We calculate the Casimir interaction between two short-range scatterers embedded in a background of one-dimensional massless Dirac fermions using a force-operator approach. We obtain the force between two finite-width square barriers and take the limit of zero width and infinite potential strength to study the Casimir force mediated by the fermions. For the case of identical scatterers, we recover the conventional attractive one-dimensional Casimir force. For the general problem with inequivalent scatterers, we find that the magnitude and sign of this force depend on the relative spinor polarizations of the two scattering potentials, which can be tuned to give an attractive, a repulsive, or a compensated null Casimir interaction.

By using the effective Hamiltonian approach, we present a self-consistent framework for the analysis of geometric phases and dynamically stable decoherence-free subspaces in open systems. Comparisons to the earlier works are made. This effective Hamiltonian approach is then extended to a non-Markovian case with the generalized Lindblad master equation. Based on this extended effective Hamiltonian approach, the non-Markovian master equation describing a dissipative two-level system is solved, an adiabatic evolution is defined, and the corresponding adiabatic condition is given.

The photoionization of Ar, Kr, and Xe rare-gas clusters was investigated using angle-resolved time-of-flight photoelectron spectroscopy. Fine-structure-resolved photoelectron angular distributions were determined for the Ar $2p$, Kr $3d$, and Xe $4d$ core levels and the Ar $3s$ inner-valence level as a function of photon energy for two average cluster sizes. Overall, the angular distributions of inner-shell photoelectrons from the cluster and the free atom are found to be very similar, except for the first $10–15\mathrm{eV}$ above the respective photoionization thresholds, where the angular anisotropy of the atomic photoelectrons is high, while our measurements demonstrate considerably less anisotropy in the cluster photoelectron emission. The angular distribution of Ar $3s$ inner-valence photoelectrons from the cluster is substantially less anisotropic than for the atomic photoelectrons throughout the covered photon energy range, but the difference decreases for increasing photon energy.

We theoretically demonstrate that the strong field dynamics such as above-threshold ionization and high-order harmonic generation can be significantly altered by the introduction of the time-delayed two-color laser field consisting of the near-infrared and mid-infrared frequencies. Specifically we apply the idea to the one-dimensional hydrogen atom, and show that the strong field dynamics significantly depend on the time delay between the two fields, as represented, for instance, by the change of the cutoff energies of above-threshold ionization and high-order harmonic generation. It turns out, however, that the delay dependence is different for those processes. In particular, if the duration of the near-infrared pulse is as short as a few cycles, its carrier-envelope phase also plays a very important role. Our classical results for the two processes are consistent with the numerical results.

We demonstrate that the soliton-effect compression to few- and single-cycle pulse widths in a highly nonlinear fiber can be optimized by properly choosing the input soliton number. Soliton compression to a $2\text{−}\mathrm{fs}$ pulse width with a compression ratio up to 50 is demonstrated for light pulses with an initial central wavelength of $1070\mathrm{nm}$ by solving the generalized nonlinear Schrödinger equation for a dispersion profile typical of a small-core photonic-crystal fiber.

The spatiotemporal evolutions of ultrashort pulses in two dimensions are investigated numerically by solving the coupled Maxwell-Bloch equations without invoking the slowly varying envelope approximation and rotating-wave approximation. For an on-axis $2n\pi$ sech pulse, local delay makes the temporal split $2\pi$ sech pulses crescent-shaped in the transverse distribution. Due to the transverse effect, the temporal split $2\pi$ sech pulses become unstable and experience reshaping during the propagation process. Then, interference occurs between the successive crescent-shaped pulses and multiple self-focusing can form.

The spectrum of non-Hermitian Hamiltonians is studied using the point-group symmetries of the Hermitian and non-Hermitian parts of the Hamiltonian. We show that, in principle, the symmetry properties of the Hamiltonian are responsible for the appearance of real eigenvalues in the spectrum of the non-Hermitian Hamiltonian. In practice, however, one must take into account the “strength” of the non-Hermitian part of the Hamiltonian. An effective energy-dependent Hermitian Hamiltonian is constructed that has the same real spectrum as the non-Hermitian Hamiltonian. Several properties, including the self-orthogonality of the states at branch points of the spectrum, are proven using this effective representation. An interesting possibility of complex eigenvalues returning to the real axis is exemplified along with several examples of non-Hermitian Hamiltonians with real eigenvalues.

We propose a scheme to realize the Heisenberg model of any spin in an arbitrary array of coupled cavities. Our scheme is based on a fixed number of atoms confined in each cavity and collectively applied constant laser fields, and is in a regime where both atomic and cavity excitations are suppressed. It is shown that as well as optically controlling the effective spin Hamiltonian, it is also possible to engineer the magnitude of the spin. Our scheme would open up a way to simulate otherwise intractable high-spin problems in many-body physics.

Using the wave-packet propagation method of Rodberg and Thaler and the density matrix method of Fano and Blum, we have defined by completely quantum-mechanical methods the cross sections for the creation, destruction, and transfer of atomic multipole moments by both elastic and inelastic scattering of electrons by atomic targets. All cross sections obtained quantum mechanically, except for the coherence transfer cross sections, agree in form with those obtained semiclassically by Fujimoto and co-workers. We also used the converged close-coupling (CCC) method to calculate numerically some of the above cross sections for selected transitions in electron scattering from hydrogen and barium atoms.

We demonstrate the implications of Efimov physics in the recently measured recombination rate of ${}^{133}\mathrm{Cs}$ atoms. By employing previously calculated results for the energy dependence of the recombination rate of ${}^4\mathrm{He}$ atoms, we obtain three independent scaling functions that are capable of describing the recombination rates over a large energy range for identical bosons with large scattering length. We benchmark these and previously obtained scaling functions by successfully comparing their predictions with full atom-dimer phase shift calculations with artificial ${}^4\mathrm{He}$ potentials yielding large scattering lengths. Exploiting universality, we finally use these functions to determine the three-body recombination rate of ${}^{133}\mathrm{Cs}$ atoms with large positive scattering length, compare our results to experimental data obtained by Kraemer et al. at Innsbruck and find excellent agreement.

The $L$-shell ionization processes of a Ne gas target associated with single-electron capture by bombardment of ${\mathrm{C}}^{q+}$ and ${\mathrm{O}}^{q+}$ $(q=2,3)$ are investigated using the projectile-recoil-ion coincidence method in the energy range from $80\text{to}400\mathrm{keV}∕\mathrm{u}$ $(v_p=1.8–4\mathrm{a.u.})$. The cross-section ratios $\left(R_{k1}\right)$ of $k$-fold ionization to single capture are compared with the results for ${\mathrm{He}}^{2+}\text{−}\mathrm{Ne}$ collisions by Dubois [Phys. Rev. A 36, 2585 (1987)]. All the velocity dependences are quite similar. The ratios increase as the projectile energy increases in the lower-energy region, reach the maxima for projectile energies around $E_{\max }=160q^{1∕2}\mathrm{keV}∕\mathrm{u}$, and then decrease at higher energies. These results qualitatively agree with our calculations in terms of the Bohr-Lindhard model within the independent-electron approximation.

We report cooling and trapping of ${}^{85}\mathrm{Rb}$ atoms in the lower hyperfine level $F=2$ of the $5{}^{2}S_{1∕2}$ ground state in a magneto-optical trap. A maximum of $\sim 6\times {10}^6$ atoms could be trapped using trap laser frequency red detuned by $12\mathrm{MHz}$ from the $F=2\to F^{\prime }=1$ cycling transition. The loading behavior of the trap in terms of loading rate, collisional loss rate, number and density of trapped atoms was studied as a function of trap laser intensity.

Quantum measurements are considered for optimal control of quantum dynamics with instantaneous and continuous observations utilized to manipulate population transfer. With an optimal set of measurements, the highest yield in a two-level system can be obtained. An analytical solution is given for the problem of population transfer by measurement-assisted coherent control in a three-level system with dynamical symmetry. The anti-Zeno effect is recovered in the controlled processes. Demonstrations show that suitable observations can be powerful tools in the manipulation of quantum dynamics.

Final-state trication spectra and electron distributions produced by soft x-ray single-photon triple ionization of rare gas atoms have been obtained by a multiple-coincidence technique using storage-ring synchrotron radiation. The technique uses electron time of flight with ion detection to overcome the problem of high repetition rates in single-bunch operation. A correction needed to the triple-ionization energy of Kr currently listed in standard tables is confirmed, and the method’s ability to examine the three-electron distributions, characterizing the ionization mechanisms and post-collision interactions, is illustrated.

By solving the Bogoliubov–de Gennes equations at zero temperature, we study the effects of a one-dimensional optical lattice on the behavior of a superfluid Fermi gas at unitarity. We show that, due to the lattice, at low densities the gas becomes highly compressible and the effective mass is large, with a consequent significant reduction of the sound velocity. We discuss the role played by the lattice in the formation of molecules and the emergence of two-dimensional effects in the equation of state. Predictions for the density profiles and for the frequency of the collective oscillations in the presence of harmonic trapping are also given.

We investigate spin squeezing of a two-mode boson system with a Josephson coupling. An exact relation between the squeezing and the single-particle coherence at the maximal-squeezing time is discovered, which provides a more direct way to measure the squeezing by readout of the coherence in atomic interference experiments. We prove explicitly that the strongest squeezing is along the $J_z$ axis, indicating the appearance of an atom number-squeezed state. Power laws of the strongest squeezing and the optimal coupling with particle number $N$ are obtained based upon a wide range of numerical simulations.

We propose a feasible scheme to realize nonlinear Ramsey interferometry with a two-component Bose-Einstein condensate, where the nonlinearity arises from the interaction between coherent atoms. In our scheme, two Rosen-Zener pulses are separated by an intermediate holding period of variable duration and through varying the holding period we have observed nice Ramsey interference patterns in the time domain. In contrast to the standard Ramsey fringes our nonlinear Ramsey patterns display diversiform structures ascribed to the interplay of the nonlinearity and asymmetry. In particular, we find that the frequency of the nonlinear Ramsey fringes exactly reflects the strength of nonlinearity as well as the asymmetry of system. Our finding suggests a potential application of the nonlinear Ramsey interferometry in calibrating the atomic parameters such as scattering length and energy spectrum.

We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.

A Bose-Einstein condensate produced by a Hamiltonian which is rotationally or translationally symmetric may be fragmented as a direct result of these symmetries. A corresponding mean-field unfragmented state, with an identical energy to leading order in the number of particles, can generally be constructed. As a consequence, vanishingly weak symmetry-breaking perturbations destabilize the fragmented state, which would thus be extremely difficult to realize experimentally and lead to an unfragmented condensate.