We theoretically study the behavior of ${\mathrm{He}}^{+}$ exposed simultaneously to an ultrashort intense Ti:sapphire laser and its 27th or 13th harmonic pulses, by solving the time-dependent Schrödinger equation using the alternating direction implicit method. This system is chosen as an interesting application of state-of-the-art high-order harmonic sources. Our results show that the simple hydrogenlike system exhibits surprising responses. The addition of the 27th harmonic enhances high-order harmonic photoemission from ${\mathrm{He}}^{+}$ even by 17 orders of magnitude compared with the case of the fundamental pulse alone, i.e., usual high-order harmonic generation, and the H13 addition also increases photoemission efficiency by more than ten orders of magnitude. Moreover, while an individual $10\mathrm{fs}$ laser (wavelength ${\lambda }_F=800\mathrm{nm}$) or its 27th harmonic pulse with a peak intensity of $3\times {10}^{14}$ and ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$, respectively, ionizes no more than $5\times {10}^{-6}$ of ${\mathrm{He}}^{+}$, their combined pulse leads to a much higher ${\mathrm{He}}^{2+}$ yield of 17%. The photoemission efficiency only weakly depends on the fundamental wavelength, and the main plateau efficiency scales as the intensity of the 27th harmonic pulse. The ${\mathrm{He}}^{2+}$ yield is linear in the intensity of the 27th harmonic and quadratic in that of the 13th harmonic pulse. Its dependence on fundamental intensity is much more complex, even containing a range where the yield decreases with increasing laser intensity, due to the dynamic Stark effect. Detailed analyses reveal that the mechanism of the enhancement of harmonic photoemission as well as ionization is a combination of harmonic generation from a coherent superposition of states and two-color frequency mixing enhanced by the presence of a near-resonant intermediate level, and that their relative importance depends on fundamental wavelength.

The effect of ambient magnetic fields on the dynamics of a single trapped ion is studied analytically. We consider two electronic states with energy separation stochastically varied by magnetic-field perturbations and coupled to the vibrational modes by a laser. For Gaussian white noise, a master equation is derived and solved. The results obtained reveal how the effective Rabi frequencies and the decay rates depend on the noise strength and on the number state index. The detection of features specific to magnetic-field noise in the evolution of states that can be prepared under standard experimental conditions is discussed. A comparison with the effects of laser intensity and phase fluctuations is presented. Implications for the realization of logic gates are analyzed.

We theoretically examine Raman photoassociation of a Bose-Einstein condensate, revisiting stimulated Raman adiabatic passage (STIRAP). Due to collisional mean-field shifts, efficient molecular conversion requires strong coupling and low density, either of which can bring about rogue photodissociation to noncondensate modes. We demonstrate explicitly that rogue transitions are negligible for low excited-state fractions and photodissociation that is slower than the STIRAP time scale. Moreover, we derive a reduced-parameter model of collisions, and thereby find that a gain in the molecular conversion efficiency can be obtained by adjusting the atom-atom scattering length with off-resonant magnetoassociation. This gain saturates when the atom-atom scattering length is tuned to a specific fraction of either the molecule-molecule or atom-molecule scattering length. We conclude that a fully optimized STIRAP scheme may offer the best chance for achieving coherent conversion from an atomic to a molecular condensate with photoassociation.

We derive a general expression for the spin-flip rate of an atom trapped near an arbitrary dielectric body and we apply this theory to the case of a two-layer cylindrical metal wire. The spin-flip lifetimes we calculate are compared with those expected for an atom near a metallic slab and with those measured by Jones et al. above a two-layer wire [M.P.A. Jones, C.J. Vale, D. Sahagun, B.V. Hall, and E.A. Hinds, Phys. Rev. Lett. 91, 080401 (2003)]. We investigate how the lifetime depends on the skin depth of the material and on the scaling of the dimensions. This leads us to some conclusions about the design of integrated circuits for manipulating ultracold atoms (atom chips).

We present a study of orbital angular momentum transfer from pump to down-converted beams in a type-II optical parametric oscillator. Cavity and anisotropy effects are investigated and demonstrated to play a central role in the transverse mode dynamics. While the idler beam can oscillate in a Laguerre-Gauss mode, the crystal birefringence induces an astigmatic effect in the signal beam that prevents the resonance of such a mode.

We report on two-dimensional near-field imaging experiments of the $11.9‐\mathrm{nm}$ $\mathrm{Sn}$ x-ray laser that were performed with a set of $\mathrm{Mo}∕\mathrm{Y}$ multilayer mirrors having reflectivities of up to $\sim 45\%$ at normal and at $45°$ incidence. Second-moment analysis of the x-ray laser emission was used to determine values of the x-ray beam propagation factor $M^2$ for a range of irradiation parameters. The results reveal a reduction of $M^2$ with increasing prepulse amplitude. The spatial size of the output is a factor of $\sim 2$ smaller than previously measured for the $14.7‐\mathrm{nm}$ $\mathrm{Pd}$ x-ray laser, while the distance of the x-ray emission with respect to the target surface remains roughly the same.

We propose a method for producing on-demand single-photon states based on collision-induced exchanges of photons and unbalanced linear absorption between two single-mode light fields. These two effects result in an effective nonlinear absorption of photons in one of the modes, which can lead to single-photon states. A quantum nonlinear attenuator based on such a mechanism can absorb photons in a normal input light pulse and terminate the absorption at a single-photon state. Because the output light pulses containing single photons preserve the properties of the input pulses, we expect this method to be a means for building a highly controllable single-photon source.

We show that interesting multigate circuits can be constructed using a postselected controlled-sign gate that works with a probability ${\left(1∕3\right)}^n$, where $n-1$ is the number of controlled-sign gates in the circuit, rather than ${\left(1∕9\right)}^{n-1}$, as would be expected from a sequence of such gates. We suggest some quantum information tasks which could be demonstrated using these circuits, such as parity checking and cluster-state computation.

We analyze, within the generalized multichannel quantum defect theory framework, atomic binary collision cross sections over the $1\mu \mathrm{K}$ to $10\mathrm{mK}$ energy range just above the entrance channel threshold, a domain where the Wigner threshold law should apply. By adjusting the strength of a constant external magnetic field a Feshbach resonance is tuned at will over this energy range. In the threshold regime, the quasibound state interacts with an opening continuum whose wave function presents a strong energy dependence which reflects the breakdown of the WKB approximation. The effective discrete-continuum interactions become very sensitive to the energy. The consequences of these variations have been investigated by including threshold effects in the analysis of the Fano configuration-interaction theory [Phys. Rev. 124, 1866 (1961)] in terms of quantum defect theory quantities proposed by [Lecomte J. Phys. B 20, 3645 (1987)]. This analysis shows that the energy variations are in general so important that it becomes meaningless to associate a width with a Feshbach resonance. However, it is still possible to define the resonance energy, as long as the energy variation of the shift of the resonance, induced by the effective discrete-continuum interaction, remains linear over an energy range corresponding to the magnitude of the shift.

We study the quasi-one-dimensional (Q1D) spin-polarized Bose-Fermi mixture of atomic gases at zero temperature. Bosonic excitation spectra are calculated in the random phase approximation on the ground state with uniform Bose-Einstein condensates (BEC’s) and the Peierls instabilities are shown to appear in bosonic collective excitation modes with wave number $2k_F$ by the coupling between the Bogoliubov-phonon mode of bosonic atoms and the fermion particle-hole excitations. The ground-state properties are calculated in the variational method, and, corresponding to the Peierls instability, the state with a periodic BEC and fermionic density waves with the period $\pi ∕k_F$ are shown to have a lower energy than the uniform one. We also briefly discuss the Q1D system confined in a harmonic oscillator potential and derive the Peierls instability condition for it.

A theoretical analysis of expanding hybrid atom-molecule Bose-Einstein condensates is presented with application to the recent experiments of the Rempe group on ${}^{87}\mathrm{Rb}$, in which the formation of ultracold molecules by Feshbach resonance was demonstrated. A mean-field approach is used to describe the molecular association process. The subsequent dissociation of the molecules is treated using a non-mean-field parametric approximation. The latter method is also used to derive optimal conditions for the formation of a molecular condensate.

The electron spectra originating from ionization of ${\mathrm{D}}_2$ by impact of $2.4\mathrm{keV}$ electrons have been measured at various emission angles. After subtraction of the direct ionization background, three peaks are clearly visible in the electron energy range $1–20\mathrm{eV}$. The existence of these peaks is confirmed by theoretical calculations. Two of these peaks are due to autoionization of doubly excited states lying above the first and second ionization thresholds. The third peak is attributed to the strong interference between direct ionization and autoionization while the molecule is already dissociating.

The time evolution of the state populations in the $v\equiv n-\ell -1=2$ and 3 metastable cascades of antiprotonic helium (${\overline{p}}^4{\mathrm{He}}^{+}$) atoms were studied using laser spectroscopy. The antiprotonic states $(n,\ell )=(39,35)$, (40,36), and (41,37) in the $v=3$ cascade were estimated to initially contain, respectively, $(0.28\pm 0.04)\%$, $(0.06\pm 0.02)\%$, and $(0.02\pm 0.01)\%$ of the antiprotons stopped in the helium target, while the corresponding values for states $(37,34)$, $(38,35)$, and $(39,36)$ in the $v=2$ cascade were $(0.21\pm 0.04)\%$, $(0.49\pm 0.07)\%$, and $(0.19\pm 0.07)\%$. The shortening of the state lifetimes due to collisions between $\overline{p}{\mathrm{He}}^{+}$ and helium atoms was studied. As the atomic density of the target was increased from $\rho =2\times {10}^{20}$ to $2\times {10}^{21}{\mathrm{cm}}^{-3}$, the lifetime of state $(37,34)$ decreased by an order of magnitude, whereas the higher states $(38,35)$ and $(39,35)$ were relatively unaffected. Between densities $\rho =6\times {10}^{20}$ and $2\times {10}^{22}{\mathrm{cm}}^{-3}$, a short-lived component with a time constant $\tau \sim 0.2\mu \mathrm{s}$ appeared at early times in the delayed annihilation time spectrum of $\overline{p}{\mathrm{He}}^{+}$, while the total fraction of long-lived antiprotons decreased from 3.0 to $2.5\%$. These effects were caused by the lifetime-shortening of specific $\overline{p}{\mathrm{He}}^{+}$ states such as $(37,34)$.

The mean excitation energy (the Bethe logarithm) is calculated for the lowest rotational (up to $L=4$) and vibrational (up to $v=4$) states of the hydrogen molecular ion ${\mathrm{HD}}^{+}$. The calculations are based on a method of the direct integration over photon momenta. The estimated accuracy of obtained values is about six significant digits.

We report Monte Carlo wave function simulation results on cold collisions between magnesium atoms in a strong red-detuned laser field. This is the normal situation, e.g., in magneto-optical traps (MOT). The Doppler limit heating rate due to radiative collisions is calculated for ${}^{24}\mathrm{Mg}$ atoms in an MOT based on the ${}^{1}S_0\text{−}{}^{1}P_1$ atomic laser cooling transition. We find that radiative heating does not seem to affect the Doppler limit in this case. We also describe a channeling mechanism due to the missing $Q$ branch in the excitation scheme, which could lead to a suppression of inelastic collisions, and find that this mechanism is not present in our simulation results due to the multistate character of the excitation process.

The line shapes of $1s\to {\pi }^{*}$-excited molecular Van der Waals clusters are compared to those of the corresponding isolated molecules. Small, but distinct spectral changes are observed, such as spectral shifts, line broadening, and changes in intensity. These are assigned in terms of variations in motion of the core-excited molecule within the molecular clusters using a simple model. Contributions from intra- and inter-molecular vibrations in core-excited clusters, which contribute to the experimentally observed spectral changes, are discussed.

We theoretically examine the quantum-state transfer process from light to a continuous atom laser by extending the original Fleischhauer-Gong scheme [M. Fleischhauer and S. Gong, 88, 070404 (2002)] to a double-$\Lambda$ atomic system. We find that the intensity of the output matter waves is controlled by the relative phase of two coherent probe lights, which may provide an interesting method for the measurement of the initial relative phase of two independent light sources.

A new superfluid phase in Fermi matter, termed as “interior gap” (IG) or “breached pair”, has been recently predicted by Liu and Wilczek [Phys. Rev. Lett. 90, 047002 (2003)]. This results from pairing between fermions of two species having essentially different Fermi surfaces. Using a nonperturbative variational approach, we analyze the features, such as energy gap, momentum distributions, and elementary excitations, associated with the predicted phase. We discuss possible realization of this phase in two-component Fermi gases in an optical trap.

We study the occupation numbers and number fluctuations of ultracold atoms in deep optical lattices for finite-temperatures within the Bose-Hubbard model. Simple analytical expressions for the mean occupation number and number fluctuations are obtained in the weak-hopping regime using an interpolation between results from different perturbation approaches in the Mott-insulator and superfluid phases. With this approach the magnitude of number fluctuations under a wide range of experimental conditions can be estimated and the properties of the finite-temperature phase diagram can be studied. These analytical results are compared to exact one-dimensional numerical calculations using a finite temperature variant of the density-matrix renormalization group (DMRG) method and found to have a high degree of accuracy. We find very good agreement, also in the crossover “thermal” region. We also analyze the influence of finite temperature on the behavior of the system in the vicinity of the zero-temperature phase transition, in one, two, and three dimensions.

We present an operator method to obtain complete sets of astigmatic Gaussian solutions of the paraxial wave equation. In case of general astigmatism, the astigmatic intensity and phase distribution of the fundamental mode differ in orientation. As a consequence, the fundamental mode has a nonzero orbital angular momentum, which is not due to phase singularities. Analogous to the operator method for the quantum harmonic oscillator, the corresponding astigmatic higher-order modes are obtained by repeated application of raising operators on the fundamental mode. The nature of the higher-order modes is characterized by a point on a sphere, in analogy with the representation of polarization on the Poincaré sphere. The north and south poles represent astigmatic Laguerre-Gaussian modes, similar to circular polarization on the Poincaré sphere, while astigmatic Hermite-Gaussian modes are associated with points on the equator, analogous to linear polarization. We discuss the propagation properties of the modes and their orbital angular momentum, which depends on the degree of astigmatism and on the location of the point on the sphere.