A numerical simulation of photodetachment of ${\mathrm{F}}^{-}$ by a circularly polarized laser pulse has been accomplished by using a Keldysh-type approach. The numerical results are in agreement with measurements of photoelectron energy spectra recently reported in the literature. The features exhibited by the spectra are traced back to quantum interference effects, in the same spirit as in a double-slit experiment in the time domain.

Frequency-domain nonlinear wave mixing processes may be described either using response functions, whereby the signal is generated after all interactions with the incoming fields, or in terms of scattering amplitudes where all fields are treated symmetrically with no specific time ordering. Closed Green’s function expressions derived for the two types of signals have different analytical properties. The recent controversy regarding the sign of radiative damping in the linear (Kramers-Heisenberg) formula is put in a broader context.

We introduce a scheme for realizing arbitrary controlled-unitary operations in a two-qubit system. If the $2\times 2$ unitary matrix is special unitary (has unit determinant), the controlled-unitary gate operation can be realized in a single pulse operation. The pulse in our scheme will constitute varying one of the parameters of the system between an arbitrarily maximum and a “calculated” minimum value. This parameter will constitute the variable parameter of the system while the other parameters, which include the coupling between the two qubits, will be treated as fixed parameters. The values of the parameters are what we solve for using our approach in order to realize an arbitrary controlled-unitary operation. We further show that the computational complexity of the operation is no greater than that required for a controlled-NOT (CNOT) gate. Since conventional schemes realize a controlled-unitary operation by breaking it into a sequence of single-qubit and CNOT gate operations, our method is an improvement because we not only require less time duration, but also fewer control lines to implement the same operation. To demonstrate improvement over other schemes, we show, as examples, how two controlled-unitary operations, one being the controlled-Hadamard gate, can be realized in a single pulse operation using our scheme. Furthermore, our method can be applied to a wide range of coupling schemes and can be used to realize gate operations between two qubits coupled via Ising, Heisenberg, and anisotropic interactions.

A comprehensive study of the electronic states at the $4s+5s$ asymptote in $\mathrm{KRb}$ is presented. Abundant spectroscopic data on the $a{}^3\Sigma ^{+}$ state were collected by Fourier-transform spectroscopy, which allows one to determine an accurate experimental potential energy curve up to $14.8\mathrm{\AA }$. The existing data set [C. Amiot et al., J. Chem. Phys. 112, 7068 (2000)] on the ground state $X{}^1\Sigma ^{+}$ was extended by several additional levels lying close to the atomic asymptote. In a coupled channels fitting routine complete molecular potentials for both electronic states were fitted. Along with the line frequencies of the molecular transitions, recently published positions of Feshbach resonances in ${}^{40}\mathrm{K}$ and ${}^{87}\mathrm{Rb}$ mixtures [F. Ferlaino et al., Phys. Rev. A 74, 039903 (2006)] were included in the fit. This makes the derived potential curves capable for an accurate description of observed cold collision features so far. Predictions of scattering lengths and Feshbach resonances in other isotopic combinations are reported.

More accurate variational calculations of the lowest three pure vibrational states $(v=0,1,2)$ of the ${}^4\mathrm{He}{\mathrm{H}}^{+}$ molecular ion have been carried out without assuming the Born-Oppenheimer approximation. In the calculations we included the complete set of ${\alpha }^2$ relativistic corrections, i.e., mass-velocity, Darwin, spin-spin, and orbit-orbit. This allowed us to improve the agreement between the theory and the experiment for the vibrational frequencies of the $1\to 0$ and $2\to 1$ transitions as compared to our previous calculations [Stanke et al., Phys. Rev. Lett. 96, 233002 (2006)].

The time and momentum distributions of electron emission from a molecule during a single laser cycle are calculated by solving a two-dimensional time-dependent Schrödinger equation. The momentum distributions strongly depend on the orbital symmetry and orientation of the molecular axis. Field-induced internal dynamics of the molecule can shift electron emission and recollision times through a large part of the laser cycle, which leads to corresponding variations of high-harmonic emission times and to the appearance of even harmonics.

Different descriptions of the light-matter interaction which include the full spatial dependence of the electromagnetic field are presented. It is demonstrated how nondipole forms of both the Kramers-Henneberger and the length gauge Hamiltonians may be obtained from the minimum-coupling Hamiltonian in the velocity gauge through the Baker-Hausdorff lemma. Furthermore, the length gauge version of the Dirac equation is presented. The applicability of the different descriptions is discussed.

A vortex in a superfluid gas inside an optical lattice can behave as a massive particle moving in a periodic potential and exhibiting quantum properties. In this paper we discuss these properties and show that the excitation of vortex dynamics in a two-dimensional lattice can lead to striking measurable changes in its dynamic response. It would be possible by means of Bragg spectroscopy to carry out the first direct measurement of the effective vortex mass. In addition, the experiments proposed here provide an alternative way to study the pinning to the underlying lattice and the dissipative damping.

Due to the finite transverse distribution of the control field and cold atoms, there can exist a set of guiding modes for ultraslow signal field propagating in an atomic medium with electromagnetically induced transparency. For cold four-level atoms, these guiding modes can be manipulated by varying the laser fields and atomic distribution. By carefully designing the distribution of the induced refractive index, we show that it is possible to realize single mode operation for slow light propagation which may have practical applications.

We study the propagation of frequency-chirped laser pulses in optically thick media. We consider a medium of atoms with a $\Lambda$ level-scheme (Lambda atoms) and also, for comparison, a medium of two-level atoms. Frequency-chirped laser pulses that induce adiabatic population transfer between the atomic levels are considered. They induce transitions between the two lower (metastable) levels of the $\Lambda$-atoms and between the ground and excited states of the two-level atoms. We show that associated with this adiabatic population transfer in $\Lambda$-atoms, there is a regime of enhanced transparency of the medium—the pulses are distorted much less than in the medium of two-level atoms and retain their ability to transfer the atomic population much longer during propagation.

The transverse correlation of triphoton entanglement generated within a single crystal is analyzed. Among many interesting features of the transverse correlation, they arise from the spectral function $F$ of the triphoton state produced in the parametric processes. One consequence of transverse effects of entangled states is quantum imaging, which is theoretically studied in photon counting measurements. Klyshko’s two-photon advanced-wave picture is found to be applicable to the multiphoton entanglement with some modifications. We found that in the two-photon coincidence counting measurement by using triphoton entanglement, although the Gaussian thin lens equation (GTLE) holds, the imaging shown in coincidences is obscure and has a poor quality. This is because of tracing the remaining transverse modes in the untouched beam. In the triphoton imaging experiments, two kinds of cases have been examined. For the case that only one object with one thin lens is placed in the system, we found that the GTLE holds as expected in the triphoton coincidences and the effective distance between the lens and imaging plane is the parallel combination of two distances between the lens and two detectors weighted by wavelengths, which behaves as the parallel combination of resistors in the electromagnetism theory. Only in this case, a point-point correspondence for forming an image is well-accomplished. However, when two objects or two lenses are inserted in the system, though the GTLEs are well-satisfied, in general a point-point correspondence for imaging cannot be established. Under certain conditions, two blurred images may be observed in the coincidence counts. We have also studied the ghost interference-diffraction experiments by using double slits as apertures in triphoton entanglement. It was found that when two double slits are used in two optical beams, the interference-diffraction patterns show unusual features compared with the two-photon case. This unusual behavior is a destructive interference between two amplitudes for two photons crossing two double slits.

We employ a recently developed $S$-matrix approach [L. Plaja and J. A. Pérez-Hernández, Opt. Express 15, 3629 (2007)] to investigate the process of harmonic generation in tunnel and multiphoton ionization regimes. In contrast with most of the previous approaches, this model is developed without the stationary phase approximation and including the relevant continuum-continuum transitions. Therefore, it provides a full quantum description of the harmonic generation process in these two ionization regimes, with a good quantitative accuracy with the exact results of the time-dependent Schrödinger equation. We show how this model can be used to investigate the contribution of the electronic population ionized at different times, thus giving a time-resolved description that, up to now, was reserved only to semiclassical models. In addition, we will show some aspects of harmonic generation beyond the semiclassical predictions as, for instance, the emission of radiation while the electron is leaving the parent ion and the generation of harmonics in semiclassically forbidden situations.

Electron-impact double-ionization cross sections for the helium atom are calculated by direct solution of a nine-dimensional Schrödinger equation using a time-dependent close-coupling method. Previous calculations are extended to higher incident electron energies using a simple factor-of-2 reduction in the mesh spacing for the three-dimensional radial lattice. The recent calculations, computationally more than an order of magnitude more difficult, are found to be in good agreement with experiment from threshold to beyond the peak of the cross section at $275\mathrm{eV}$.

A class of squeezed boson and fermion states is studied with particular emphasis on the nature of entanglement. We first investigate the case of bosons, considering two-mode squeezed states. Then we construct the fermion version to show that such states are maximum entangled, for both bosons and fermions. To achieve these results, we demonstrate some relations involving squeezed boson states. The generalization to the case of fermions is made by using Grassmann variables.

We present a detailed experimental and theoretical study of the effect of nuclear spin on the performance of optical lattice clocks. With a state-mixing theory including spin-orbit and hyperfine interactions, we describe the origin of the ${}^{1}S_0\text{−}{}^{3}P_0$ clock transition and the differential $g$ factor between the two clock states for alkaline-earth-metal(-like) atoms, using ${}^{87}\mathrm{Sr}$ as an example. Clock frequency shifts due to magnetic and optical fields are discussed with an emphasis on those relating to nuclear structure. An experimental determination of the differential $g$ factor in ${}^{87}\mathrm{Sr}$ is performed and is in good agreement with theory. The magnitude of the tensor light shift on the clock states is also explored experimentally. State specific measurements with controlled nuclear spin polarization are discussed as a method to reduce the nuclear spin-related systematic effects to below ${10}^{-17}$ in lattice clocks.

A three-dimensional imaging technique installed at the Heidelberg Test Storage Ring (TSR) has been used to investigate the three-body breakup channels occurring in the dissociative recombination process of the methylene ion ${\text{CH}}_2^{+}$. By selecting dissociation planes perpendicular to the molecular beam direction the dissociation kinematics could be measured with unprecedented momentum resolution. Release energies, the relative branching ratio, and the kinematical correlations between the three fragments were determined for the two energetically allowed channels: $\text{C}\left({}^{3}P\right)+\text{H}\left({}^{2}S\right)+\text{H}\left({}^{2}S\right)$ and $\text{C}\left({}^{1}D\right)+\text{H}\left({}^{2}S\right)+\text{H}\left({}^{2}S\right)$.

The theory of laser cooling assisted by transverse magnetic field ${\mathbf{B}}_{\mathbf{t}}$ based on the $(1+3)$-level atomic system is presented. With the additional ${\mathbf{B}}_{\mathbf{t}}$, atoms could be redistributed among the upper Zeeman sublevels via Larmor precession, and results in large stimulated radiation force and low temperature. Here we consider this cooling model both for broad transition line and narrow line. A Fokker-Planck-type kinetic equation is derived for a broad line. Numerical result shows that the final temperature could be lower than the Doppler limit. For a narrow line, the Monte Carlo approach is applied to simulate the distribution of atoms in the momentum regime and the result shows that most atoms are distributed around zero velocity with width about several $\hslash k∕m$.

We investigate bright matter-wave solitons in the presence of a spatially varying nonlinearity. It is demonstrated that a translation mode is excited due to the spatial inhomogeneity and its frequency is derived analytically and also studied numerically. Both cases of purely one-dimensional and “cigar-shaped” condensates are studied by means of different mean-field models, and the oscillation frequencies of the pertinent solitons are found and compared with the results obtained by the linear stability analysis. Numerical results are shown to be in very good agreement with the corresponding analytical predictions.

Single fluorophore systems attached to complex hosting molecules may exhibit a light-assisted fluorescence blinking phenomenon between two or more different intensity states whose sojourn statistic depends on the pumping laser intensity and also may depart from an exponential law. In contrast with standard phenomenological models, here we demonstrate that such kind of radiation patterns can be microscopically derived and characterized by describing the fluorophore decay through a composite reservoir where quantum degrees of freedom associated to the host molecule mediate the interaction between the fluorophore and a bosonic bath associated to its natural decay.