Creation of entanglement is considered theoretically and numerically in an ensemble of spin chains with dipole-dipole interaction between the spins. The unwanted effect of the long-range dipole interaction is compensated by the optimal choice of the parameters of radio-frequency pulses implementing the protocol. The errors caused by (i) the influence of the environment, (ii) nonselective excitations, (iii) influence of different spin chains on each other, (iv) displacements of qubits from their perfect locations, and (v) fluctuations of the external magnetic field are estimated analytically and calculated numerically. For the perfectly entangled state the $z$ component $M$ of the magnetization of the whole system is equal to zero. The errors lead to a finite value of $M$. If the number of qubits in the system is large, $M$ can be detected experimentally. Using the fact that $M$ depends differently on the parameters of the system for each kind of error, varying these parameters would allow one to experimentally determine the most significant source of errors and to optimize correspondingly the quantum computer design in order to decrease the errors and $\mid M\mid$. Using our approach one can benchmark the quantum computer, decrease the errors, and prepare the quantum computer for implementation of more complex quantum algorithms.

We develop a theoretical treatment of polarization spectroscopy and use it to make predictions about the general form of polarization spectra in the alkali-metal atoms. Using our model, we generate theoretical spectra for the $D2$ transitions in ${}^{87}\mathrm{Rb}$, ${}^{85}\mathrm{Rb}$, and ${}^{133}\mathrm{Cs}$. Experiments demonstrate that the model accurately reproduces spectra of transitions from the upper hyperfine level of the ground state only. Among these, the closed transition $F\to F^{\prime }=F+1$ dominates, with a steep gradient through line center ideally suited for use as a reference in laser locking.

When cold atoms approach a periodically magnetized surface, they are scattered by the effective repulsive potential $U(x,y)={\mu }_B{m}_{F}gB(x,y)$. If the period $a$ of the magnetized surface is larger than the de Broglie wavelength $\lambda$ of the atoms, the atoms are diffracted. We have developed a method for calculating the location and intensity of the diffraction peaks using formal scattering theory. We solve the exact two-dimensional Schrödinger equation with the finite element method and calculate the scattering amplitude $f\left(\varphi \right)$ using the integral formula; a plot of $\mid f\left(\varphi \right){\mid }^2$ provides a visualization of the diffraction pattern. By varying the experimental parameters within a realistic range, we predict the optimal conditions for observing atom diffraction.

It is demonstrated that outer and inner electron shells, including that formed by collectivized electrons of the fullerene ${\mathrm{C}}_{60}$, affects dramatically the cross section of the subvalent ns subshells of the noble-gas endohedral atoms $A@{\mathrm{C}}_{60}$. The calculations are performed within the framework of a very simple, so-called “orange skin,” model that makes it possible, in spite of its simplicity, to take into account the modification of the ns subshell due to its interaction with inner and outer atomic shells, as well as with the collectivized electrons of the ${\mathrm{C}}_{60}$. As a concrete example, we consider the $\mathrm{Xe}5s$ electrons completely collectivized by the powerful action of the Xe close and remote multielectron neighboring shells.

We investigate the influence of the dynamic polarization of the carbon valence electrons on the angular distributions of protons channeled through short $(11,9)$ single-wall carbon nanotubes at speeds of 3 and $5\mathrm{a}.\mathrm{u}.$ (corresponding to the proton energies of 0.223 and $0.621\mathrm{MeV}$), with the nanotube length varied from 0.1 to $0.3\mathrm{\mu }\mathrm{m}$. The dynamic image force on protons is calculated by means of a two-dimensional hydrodynamic model for the nanotube’s dielectric response, whereas the repulsive interaction with the nanotube’s cylindrical wall is modeled by a continuum potential based on the Doyle-Turner interatomic potential. The angular distributions of channeled protons are generated by a computer simulation method using the numerical solution of the proton equations of motion in the transverse plane. Our analysis shows that the inclusion of the image interaction causes qualitative changes in the proton deflection function, giving rise to a number of rainbow maxima in the corresponding angular distribution. We propose that observations of those rainbow maxima could be used to deduce detailed information on the relevant interaction potentials, and consequently to probe the electron distribution inside carbon nanotubes.

On the basis of the analytical solution of the Dirac equation the resonant multiphoton excitation of highly charged hydrogenlike ions in a strong high-frequency laser field is investigated. It is shown that the dynamics of the relativistic system is equivalent to two independent four-level systems (in the electrical-dipole approximation). The time evolution of the system is found using the nonperturbative resonant approach. We predict that due to multiphoton excitation by an appropriate laser pulse one can achieve various coherent superposition states in atomic or ionic systems with a high nuclear charge.

We report on studies of simultaneous trapping of ${}^{85}\mathrm{Rb}$ atoms in a magneto-optical trap (MOT) and one-dimensional optical lattice. Using Raman pump-probe spectroscopy, we observe the coexistence of two atomic fractions: the first consists of free, unbound atoms trapped in a MOT and the second is localized in the micropotentials of the optical lattice. We show that recoil-induced resonances allow not only temperature determination of the atomic cloud but, together with vibrational resonances, can also be used for real-time, nondestructive studies of the lattice loading and of the dynamics of systems comprising unbound and bound atomic fractions.

We investigate the structure of resonance widths of a Bose-Hubbard dimer with intersite hopping amplitude $k$, which is coupled to a continuum at one of the sites with strength $\gamma$. Using an effective non-Hermitian Hamiltonian formalism, we show that by varying the on-site interaction term $\chi$ the resonances undergo consequent bifurcations. For $\Lambda =k∕\gamma ⩾0.5$, the bifurcation points follow a scaling law ${\tilde{\chi }}_m\equiv {\chi }_{m}N∕k=f_{\Lambda }(m-0.5∕\Lambda )$, where $N$ is the number of bosons. For the function $f_{\Lambda }$ two different $\Lambda$ dependences are found around the minimum and maximum bifurcation points.

In this work we develop a complete variational many-body theory for a system of $N$ trapped bosons interacting via a general two-body potential. The many-body solution of this system is expanded over orthogonal many-body basis functions (configurations). In this theory both the many-body basis functions and the respective expansion coefficients are treated as variational parameters. The optimal variational parameters are obtained self-consistently by solving a coupled system of noneigenvalue—generally integro-differential—equations to get the one-particle functions and by diagonalizing the secular matrix problem to find the expansion coefficients. We call this theory multiconfigurational Hartree theory for bosons or $\mathrm{MCHB}\left(M\right)$, where $M$ specifies explicitly the number of one-particle functions used to construct the configurations. General rules for evaluating the matrix elements of one- and two-particle operators are derived and applied to construct the secular Hamiltonian matrix. We discuss properties of the derived equations. We show that in the limiting cases of one configuration the theory boils down to the well-known Gross-Pitaevskii and the recently developed multi-orbital mean fields. The invariance of the complete solution with respect to unitary transformations of the one-particle functions is utilized to find the solution with the minimal number of contributing configurations. In the second part of our work we implement and apply the developed theory. It is demonstrated that for any practical computation where the configurational space is restricted, the description of trapped bosonic systems strongly depends on the choice of the many-body basis set used, i.e., self-consistency is of great relevance. As illustrative examples we consider bosonic systems trapped in one- and two-dimensional symmetric and asymmetric double well potentials. We demonstrate that self-consistency has great impact on the predicted physical properties of the ground and excited states and show that the lack of self-consistency may lead to physically wrong predictions. The convergence of the general $\mathrm{MCHB}\left(M\right)$ scheme with a growing number $M$ is validated in a specific case of two bosons trapped in a symmetric double well.

In most proposals for the generation of entanglement in large ensembles of atoms via projective measurements, the interaction with the vacuum is responsible for both the generation of the signal that is detected and the spin depolarization or decoherence. In consequence, one must usually work in a regime where the information acquisition via detection is sufficiently slow (weak measurement regime) such as not to strongly disturb the system. We propose here a four-wave mixing scheme where, owing to the pumping of the atomic system into a dark state, the polarization of the ensemble is not critically affected by spontaneous emission. In the language of spin squeezing, the removal of the limitations imposed by spontaneous emission allows one to work in a strong signal regime where the Heisenberg limit can be reached.

We study the efficiency of atom-molecule conversion in a sweep of the magnetic field across a Feshbach resonance in a nondegenerate gas by integrating numerically the time-dependent Schrödinger equation. In an approach that works at low conversion efficiencies, we show that in the limit of a slow sweep the atom-molecule conversion efficiency is proportional to the phase-space density.

We examine an analytical expression for the survival probability for the time evolution of quantum decay to discuss a regime where quantum decay is nonexponential at all times. We find that the interference between the exponential and nonexponential terms of the survival amplitude modifies the usual exponential decay regime in systems where the ratio of the resonance energy to the decay width is less than 0.3. We suggest that such a regime could be observed in semiconductor double-barrier resonant quantum structures with appropriate parameters.

We describe a class of programmable devices that can discriminate between two quantum states. We consider two cases. In the first, both states are unknown. One copy of each of the unknown states is provided as an input, or program, for the two program registers, and the data state, which is guaranteed to be prepared in one of the program states, is fed into the data register of the device. This device will then tell us, in an optimal way, which of the templates stored in the program registers the data state matches. In the second case, we know one of the states while the other is unknown. One copy of the unknown state is fed into the single program register, and the data state which is guaranteed to be prepared in either the program state or the known state, is fed into the data register. The device will then tell us, again optimally, whether the data state matches the template or is the known state. We determine two types of optimal devices. The first performs discrimination with minimum error, and the second performs optimum unambiguous discrimination. In all cases we first treat the simpler problem of only one copy of the data state and then generalize the treatment to $n$ copies. In comparison to other works we find that providing $n>1$ copies of the data state yields higher success probabilities than providing $n>1$ copies of the program states.

A Rydberg molecule is composed of an outer electron that collides on the residual ionic core. Typical states of Rydberg molecules display entanglement between the outer electron and the core. In this work, we quantify the average entanglement of molecular eigenstates and further investigate the time evolution of entanglement production from initially unentangled states. The results are contrasted with the underlying classical dynamics, obtained from the semiclassical limit of the core-electron collision. Our findings indicate that entanglement is not simply correlated with the degree of classical chaos, but rather depends on the specific phase-space features that give rise to inelastic scattering. Hence mixed phase-space or even regular classical dynamics can be associated with high entanglement generation.

Absolute $K$-shell ionization and $L\alpha$ and $L{\beta }_1$ x-ray production cross sections for Ga and As have been measured for incident electrons in the energy range from $1.5\text{to}39\mathrm{keV}$. The cross sections were deduced from $K\alpha$, $L\alpha$, and $L{\beta }_1$ x-ray intensities emitted from ultrathin GaAs samples deposited onto self-supporting carbon films. The x-ray intensities were measured on an electron microprobe equipped with several wavelength-dispersive spectrometers and were converted into absolute cross sections by using estimated values of the target thickness, spectrometer efficiency, and number of incident electrons. Experimental results are compared with cross sections calculated from the plane-wave and distorted-wave Born approximations, the relativistic binary-encounter-Bethe model, the results of two widely used simple analytical formulas, and, whenever possible, experimental data from the literature.

The double autoionization rate for the ${\mathrm{He}}^{-}\left(2s^{2}2p{}^{2}P\right)$ hollow atom state is calculated using a nonperturbative time-dependent close-coupling method. The nine-dimensional wave function for the three electron atom is expanded in coupled spherical harmonics. The time-dependent Schrödinger equation is then reduced to a set of close-coupled partial differential equations for the three-dimensional radial expansion functions. Relaxation in imaginary time subject to orthogonality constraints yields a $2s^{2}2p{}^{2}P$ hollow atom state with real energy, while propagation in real time yields total and double Auger rates. The total Auger rate is in reasonable agreement with previous saddle-point complex-rotation calculations. The double Auger rate is found to be 10% of the total Auger rate, in keeping with the relatively large double to total ratio found in recent experiments for ${\mathrm{He}}^{-}\left(2s2p^2{}^{4}P\right)$.

Fine-structure resolved $5p$ photoemission spectra of Cs in the ground state and after laser excitation into the $\left[\mathrm{Xe}\right]6p{}^{2}P_{1∕2}$ and $6p{}^{2}P_{3∕2}$ states have been studied. The $5p^{5}6p$ final states have been reached by the $5p^{6}6s\to 5p^{5}6p$ conjugate shakeup process from ground-state atoms as well as by direct photoemission from laser-excited atoms. The laser-excited spectra can be well described with calculations based on the $jK$-coupling model. Calculations based on a multiconfiguration Dirac-Fock approach have been performed to investigate the deviations created by intermediate coupling from the pure $jK$-coupling scheme.

The efficiency of evaporative cooling, which is used for the creation of a Bose-Einstein condensate, depends strongly on the number of particles at the start of the evaporation. A high efficiency can be reached by filling the magneto-optical trap with a large number of atoms and subsequently transferring these atoms to the magnetic trap as efficiently as possible. In our case (for sodium) this efficiency is limited to $1∕3$, because the magnetic substates of the $F=1$ state, which is used in the trapping process, are equally populated. This limit can be overcome by spin-polarizing the sample before the transfer. For sodium atoms, however, the improvement is very small when it is done in a small magnetic field due to the large number of optical transitions in combination with the high optical density. In this paper, we describe spin-polarizing sodium atoms in a high magnetic field. The transfer efficiency is increased by a factor of 2. The high magnetic field makes the process also more robust against variations in the magnetic field, the laser frequency, and the polarization of the laser beam.

We have observed the effects of magnetic field gradients and gravitational acceleration on grating echoes in a time-domain single state atom interferometer that uses laser cooled Rb atoms. These observations are compared to theoretical predictions based on a simplified model. The oscillatory dependence of the echo amplitude due to the magnetic field gradient is in agreement with the predicted quadratic scaling as a function of the time between excitation pulses. We also observe a linear dependence of this oscillation frequency as a function of the magnetic field gradient which is predicted by theory. In the presence of gravity, the calculations predict a quadratic dependence for the echo phase on the time between excitation pulses as well as a change in the shape of the echo envelope. We have observed both of these effects in the experiment, and we find that the change in shape is qualitatively consistent with our prediction. It is necessary to understand these effects in order to carry out high precision studies of the atomic fine-structure constant and gravitational acceleration using this interferometric technique. We also present an improved measurement of gravitational acceleration using this technique that is precise to $\sim 15\mathrm{ppm}$ by exploiting the quadratic phase dependence.

We show theoretically the possibility of excitation of a special class of two-frequency solitons, sustained by the nonlinearity provided by the nonradiative intervalence band coherence between heavy-hole and light-hole excitonic transitions in semiconductor quantum wells. The formation of such resonant solitons excited by femtosecond pulses in ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_y{\mathrm{P}}_{1-y}$ quantum wells is investigated numerically using a phenomenological model based on the local-field approximation, and a realistic configuration for their experimental observation is proposed. The pumping conditions for using complex resonant soliton dynamics as an efficient source of continuum generation are also discussed.