We report on hyperfine-resolved spectroscopic measurements of the electric-dipole-forbidden $5p_{3/2}\to 8p_{1/2}$ transition in a sample of ultracold ${}^{87}\text{R}\text{b}$ atoms. The hyperfine selection rules enable the weak magnetic dipole $\left(M1\right)$ contribution to the transition strength to be distinguished from the much stronger electric quadrupole $\left(E2\right)$ contribution. An upper limit on the $M1$ transition strength is determined that is about 50 times smaller than an earlier experimental determination. We also calculate the expected value of the $M1$ matrix element and find that it is less than the upper limit extracted from the experiment.

Frequency doubling in interference oscillations in fast-ion-induced electron emission spectrum from ${\text{H}}_2$ is investigated. Experimentally observed oscillatory structure is well explained by a model calculation based on the rescattering of emitted electron from the second H center. The second-order contribution is found to be as large as 10%. The doubling of oscillation frequency is found out to be independent of angle of observation. Derived analytical expression for the double differential cross section ratio including the first- and second-order interference terms, fits the observed oscillatory structure quite well. The present analysis is in broad agreement with the earlier observations by Stolterfoht et al.

Three-body recombination in helium-helium–alkali-metal collisions at cold temperatures is studied using the adiabatic hyperspherical representation. The rates for the three-body recombination processes ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+X\to {}^4\text{H}\text{e}+{}^4\text{H}\text{e}X$ and ${}^4\text{H}\text{e}+{}^4\text{H}\text{e}+X\to {{}^4\text{H}\text{e}}_2+X$, with $X={}^7\text{L}\text{i}$, ${}^{23}\text{N}\text{a}$, ${}^{39}\text{K}$, ${}^{85}\text{R}\text{b}$, and ${}^{133}\text{C}\text{s}$, are calculated at nonzero collision energies by including not only zero total angular momentum, $J=0$, states but also $J>0$ states. The three-body recombination rates show a relatively weak dependence on the alkali-metal species, differing from each other only by about one order of magnitude, except for the ${}^4\text{H}\text{e-}{}^4\text{H}\text{e-}{}^{23}\text{N}\text{a}$ system.

Photoionization processes for the ground state and $n\le 3$ excited states of hydrogenlike ions embedded in a weakly coupled plasma are investigated in the entire energy range of a nonrelativistic regime. The plasma screening of the Coulomb interaction between charged particles is described by the Debye-Hückel model. The energy levels and wave functions for both the bound and continuum states are calculated by solving the Schrödinger equation numerically by the symplectic integrator. The screening of Coulomb interactions reduces the number of bound electron states, decreases their binding energies, broadens the radial distribution of electron wave functions of these states, and changes significantly the phases and the amplitudes of continuum wave functions. These changes strongly affect the dipole matrix elements between the bound and continuum states and, hence, the photoionization cross sections. The most significant effects of the screened Coulomb interactions on the energy behavior of photoionization cross sections are manifested in its low-energy behavior (Wigner threshold law), the appearance of multiple shape and virtual-state resonances when the energy levels of upper bound states enter the continuum after certain critical strength of the screening, and in the (slight) reduction of the cross section at high photon energies. All these features of the photoionization cross section are related to the short-range character of the Debye-Hückel potential. The effects of the potential screening on the Combet-Farnoux and Cooper minima in the photoionization cross section are also investigated. Comparison of calculated photoionization cross sections with the results of other authors, when available, is made.

We have studied nonlinear absorption from the In $P_{1/2,3/2}$ ground-state doublet in a resistively heated high-temperature cell and a hollow cathode lamp. Using probe and pump lasers at 410 and 451 nm, respectively, absorption spectra with nonlinear properties caused by saturated absorption, coherent dark resonances, and optical pumping are observed. A theoretical description in terms of a density-matrix theory agrees very well with the observed spectra and identifies optical pumping as a dominating process of broadening in the stepwise contribution rather than velocity-changing collisions. Our experiments suggest that the theory used here is widely applicable in saturation spectroscopy on three-level $\Lambda$ systems.

The interrogation of an ultranarrow clock transition of a single trapped ion for optical frequency metrology requires a laser stabilized to a couple of Hz per second with a linewidth of the same order of magnitude. Today, lasers in the visible have reached the Hz-range in frequency stability, if locked onto a high-finesse, ultrastable reference cavity. Vertical mounting of the reference cavity can reduce its sensitivity to vibrations as described in [M. Notcutt, L. Ma, J. Ye, and J. Hall, Opt. Lett. 30, 1815 (2005)]. We have designed a comparable vertical cavity with an overall length of 150 mm resulting in a free spectral range of 1 GHz. Optimization of the cavity design has been carried out with a finite elements method, leading to expected relative length variations below ${10}^{-14}$ under the influence of gravity acceleration $\left(1g\right)$. The variation in different geometric parameters has been studied. The analysis of the different noise sources shows that, for a regime superior to a tenth of a hertz, the fast linewidth of the laser will not be limited by the cavity characteristics.

We optimize two-mode entangled number states of light in the presence of loss in order to maximize the extraction of the available phase information in an interferometer. Our approach optimizes over the entire available input Hilbert space with no constraints, other than fixed total initial photon number. We optimize to maximize the Fisher information, which is equivalent to minimizing the phase uncertainty. We find that in the limit of zero loss, the optimal state is the maximally path-entangled (so-called N00N) state, for small loss, the optimal state gradually deviates from the N00N state, and in the limit of large loss, the optimal state converges to a generalized two-mode coherent state, with a finite total number of photons. The results provide a general protocol for optimizing the performance of a quantum optical interferometer in the presence of photon loss, with applications to quantum imaging, metrology, sensing, and information processing.

Using a tapered undulator and a double grating system we have compressed soft-x-ray photon wave packets into 37% of the original length. To confirm the shortening of the length of wave packets, we employed a special analog method to measure two-photon correlation as it is without elongating the wave-packet length, while the previous two-photon correlation measurements had adopted the method to largely elongate the wave-packet length up to several hundred fs using a monochromator. The present method gives a new prospect in that the compressed wave-packet length is extremely short and of the order of 1 fs, which enables various soft-x-ray spectroscopic experiments to detect in the time domain fast elementary excitations in a solid.

Single $\gamma$ photon propagation in a dense absorptive medium with two widely spaced resonances is experimentally studied. After an initial fast decay, a revival of the photon amplitude in the form of a bump, exceeding the probability amplitude of the incident photon, is observed. The irradiation time of this bump delays approximately by the lifetime of the excited nuclei in the absorber. This effect is explained by the interference of the incoming radiation with the collectively scattered radiation, the phase of which is modulated with the frequency of the doublet splitting. Initially, the destructive interference changes to a constructive one, distinguishing the storage and retrieval stages of the photon propagation in a dense medium, i.e., the collective absorption and collective re-emission processes.

We derive the two-channel (TC) description of the photoassociation (PA) process in the presence of a magnetic Feshbach resonance and compare to full coupled multichannel calculations for the scattering of ${}^6\text{L}\text{i-}{}^{87}\text{R}\text{b}$. Starting from a similar approach as that of Pellegrini et al. [Phys. Rev. Lett. 101, 053201 (2008)] we arrive at a simpler expression which fully describes the PA process by two parameters: the maximal transition rate and the point of vanishing transition rate. The TC approximation reproduces excellently the PA transition rates of the full multichannel calculation and reveals, e.g., that the enhancement of the rate at a resonance is directly connected to the position of vanishing rate. For the description of two independent resonances it was found that only three parameters completely characterize the PA process.

In a previous paper [G. E. Hahne, J. Phys. A 36, 7149 (2003)] the author studied a nontraditional boundary value problem associated with Schrödinger’s partial differential equation for the wave function of a structureless particle moving in four-dimensional spacetime: in this boundary value problem, instead of the conventional specification of initial wave-function values on a $\text{time}=\text{constant}$ surface, suitable time-dependent boundary and normal-derivative values are given on a three-dimensional space-time surface surrounding a slablike region of interaction in four-dimensional spacetime. The particle’s time coordinate plays a natural role as an operator and observable in the modified formalism. In the present paper, the formalism is extended to describe a system of two nonrelativistic particles—each with its own time coordinate—scattering from background potentials and from one another in four-dimensional spacetime. The two-body interaction is taken as a generic noninstantaneous action-at-a-distance, which depends independently on the space-time positions of the two particles. The dynamics is expressed in terms of an integral equation for the wave function, that is, a nonrelativistic version of the Bethe-Salpeter equation. An optical theorem is derived for the transition operator associated with scattering processes; when the theorem holds, the pointwise probability current density derivable from the wave function is conserved globally, that is, in a region covering the space-time domain of significant interparticle interaction. A general formula for the expected dwell-correlation time for the two particles in the space-time region in terms of the scattering matrices is worked out.

Arbitrary exponentially large unitaries cannot be implemented efficiently by quantum circuits. However, we show that quantum circuits can efficiently implement any unitary provided it has at most polynomially many nonzero entries in any row or column, and these entries are efficiently computable. One can formulate a model of computation based on the composition of sparse unitaries which includes the quantum Turing machine model, the quantum circuit model, anyonic models, permutational quantum computation, and discrete time quantum walks as special cases. Thus, we obtain a simple unified proof that these models are all contained in BQP. Furthermore, our general method for implementing sparse unitaries simplifies several existing quantum algorithms.

A comprehensive study of the $X{{}^1\Sigma }^{+}$ and $a{{}^3\Sigma }^{+}$ electronic states of the K and Cs atom pair is presented. Abundant spectroscopic data include 1937 transitions to the $a{{}^3\Sigma }^{+}$ state and $13724$ transitions to the $X{{}^1\Sigma }^{+}$ state for ${{}^{39}\text{K}}^{133}\text{Cs}$ which were obtained by Fourier-transform spectroscopy. From these data potential energy curves were constructed simultaneously for both states $X{{}^1\Sigma }^{+}$ and $a{{}^3\Sigma }^{+}$ which are coupled by the hyperfine interaction. This allows us to accurately model the potential close to $\text{K}\left(4s\right)+\text{Cs}\left(6s\right)$ atom-pair asymptote which is required to simulate cold collision processes. Dissociation energies of the $X{{}^1\Sigma }^{+}$ state as $D_e^X=4069.208\left(40\right){\text{cm}}^{-1}$ and of the $a{{}^3\Sigma }^{+}$ state as $D_e^a=267.141\left(20\right){\text{cm}}^{-1}$ were determined. Scattering lengths are predicted for different KCs isotopologs and Feshbach resonances were calculated for magnetic fields up to 1000 G.

The stable structures and melting properties of ion clouds in isotropic octupole traps are investigated using a combination of semianalytical and numerical models, with a particular emphasis at finite-size scaling effects. Small-size clouds are found to be hollow and arranged in shells corresponding approximately to the solutions of the Thomson problem. The shell structure is lost in clusters containing more than a few thousands of ions, the inner parts of the cloud becoming soft and amorphous. While melting is triggered in the core shells, the melting temperature follows the rule expected for three-dimensional dense particles, with a depression scaling linearly with the inverse radius.

A closed-loop feedback system is used to determine the optimal pulse shapes for manipulating the branching ratio of carbon monoxide following ionization by an intense laser pulse. We focus on manipulating the ${\text{C}}^{+}+\text{O}$ and $\text{C}+{\text{O}}^{+}$ branching ratios of excited states of transient ${\text{CO}}^{+}$. The feedback control system consists of a high resolution time-of-flight spectrometer coupled via a genetic feedback algorithm to an acousto-optical programmable dispersive filter that is incorporated into the ultrafast laser system. Using the spectrometer resolution to distinguish dissociation pathways and select a specific pathway to drive the algorithm, we are able to demonstrate enhanced control of some fragmentation channels. Principal control analysis indicates that the more specific feedback results in numerically simpler optimal pulse shapes. The combination of a more specific target and reduction in pulse complexity could lead to more straightforward investigations of the control mechanism. Analysis of the pulse shapes in conjunction with measurement of the fragment kinetic energy release distributions obtained from the optimized laser pulses is used to probe the dissociative ionization mechanisms.

Ionization of an atom by a few-cycle attosecond xuv pulse is analyzed using perturbation theory (PT), keeping terms in the transition amplitude up to second order in the pulse electric field. Within the PT approach, we present an ab initio parametrization of the ionized electron angular distribution (AD) using rotational invariance and symmetry arguments. This parametrization gives analytically the dependence of the AD on the carrier envelope phase (CEP), the polarization of the pulse, and on the ionized electron momentum direction, $\hat{\mathbf{p}}$. For the general case of an elliptically polarized pulse, we show that interference of the first- and second-order transition amplitudes causes a CEP-dependent asymmetry (with respect to $\hat{\mathbf{p}}\to -\hat{\mathbf{p}}$) and both elliptic and circular dichroism effects. All of these effects are maximal in the polarization plane and depend not only on the CEP but also on the phase of dynamical atomic parameters that enter our parametrization of the AD. Within the single active electron model of an atom, for an initial $s$ or $p$ state we define all dynamical parameters in terms of radial matrix elements (analytic expressions for which are given for the Coulomb and zero-range potentials). For ionization of the H atom by linearly polarized pulses, our PT results are in excellent agreement with results of numerical solutions of the time-dependent Schrödinger equation of Peng et al. [New J. Phys. 10, 025030 (2008)]. Also, our numerical results show that the asymmetries and dichroism effects at low electron energies have a different physical origin from those at high electron energies. Moreover, our results for Gaussian and cosine-squared pulse shapes are in good qualitative agreement. Finally, we show that our analytic formulas may prove useful for determining few-cycle extreme ultraviolet (xuv) pulse characteristics, such as the CEP and the polarization.

In calculations to date [D.-W. Wang and E. Demler, e-print arXiv:0812.1838; M. Klawunn and L. Santos, Phys. Rev. A 80, 013611 (2009)] of multilayer stacks of dipolar condensates, created in one-dimensional optical lattices, the condensates have been assumed to be two dimensional. In a real experiment, however, the condensates do not extend to infinity in the oblate direction, but have to be confined by a trap potential, too. By three-dimensional numerical simulations of this realistic experimental situation we find a crucial dependence of the phonon instability boundary on the number of layers. Moreover, near the boundary of the phonon instability, a variety of structured ground-state wave functions emerges, which may indicate the onset of a roton instability [S. Ronen, D. C. E. Bortolotti, and J. L. Bohn, Phys. Rev. Lett. 98, 030406 (2007); R. M. Wilson, S. Ronen, J. L. Bohn, and H. Pu, Phys. Rev. Lett. 100, 245302 (2008)]. We also consider the effect of a variable number of atoms per layer on the appearance of the phonon instability.

We show that tunneling and localization properties of interacting ultracold atoms in an optical lattice can be controlled by adiabatically turning on a fast oscillatory force even in the presence of disorder. Our calculations are based on the exact solution of the time-dependent Schrödinger equation, using the Floquet formalism. Implications of our findings for larger systems and the possibility of controlling the phase diagram of disordered-interacting bosonic systems are discussed.

We propose an experimental setup for the observation of quasirelativistic massless fermions. It is based on a ${\mathcal{T}}_3$ optical lattice, realized by three pairs of counterpropagating lasers, filled with fermionic cold atoms. We show that in the long wavelength approximation the ${\mathcal{T}}_3$ Hamiltonian generalizes the Dirac-Weyl Hamiltonian for the honeycomb lattice, however, with a larger value of the pseudospin $S=1$. In addition to the Dirac cones, the spectrum includes a dispersionless branch of localized states producing a finite jump in the atomic density. Furthermore, implications for the Landau levels are discussed.