Calculated and experimental differential direct, charge-transfer, and total scattering cross sections are presented for collisions of ${\mathrm{H}}^{+}$ with ${\mathrm{O}}_2$. Experimental cross sections are obtained for projectile energies of 0.5, 1.5, and $5.0\mathrm{keV}$, and scattering angles of 0.15° to 5° while the theoretical results extend from $0.5\text{to}25\mathrm{keV}$ and encompass scattering angles from 0.01° to 180°. We find good agreement between the calculated and measured differential and total cross sections. Also, a diffraction slit effect, which is target orientation dependent, is found in the differential scattering cross section. A theoretical explanation of the effect is presented.

We derive a universal formula for the rate constant $\beta$ for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length $a$. We show that $\beta$ is determined by $a$ and by 2 three-body parameters that also determine the binding energies and widths of Efimov states. The rate constant $\beta$ scales like $\hslash a∕m$ near the resonance, but the coefficient is a periodic function of $\ln \left(a\right)$ that may have resonant enhancement at values of $a$ that differ by multiples of 22.7.

We study the quantum dynamics of a two-level system driven by a pulse that starts near-resonant for small amplitudes, yielding nonadiabatic evolution, and induces an adiabatic evolution for larger amplitudes. This problem is analyzed in terms of lifting of degeneracy for rising amplitudes. It is solved exactly for the case of linear and exponential rising. Approximate solutions are given in the case of power-law rising. This allows us to determine approximative formulas for the line shape of resonant excitation by various forms of pulses such as truncated trigonometric pulses. We also analyze and explain the various superpositions of states that can be obtained by the half Stark chirped rapid adiabatic passage process.

We investigate coherent accumulation processes in three-level atoms excited by a train of ultrashort pulses in the case where the atomic relaxation times are greater than the laser repetition period. In this situation the resonances of the laser field with the atomic system are determined by the laser frequency comb rather than by the spectrum of a single pulse. Using the density matrix formalism, we develop a perturbative theory that is valid for arbitrary pulse shapes. The excitation of a Doppler-broadened atomic vapor by hyperbolic-secant pulses and $0\pi$ pulses is analyzed. It is shown that pulse shape has a great influence on the accumulation process and can change the spectral periodicity of the pattern impressed on the Doppler profile of the medium due to the two-photon absorption process. The effect of interpulse phases is also investigated, and we show that the atomic populations can vary by more than one order of magnitude with small variations of the laser repetition rate, while being insensitive to variations of the laser offset. Finally, the theory is adapted for the temporal-coherent-control technique, and its results are compared with previously reported experimental data.

We investigate Bose-Einstein condensation of trapped spin-1 atoms with ferromagnetic or antiferromagnetic two-body contact interactions. We adopt the mean field theory and develop a Hartree-Fock-Popov type approximation in terms of a semiclassical two-fluid model. For antiferromagnetic interactions, our study reveals double condensations as atoms in the $\mid m_F=0⟩$ state never seem to condense under the constraints of both the conservation of total atom number $N$ and magnetization $M$. For ferromagnetic interactions, however, triple condensations can occur. Our results can be conveniently understood in terms of the interplay of three factors: (anti)ferromagnetic atom-atom interactions, $M$ conservation, and the miscibilities between and among different condensed components.

We numerically study the superfluid to Mott insulator transition for bosonic atoms in a one-dimensional lattice by exploiting a recently developed simulation method for strongly correlated systems. We demonstrate this method's accuracy and applicability to Bose-Hubbard model calculations by comparison with exact results for small systems. By utilizing the efficient scaling of this algorithm we then concentrate on systems of comparable size to those studied in experiments and in the presence of a magnetic trap. We investigate spatial correlations and fluctuations of the ground state as well as the nature and speed at which the superfluid component is built up when dynamically melting a Mott insulating state by ramping down the lattice potential. This is performed for slow ramping, where we find that the superfluid builds up on a time scale consistent with single-atom hopping and for rapid ramping where the buildup is much faster than can be explained by this simple mechanism. Our calculations are in remarkable agreement with the experimental results obtained by Greiner et al. [Nature (London) 415, 39 (2002)].

We theoretically investigate vortex-lattice phases of rotating spinor Bose-Einstein condensates (BEC’s) with a ferromagnetic spin interaction by numerically solving the Gross-Pitaevskii equation. The spinor BEC under slow rotation can sustain a rich variety of exotic vortices due to the multicomponent order parameters, such as Mermin-Ho and Anderson-Toulouse coreless vortices (the two-dimensional Skyrmion and meron) and nonaxisymmetric vortices with shifting vortex cores. Here, we present the spin texture of various vortex-lattice states at higher rotation rates and in the presence of an external magnetic field. In addition, the vortex phase diagram is constructed in the plane of the total magnetization $M$ and the external rotation frequency $\Omega$ by comparing the free energies of possible vortices. It is shown that the vortex phase diagrams in the $M\text{−}\Omega$ plane may be divided into two categories: (i) the coreless vortex lattice formed by the several types of Mermin-Ho vortices and (ii) the vortex lattice filling in the cores with the pure polar (antiferromagnetic) state. In particular, it is found that the type-(ii) state forms composite lattices of coreless and polar-core vortices. The difference between type (i) and type (ii) results from the existence of the singularity of the spin textures, which may be experimentally confirmed by the spin imaging within polarized light recently proposed by Carusotto and Mueller. We also discuss the stability of triangular and square lattice states for rapidly rotating condensates.

We show that the classical dynamics underlying the mean-field description of homogeneous mixtures of spinor $F=1$ Bose-Einstein condensates in an external magnetic field is integrable as a consequence of number conservation and axial symmetry in spin space. The population dynamics depends only on the quadratic term of the Zeeman energy and on the strength of the spin-dependent term of the atom-atom interaction. We determine the equilibrium populations as function of the ratio of these two quantities and the miscibility of the hyperfine components in the ground state spinors are thoroughly discussed. Outside the equilibrium, the populations are always a periodic function of time where the periodic motion can be a libration or a rotation. Our studies also indicate the absence of metastability.

A protocol for synchronizing distant clocks is proposed that does not rely on the arrival times of the signals which are exchanged, and an optical implementation based on coherent-state pulses is described. This protocol is not limited by any dispersion that may be present in the propagation medium through which the light signals are exchanged. Possible improvements deriving from the use of quantum-mechanical effects are also addressed.

We study the quantum Zeno effect in the case of indirect measurement, where the detector does not interact directly with the unstable system. Expanding on the model of Koshino and Shimizu [Phys. Rev. Lett. 92, 030401 (2004)] we consider a realistic Hamiltonian for the detector with a finite bandwidth. We also take explicitly into account the position, the dimensions, and the uncertainty in the measurement of the detector. Our results show that the quantum Zeno effect is not expected to occur, except for the unphysical case where the detector and the unstable system overlap.

We experimentally investigate the atom-optical $\delta$-kicked harmonic oscillator for the case of nonlinearity due to collisional interactions present in a Bose-Einstein condensate. A Bose condensate of rubidium atoms tightly confined in a static harmonic magnetic trap is exposed to a one-dimensional optical standing-wave potential that is pulsed on periodically. We focus on the quantum antiresonance case for which the classical periodic behavior is simple and well understood. We show that after a small number of kicks the dynamics are dominated by dephasing of matter wave interference due to the finite width of the condensate’s initial momentum distribution. In addition, we demonstrate that the nonlinear mean-field interaction in a typical harmonically confined Bose condensate is not sufficient to give rise to chaotic behavior.

The optimized version of the Deutsch-Jozsa algorithm proposed by Collins et al. was implemented using the three ${}^{19}\mathrm{F}$ nuclear spins of 2,3,4-trifluoroaniline as qubits. To emulate the behavior of pure quantum-mechanical states pseudopure states of the ensemble were prepared prior to execution of the algorithm. Full tomography of the density matrix was employed to obtain detailed information about initial, intermediate, and final states. Information, thus obtained, was applied to optimize the pulse sequences used. It is shown that substantial improvement of the fidelity of the preparation may be achieved by compensating the effects caused by the different relaxation behavior of the different substates of the density matrix. All manipulations of the quantum states were performed under the conditions of unresolved spin-spin interactions.

We recast the Sturmian expansion of the one-particle Coulomb Green function as an integral which, through an appropriate choice of contour, is applicable anywhere on the Riemann energy surface (excluding the neighborhood of the negative real axis on the physical energy sheet, a region to which the series representation is ideally suited). As a numerical test we have used this integral representation, in conjunction with a two-particle convolution of one-particle Coulomb Green functions, to calculate the cross sections for both partial and complete breakup of the negative hydrogen ion by one-photon absorption.

We consider the splitting mechanism of a multiply charged vortex into singly charged vortices in a Bose-Einstein condensate confined in a harmonic potential at zero temperature. The Bogoliubov equations support unstable modes with complex eigenfrequencies (CE modes), which cause the splitting instability without the influence of thermal atoms. The investigation of the excitation spectra shows that the negative-energy (NE) mode plays an important role in the appearance of the CE modes. The configuration of vortices in splitting is determined by the angular momentum of the associated NE mode. This structure has also been confirmed by the numerical simulation of the time-dependent Gross-Pitaevskii equation.

We predict a large cooperative effect involving two-atom two-photon vacuum Rabi oscillations in a high-quality cavity. The two-photon emission occurs as a result of simultaneous deexcitation of both atoms with two-photon resonance condition ${\omega }_1+{\omega }_2\approx {\omega }_a+{\omega }_b$, where ${\omega }_1$,${\omega }_2$ are the atomic transition frequencies and ${\omega }_a$,${\omega }_b$ are the frequencies of the emitted photons. The actual resonance condition depends on the vacuum Rabi couplings. The effect can be realized either with identical atoms in a bimodal cavity or with nonidentical atoms in a single-mode cavity.

We show that a thermal light source which is random in the transverse direction can produce a sub-wavelength double slit interference in a joint intensity measurement. This is the classical version of quantum lithography, and it can be explained with the correlation of rays instead of the entanglement of photons.

We investigate coherent population transfer in double-$\Lambda$ and diamond-type four-level systems driven by two pairs of time-delayed laser pulses. We show that the relative phase between the pulses induces interference so that the adiabatic passage dynamics is only possible for a particular phase. Both pulse area and phase are control knobs that can be used to prepare specific coherent superpositions using counterintuitive and intuitive pulse sequences. Since the diamond-type four-level system maps the Hamiltonian of two interacting two-level systems, the schemes can be used to manipulate entanglement. In particular we propose robust schemes to prepare specific entangled states by phase control with time-delayed pulse sequences.

A method of entangled states preparation of two-qubit systems is proposed. The method combines the techniques of coherent control by manipulation of the relative phase between the pulses and adiabatic control by using time-delayed pulse sequences. Simple analytic expressions are given for the wave function of the system as a function of phase and pulse area which show that complete control of entanglement is possible with resonant pulses. The connection between the phase of the entanglement and the control parameters is clarified and the effects of different pulse sequences are analyzed to design the optimal schemes. An off-resonant scheme is proposed that simplifies the preparation of certain entangled states.

We propose quantum key distribution protocols based on coherent single-photon optical pulses with duration $T$ and with minimum time-frequency uncertainty. The pulses are sent with possible delays (e.g., 0, $T∕2$) that are used to code the information (e.g., bit 0, bit 1) and that are shorter than the pulse width. Therefore, the time detection of the photons may result in a ambiguity of the delay evaluation for a potential eavesdropper. The duration of the received pulses is controlled thanks to a contrast measurement using an interferometer. A quantum formalism is given, allowing us to model the transmission of the key and the consequences of a possible eavesdropping. Two protocols are proposed and discussed. The first one involves two states and is limited to channels with losses lower than 50%. The second one involves four states, which prevents the eavesdropper from exploiting the losses of the line. The security of each protocol is evaluated as a function of channel losses, quantum bit error rate, and contrast loss in the case of intercept-resend attacks. It is applied to situations where photocounters dark counts are the main limitation of the system. The resulting maximum propagation distance allowing secure communication is evaluated.

The results of a theoretical investigation of the coherent interaction between many Rydberg atoms are reported. The atoms are assumed to move very little during the time range we investigate. We describe the basic interaction between atoms and show that (contrary to previous theoretical studies) the interaction between the atoms can be coherent. The band structure for a perfect lattice of atoms and the density of states for an amorphous distribution of atoms are presented. We also give results for when the atoms are roughly positioned in a lattice. Finally, we performed detailed calculations to understand when the Rydberg interactions are too strong for an essential states type of approximation. The relevance of our results to previous measurements in a Rydberg gas and to possible future experiments is discussed.