at the incident proton energies investigated.

We report the numerical calculation of Ar${}^{9+}\cdots$ Ar${}^{13+}$, Kr${}^{13+}\cdots$ Kr${}^{17+}$, and Xe${}^{19+}\cdots$ Xe${}^{23+}$ ion yield in the laser field with intensity exceeding ${10}^{19}$ W/cm${}^2$. The results of the calculations agree with the experimental data [K. Yamakava et al., Phys. Rev. A 68, 065403 (2003)] quantitatively (for the Ar ions) or qualitatively (for the Kr ions). The theoretical results disagree with the experimental data for the Xe ions. We discuss the possible influence of the relativistic effects on this disagreement between theory and experiment. We obtained the approximation formula for the position of the maximum ionic population with the given ionization multiplicity $Z$ depending on the radiation intensity. This position is described by the power function of $Z$; the exponent is determined by the dependence of sequential ionization potentials on $Z$ value. We discuss the dependence of the approximation formula parameters on the value of the FWHM of the laser pulse.

We investigate theoretically the transition from two to three dimensions in a weakly interacting ultracold Fermi gas. This transition was recently observed by Dyke et al. [Phys. Rev. Lett. 106, 105304 (2011)] in a cloud of fermionic ${}^6$Li atoms trapped in an oblate harmonic potential. We calculate the density distribution and cloud size of the Fermi cloud by numerically solving three-dimensional Hartree-Fock mean-field equations. Local density approximation is used to ease the calculations in the weakly confined radial direction. Our theoretical results are shown to be in good agreement with the experimental measurements.

We show a procedure for engineering effective interactions between two modes in a bimodal cavity. Our system consists of one or more two-level atoms, excited by a classical field, interacting with both modes. The two effective Hamiltonians have forms similar to beam-splitter and quadratic beam-splitter interactions. We also demonstrate that the nonlinear Hamiltonian can be used to prepare an entangled coherent state, also known as a multidimensional entangled coherent state, which has been pointed out as an important entanglement resource. We show that the nonlinear interaction parameter can be enhanced considering $N$ independent atoms trapped inside a high-finesse optical cavity.

A spatial quantum model of spontaneous parametric down-conversion in nonlinear layered structures is developed expanding the interacting vectorial fields into monochromatic plane waves. A two-photon spectral amplitude depending on the signal- and idler-field frequencies and propagation directions is used to derive transverse profiles of the emitted fields as well as their spatial correlations. Intensity spatial profiles and their spatial correlations are mainly determined by the positions of transmission peaks formed in these structures with photonic bands. A method for geometry optimization of the structures with respect to efficiency of the nonlinear process is suggested. Several structures composed of GaN/AlN layers are analyzed as typical examples. They allow the generation of photon pairs correlated in several emission directions. Photon-pair generation rates increasing better than the second power of the number of layers can be reached. Also, structures efficiently generated photon pairs showing antibunching and anticoalescence can be obtained. Three reasons for splitting the correlated area in photonic-band-gap structures are revealed: zig-zag movement of photons inside the structure, spatial symmetry, and polarization-dependent properties. Also, spectral splitting can be observed in these structures.