Quantum-mechanical calculations are reported for hydrogen recombination in the presence of a chemically inert spectator. The calculations employ a square integrable Sturmian basis set to provide a discrete representation of the ${\mathrm{H}}_2$ continuum. Direct three-body recombination is approximated by computing transitions from the nonresonant continuum. Resonant and nonresonant states are handled on equal footing within the sequential two-step energy transfer mechanism. Theoretical rate coefficients are computed within the equilibrium and steady-state approximations for the density of intermediate molecules. The results are compared with existing experimental data for He and Ar. The sensitivity of the calculations to pressure variations and to changes in the potential energy surface are investigated for He. The reliability of these calculations and their relevance for astrophysical models are discussed.

Strong-field closed-loop control schemes using shaped ultrafast laser pulses have been used to selectively fragment a variety of molecules in recent years. The resulting pulses are often complex and resist an easy mechanistic interpretation. We report on the use of velocity map imaging to study the dissociative ionization of CO molecules by optimally-shaped ultrafast laser pulses. Using this technique, a mechanism is identified for the optimized CO${}^{+}$ $\to$ C $+$ ${\mathrm{O}}^{+}$ dissociation, and some of the observed control over the CO${}^{+}$ dissociation branching ratio is ascribed to an angular discrimination effect. Furthermore, we demonstrate that the acquisition of two-dimensional velocity map images is rapid enough to incorporate directly into the adaptive control loop.

We propose to test the theory of continuous spontaneous localization (CSL) in an all-optical time-domain Talbot-Lau interferometer for clusters with masses exceeding ${10}^6\hspace{0.5em}$ amu. By assessing the relevant environmental decoherence mechanisms, as well as the growing size of the particles relative to the grating fringes, we argue that it will be feasible to test the quantum superposition principle in a mass range excluded by recent estimates of the CSL effect.

Quantum fluctuations in an ultrafast rotating Bose gas at zero temperature are investigated. We calculate the condensate density perturbatively to show that no condensate is present in the thermodynamic limit. The excitation from Gaussian fluctuations around the mean-field solution causes infrared divergences in loop diagrams, nevertheless, in calculating the atom number density, the correlation functions and the free energy, we find that the sum of the divergences in the same loop order vanishes and we obtain finite physical quantities. The long-range correlation is explored and the algebraic decay exponent for the single-particle correlation function is obtained. The atom number density distribution is obtained at the one-loop level, which illustrates the quantum fluctuation effects to melt the mean-field vortex lattice. By the nonperturbative Gaussian variational method, we locate the spinodal point of the vortex-lattice state.

We report solutions for expanding dipole-type optical solitary waves in two-dimensional Kerr media with the self-focusing nonlinearity, using exact analytical (Hirota) and numerical methods. Such localized beams carry intrinsic vorticity and exhibit symmetric shapes for both scalar and vector solitary modes. When vector beams are close to the scalar limit, simulations demonstrate their stability over propagation distances exceeding 50 diffraction lengths. In fact, the continuous expansion helps the vortical beams avoid the instability against the splitting, collapse, or decay, making them “convectively stable” patterns.

The spurious self-interaction energy, which is one-half the integrated electrostatic interaction energy of a normalized electronic charge distribution with the potential field generated by itself, is calculated analytically for a $1s$-like electron charge distribution governed by an attractive screened Hulthen-type model potential. The exact result obtained is used, via an energetic cancellation constraint and a convenient Hölder’s integral inequality, to deduce an analytical lower bound for the screening-dependent positive coefficient of a negative exchange-like energy term applied routinely in the local-density approximation to density functional theory with Coulomb potentials. The bare Coulomb case is investigated by Sobolev’s integral inequality as well.

Families of dark solitons exist in superfluid Fermi gases. The energy-velocity dispersion and number of depleted particles completely determine the dynamics of dark solitons on a slowly varying background density. For the unitary Fermi gas, we determine these relations from general scaling arguments and conservation of local particle number. We find solitons to oscillate sinusoidally at the trap frequency reduced by a factor of $1/\sqrt{3}$. Numerical integration of the time-dependent Bogoliubov–de Gennes equation determines spatial profiles and soliton-dispersion relations across the BEC-BCS crossover, and proves consistent with the scaling relations at unitarity.

In the present paper, we investigate the Berry phase and the Hannay angle of an interacting two-mode boson system and obtain their analytic expressions in explicit forms. The relation between the Berry phase and the Hannay angle is discussed. We find that, in the large-particle-number limit, the classical Hannay angle equals the particle number derivative of the quantum Berry phase except for a sign. This relationship is applicable to other many-body boson systems where the coherent-state description is available and the total particle number is conserved. The measurement of the classical Hannay angle in the many-body systems is briefly discussed as well.

A complete classification is given for one-dimensional chains with nearest-neighbor interactions having two states in each site, for which a matrix product ground state exists. The Hamiltonians and their corresponding matrix product ground states are explicitly obtained.

Our previous paper [Phys. Rev. Lett. 104, 060401 (2010)] predicted that Casimir forces induced by the material-dispersion properties of certain dielectrics can give rise to stable configurations of objects. This phenomenon was illustrated via a dicluster configuration of nontouching objects consisting of two spheres immersed in a fluid and suspended against gravity above a plate. Here, we examine these predictions from the perspective of a practical experiment and consider the influence of nonadditive, three-body, and nonzero-temperature effects on the stability of the two spheres. We conclude that the presence of Brownian motion reduces the set of experimentally realizable silicon-teflon spherical diclusters to those consisting of layered microspheres, such as the hollow core (spherical shells) considered here.

We present normalized doubly differential cross sections (DDCS's) for the near-threshold, electron-impact single ionization of argon and krypton, similar to those taken earlier for Ne and Xe [Yates et al., J. Phys. B 42, 095206 (2009)]. The Ar measurements were taken at incident energies of 17, 18, 20, and 30 eV while the Kr measurements were taken at 15, 16, 17.5, and 20 eV. The DDCS scattering angles range from 15${}^{°}$ to 120${}^{°}$. The differential data are initially normalized to available experimental cross sections for excitation of the ground ${\mathit{np}}^6$ to the ${\mathit{np}}^5(n+1)s$ excited states of the noble gas and, after integration, to well-established experimental total ionization cross sections of Rapp and Englander-Golden [J. Chem. Phys. 43, 1464 (1965)].

High-order-harmonic generation (HHG) by atoms in a strong laser field is analyzed theoretically, taking into account atomic potential effects beyond the strong field approximation (SFA). Our analytical derivation extends the time-dependent effective range (TDER) theory, developed previously for a short-range potential supporting only a single bound state, to the case of a potential supporting two bound states having different angular momenta and dynamically interacting with the continuum. In contrast to the SFA and the single-state TDER model, in both of which the HHG rates in the region of the high-energy plateau cutoff involve only the plane-wave (first Born) approximation for the photorecombination cross section, our analytic expression for the HHG rates in the two-state TDER model involves the exact photorecombination cross section for this model. These results justify the factorization of HHG rates in the high-energy plateau region in terms of the electron wave packet and the exact (non-Born) photorecombination cross section, which was suggested previously using only phenomenological arguments.

Amplitude-modulated nonlinear magneto-optical rotation is a powerful technique that offers a possibility of controllable generation of given quantum states. In this paper, we demonstrate creation and detection of specific ground-state magnetic-sublevel superpositions in ${}^{87}\mathrm{Rb}$. By appropriate tuning of the modulation frequency and magnetic-field induction the efficiency of a given coherence generation is controlled. The processes are analyzed versus different experimental parameters.

We study ultracold neutral fermion superfluids in the presence of fictitious magnetic fields, as well as charged fermion superfluids in the presence of real magnetic fields. Charged fermion superfluids undergo a phase transition from type-I to type-II superfluidity, where the magnetic properties of the superfluid change from being a perfect diamagnet without vortices to a partial diamagnet with the emergence of the Abrikosov vortex lattice. The transition from type-I to type-II superfluidity is tuned by changing the scattering parameter (interaction) for fixed density. We also find that neutral fermion superfluids such as ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$ are extreme type-II superfluids and are more robust to the penetration of a fictitious magnetic field in the BCS-BEC crossover region near unitarity, where the critical fictitious magnetic field reaches a maximum as a function of the scattering parameter (interaction).

Weak measurements in combination with postselection can give rise to a striking amplification effect (related to a large “weak value”). We show that this effect can be understood by viewing the initial state of the pointer as the ground state of a fictional harmonic oscillator. This perspective clarifies the relationship between the weak-value regime and other measurement techniques and inspires a proposal to implement fully quantum weak-value measurements combining photons and atomic ensembles.

The Kohn-Sham (KS) potential of density-functional theory (DFT) emerges as the minimizing effective potential in a variational scheme that does not involve fixing the unknown single-electron density. Using Rayleigh Schrödinger (RS) perturbation theory (PT), we construct ab initio approximations for the energy difference, the minimization of which determines the KS potential directly—thereby bypassing DFT’s traditional algorithm to search for the density that minimizes the total energy. From second-order RS PT, we obtain variationally stable energy differences to be minimized, solving the severe problem of variational collapse of orbital-dependent exchange-correlation functionals based on second-order RS PT.

The existence of localized modes supported by the $\mathcal{PT}$-symmetric nonlinear lattices is reported. The system considered reveals unusual properties: unlike other typical dissipative systems, it possesses families (branches) of solutions, which can be parametrized by the propagation constant; relatively narrow localized modes appear to be stable, even when the conservative nonlinear lattice potential is absent; and finally, the system supports stable multipole solutions.