We present experimental results on the coherent transfer of orbital angular momentum (OAM) from optical fields to the center-of-mass motion of a Bose-Einstein condensate (BEC), using an approach which results in negligible linear momentum change. Two collinear optical beams of differing OAM are used to couple discrete sublevels of the atomic ground state via a stimulated Raman process. We demonstrate several of the possible optical field configurations which place the BEC into various spinor and vortex states. We also show how this approach can be used to create coherent superpositions of these states and use the interference patterns of such superpositions to confirm the presence of quantized vortices.

In a recent paper, we have shown that the QED nonlinear corrections imply a phase correction to the linear evolution of crossing electromagnetic waves in vacuum. Here, we provide a more complete analysis, including a full numerical solution of the QED nonlinear wave equations for short-distance propagation in a symmetric configuration. The excellent agreement of such a solution with the result that we obtain using our perturbatively motivated variational approach is then used to justify an analytical approximation that can be applied in a more general case. This allows us to find the most promising configuration for the search of photon-photon scattering in optics experiments. In particular, we show that our previous requirement of phase coherence between the two crossing beams can be released. We then propose a very simple experiment that can be performed at future exawatt laser facilities, such as ELI, by bombarding a low power laser beam with the exawatt bump.

We present an example for broadcasting of the entanglement of a two-mode squeezed state of the electromagnetic field shared by two distant parties into two nonlocal bipartite entangled states. Using the technique of covariance matrices we demonstrate the entanglement between the nonlocal output modes and the separability of the local output modes. We find the range of values for the squeezing parameter and the amplifier phase for which broadcasting of continuous-variable entanglement can be implemented for physical states.

The relativistic Hartree-Fock method together with many-body perturbation theory and a configuration-interaction technique are used to calculate relativistic energy shifts for frequencies of the strong electric-dipole transitions of C III, C IV, Na I, Mg I, Mg II, Al II, Al III, Si IV, Ca II, and Zn II. These transitions are used for a search of the variation of the fine-structure constant in quasar absorption spectra. The results are in good agreement with previous calculations. The analysis of Breit contributions is also presented.

The hyperfine structure of transitions between $n=51–53d$ and $n=54–57f$ Rydberg states belonging to series converging on the $X{{{}^2\Sigma }_g}^{+}$ $\left(v^{+}=0,N^{+}=1\right)$, ground state of para-$\text{D}_2{}^{+}$ has been measured at an experimental resolution of about 1 MHz by millimeter-wave spectroscopy and assigned on the basis of combination differences. A map of the hyperfine structure of these Rydberg states has been determined. The analysis of the hyperfine structure of the $nf$ series by multichannel quantum defect theory has confirmed the experimental assignments and enabled the derivation of the hyperfine structure of the ground state of para-$\text{D}_2{}^{+}$ with a precision of better than 1 MHz.

Systems whose underlying classical dynamics are chaotic exhibit signatures of the chaos in their quantum mechanics. We investigate the possibility of using the linear response formalism of time-dependent density functional theory (TDDFT) to study the case when chaos is induced by electron-interaction alone. Nearest-neighbor level-spacing statistics are in principle exactly and directly accessible from TDDFT. We discuss how the TDDFT linear response procedure can reveal information about the mechanism of chaos induced by electron-interaction alone. A simple model of a two-electron quantum dot highlights the necessity to go beyond the adiabatic approximation in TDDFT.

A method is described for computing total cross sections for the ionization of inner shells of atoms and positive ions by impact of electrons and positrons with arbitrary energies. The method combines the relativistic plane-wave Born approximation (PWBA) with a semirelativistic version of the distorted-wave Born approximation (DWBA). Formal expressions for the longitudinal and transverse generalized oscillator strengths (GOSs) of closed shells are derived. Tables of GOSs for $K$ shells and for $L$ and $M$ subshells of neutral atoms have been calculated for a discrete grid of energy losses and recoil energies. A suitable interpolation scheme allows the easy evaluation of PWBA ionization cross sections from these GOS tables. The difference between the total ionization cross sections that result from the DWBA and the PWBA (considering the longitudinal interaction only) has been calculated numerically for projectiles with kinetic energies up to 16 times the ionization energy of the active shell. In this energy range, ionization cross sections with the accuracy of a distorted-wave calculation are obtained by simply adding this difference to the cross section resulting from the conventional PWBA. For higher energies, the cross section is obtained by multiplying the PWBA cross section by an energy-dependent scaling factor that is determined by a single fitted parameter. Numerical results are shown to agree with experimental data, when these are available.

In this paper, the Tikhonov regularization method and the classical molecular dynamics method are used to deal with the inverse problem involved in the measurement of inner-shell ionization cross sections by using the thick-target method. These two methods are applied to simulated and real experimental data for the $K$-shell ionization of a Ni element by electron impact. The satisfactory results can be obtained by using these two methods to treat the inverse problem involved in the thick-target method. The estimated total error for the method described in this paper is about 10%, which is the same order as the experimental error with the thin-target method. It can be concluded that the thick-target method can be reliably used in the future for the measurement of inner-shell ionization cross sections by electron or positron impact near the threshold energy region.

We explain how a proper specification of the spatial field distribution and angular momentum content of a twisted light beam propagating in an arbitrary direction can be made using appropriate transformations. Such transformations are needed whenever a light beam is to be combined with other similar beams propagating in specified directions. The transformation procedure greatly facilitates the evaluations of the radiation forces acting on atoms subject to an arbitrary set of twisted light beams. It allows atomic trajectories in one-, two-, and three-dimensional optical molasses configurations to be correctly evaluated. We find that multiple twisted beams offer a flexible means of controlling the motion of atoms, but there are notable features attributable only to the orbital optical angular momentum property of the twisted light. Under suitable conditions, atoms can be decelerated and ultimately made to congregate in specific regions of space. The implications of this for all-optical atomic cooling and trapping using twisted light are pointed out and discussed.

The condition for the appearance of dynamical instability of the Bose-condensed system, characterized by the emergence of complex eigenvalues in the Bogoliubov–de Gennes equations, is studied analytically. It is concluded that the degeneracy between a positive-norm eigenmode and a negative-norm one is essential for the emergence of complex modes. Based on the conclusion, we justify the two-mode approximation applied in our previous work [E. Fukuyama et al., Phys. Rev. A 76, 043608 (2007)], in which we analytically studied the condition for the existence of complex modes when the condensate has a highly quantized vortex.

We present a numerical calculation of the velocity field of an off-axis vortex within a harmonic trapping potential. We consider a condensate with a large number of particles which, in spite of being in the Thomas-Fermi regime, possesses a non-totally-negligible vortex core size. Via a simple, yet realistic, modeling of the vortex-state density, we derive, by treating the equation of continuity outside and inside the vortex core, respective equations for the velocity field and the vortex precession velocity. We find that the vortex precession velocity is given by two contributions: the background velocity field evaluated around the border of the core and another term which depends on the core shape. Our findings concerning the velocity field outside the vortex core are in good agreement with previous theoretical predictions in a narrow region around it, while far away from the vortex we observe a field with a large asymmetry with respect to the vortex position. We show that a better approximation may be obtained by adding the velocity field produced by an antivortex located outside the condensate.

The high peak intensity achieved with ultrashort pump pulses drastically increases the conversion efficiency in spontaneous parametric down-conversion. However, when ultrashort pulses are used, dispersion limits the degree of squeezing. Here, we investigate the effects of dispersion on both quadrature squeezing and photon statistics by varying the interaction length when pumping a periodically poled lithium niobate crystal with femtosecond pulses. The down-converted light in the 1550 nm telecom band attains its maximum observed squeezing level of 3.1 dB for the shortest interaction length. Our photon-statistics measurements agree with the photon-pair distribution going from thermal to Poissonian as the interaction length is increased. This is explained by considering the dispersion-induced distinguishability of the generated photon pairs.

We experimentally investigate the evolution of an angularly resolved spectrum of third harmonic generated by infrared femtosecond laser pulse filamentation in air. We show that at low pump intensity, phase matching between the fundamental and third-harmonic waves dominates the nonlinear optical effect and induces a ring structure of the third-harmonic beam, whereas at high pump intensity, the dispersion properties of air begin to affect the angular spectrum, leading to the formation of a nonlinear $\text{X}$ wave at third harmonic.

We study experimentally the role of the bias current sweep rate in measurements of polarization switching (PS) of vertical-cavity surface-emitting lasers. We find that the size of the hysteresis cycle of the PS for increasing and decreasing current follows a power-law relationship with the speed of the current ramp. A similar relation is found for the laser turn-on. Numerical calculations based on the spin-flip model are in good agreement with the observations. We also show that the PS points and the power-law exponents depend critically on the noise level included in the simulations.

The density matrix of a two-level system (spin, atom) is usually determined by measuring the three noncommuting components of the Pauli vector. This density matrix can also be obtained via the measurement data of two commuting variables, using a single apparatus. This is done by coupling the two-level system to a mode of radiation field, where the atom-field interaction is described with the Jaynes-Cummings model. The mode starts its evolution from a known coherent state. The unknown initial state of the atom is found by measuring two commuting observables: the population difference of the atom and the photon number of the field. We discuss the advantages of this setup and its possible applications.

The problem of on-demand generation of entanglement between single-atom qubits via a common photonic channel is examined within the framework of optical interferometry. As expected, for a Mach-Zehnder interferometer with coherent laser beam as input, a high-finesse optical cavity is required to overcome sensitivity to spontaneous emission. We show, however, that with a twin-Fock input, useful entanglement can in principle be created without cavity enhancement. Both approaches require single-photon resolving detectors, and best results would be obtained by combining both cavity feedback and twin-Fock inputs. Such an approach may allow a fidelity of 0.99 using a two-photon input and currently available mirror and detector technology. In addition, we study interferometers based on NOON states, i.e., maximally entangled $N$-particle states, and show that they perform similarly to the twin-Fock states, yet without the need for high-precision photodetectors. The present interferometrical approach can serve as a universal, scalable circuit element for quantum information processing, from which fast quantum gates, deterministic teleportation, entanglement swapping, etc., can be realized with the aid of single-qubit operations.

We study properties of two different atoms at a single optical lattice site at a heteronuclear atomic Feshbach resonance. We calculate the energy spectrum, the efficiency of rf association, and the lifetime as a function of magnetic field and compare the results with the experimental data obtained for ${}^{40}\text{K}$ and ${}^{87}\text{R}\text{b}$ [C. Ospelkaus et al., Phys. Rev. Lett. 97, 120402 (2006)]. We treat the interaction in terms of a regularized $\delta$ function pseudopotential and consider the general case of particles with different trap frequencies, where the usual approach of separating center-of-mass and relative motion fails. We develop an exact diagonalization approach to the coupling between center-of-mass and relative motion and numerically determine the spectrum of the system. At the same time, our approach allows us to treat the anharmonicity of the lattice potential exactly. Within the pseudopotential model, the center of the Feshbach resonance can be precisely determined from the experimental data.

Stimulated Raman transition is generally used for a coherent population transfer in a cold atom interferometer. We have experimentally investigated the magnetic field dependence of coherent population transfer by the stimulated Raman process. Experimental data show that both Rabi frequency and population greatly depend on the amplitude and sense of the magnetic field. Theoretical analysis is also carried out, and the experimental results are in good agreement with the theoretical calculations. The study is helpful for optimizing the interferometer fringes and for improving the rotation measurement precision of a Sagnac interferometer.