We develop an $R$-matrix approach to treating collision processes which explicitly takes into account, by means of a simple energy-dependent analytic function, the out-of-phase oscillations of the incident and scattered standing waves in the interior region. Thereby we avoid the use of the Bloch operator. In place of the Bloch operator the incident wave provides the source term in an inhomogeneous equation for the scattered wave. We take those subchannels not treated exactly into account via the optical potential, which is generally non-Hermitian due to dissipation at the boundary. The optical potential is constructed on a real analytic basis using a resolvent that satisfies outgoing-wave boundary conditions. The use of an analytic basis together with the direct determination of the $K$ matrix, rather than the $R$ matrix, at the boundary (this is done by matching the interior wave function to the nearly exact analytic solution beyond the boundary) makes the method particularly well suited to the treatment of ultracold collisions. We have tested our method by applying it to one-photon single-ionization of ($\mathrm{He}1s^2$) accompanied by excitation to ${\mathrm{He}}^{+}(2s)$ or ${\mathrm{He}}^{+}(2p)$ for photon energies above the complete breakup threshold, where the optical potential is non-Hermitian. Excellent agreement with experiment is obtained for the cross sections for photoionization to both ${\mathrm{He}}^{+}\hspace{0.5em}(n=1)$ and to ${\mathrm{He}}^{+}\hspace{0.5em}(n=2)$. The $2s$-to-$2p$ branching ratio is strongly influenced by both the optical potential and, at photon energies less than a few tens of eV above the breakup threshold, the nonadiabatic dipole mixing of the $2s$ and $2p$ states.

Total, electronic, and nuclear energy loss as well as stopping cross sections are calculated for He${}^{2+}$ ions incident on atomic hydrogen, deuterium, and tritium at low to intermediate energies by means of an ab initio, nonadiabatic approach for solving the Schrödinger equation incorporating coupled electron and nuclear dynamics. Comparison of this ab initio treatment with classical nuclear stopping cross-section formulations obtained from Coulomb and screened potential models, and an ab initio theory, allows us to deduce scaling laws that incorporate the different target masses (target isotopic effect). We provide a discussion on the range of validity of the use of classical trajectories. We verify that the nuclear energy loss is a universal function of the center-of-mass (c.m.) scattering angle. The scattering angle in the c.m. system shows a dependence on the projectile charge due to a strong isotopic effect on the charge-transfer cross section. In the case of a Coulombic interaction, that dependence disappears, and leads to a formulation based only on the c.m. collision energy for the nuclear stopping cross section. Due to the small electron capture cross section for He${}^{2+}$ on H, D, and T in the low-energy region, it is shown that the effective charge model that assumes neutralization of the projectile does not apply to the energy loss of He${}^{2+}$ ions in the calculation of stopping cross sections. Thus, for this system, there is no influence of the charge exchange isotope effect of the target in the nuclear stopping cross section of the projectile. In the electronic energy loss, such an isotopic effect is present through Stueckelberg oscillations, but its contribution is small. Furthermore, the electronic stopping cross section shows a threshold effect that results from the minimum momentum transfer necessary to produce an electronic excitation in the target. Finally, the nuclear stopping cross section has a universal behavior as a function of the c.m. collision energy, and care must be taken when comparing ionic systems stopping cross-section results to those of neutral systems as obtained by effective charge models.

We report on a study of one-photon single ionization of He($1s^2$) accompanied by excitation to He${}^{+}(2s)$ or He${}^{+}(2p)$ for photon energies at, and up to a few eV above, the excitation threshold. We find, both numerically and analytically, that as the photon energy approaches threshold from above the photoionization cross section turns sharply at about 200 meV and has a cusp at threshold. The cusp is associated with the adiabatic transfer of population between the $2s$ and $2p$ bound states of the ion. The photoelectron’s electric field induces an energy splitting between the otherwise degenerate $2s$ and $2p$ states, and consequently the $2s$ and $2p$ populations oscillate with a period defined by this energy splitting. The number of oscillations is almost independent of the photoelectron’s asymptotic speed $v$ since over most of its outward journey the photoelectron moves with a speed much larger than $v$. However, on the last leg of its journey, after it has slowed down sufficiently in the Coulomb field of the ion, the photoelectron does move with an almost constant speed $v$. On this last leg the energy splitting is so small that there is insufficient time for $2s$ and $2p$ populations to undergo a full oscillation; rather, the (equal and opposite) changes in the $2s$ and $2p$ populations are proportional to $v$ (i.e., to the square root of the excess photoelectron energy, which gives rise to a cusp).

The collectivity of the electronic motion in finite systems is studied by using both the linear response density functional theory (LRDFT) and the collectivity index defined by the transition density matrix. We demonstrate a collectivity analysis on the size-dependent peaks of electronic excitations of small sodium clusters (rings and linear chains). We find the excitation-mode dependence of the collectivity and large collectivities for the higher-energy plasmonic excitations. The collectivity analysis also clarifies the existence of the nondipolar collective motion at the energies very close to the higher-energy plasmonic excitations. The importance of the nondipolar motion is pointed out in light of nano-optics.

We study the effect of coupling between molecular vibrational modes attendant the excitation of Raman transitions using ultrafast chirped laser pulses. We model Raman-active vibrational modes by two-level systems (TLSs) with nondegenerate ground states and a predetermined initial relative phase. Chirp of the pump and Stokes pulses is the same in magnitude and opposite in sign for the whole pulse duration. To reveal the nonadiabatic effects induced by the coupling between the vibrational modes, we compare the model of two uncoupled TLSs with the one of two TLSs coupled by the external fields. The first model shows population inversion. Within the second model, the coupling induces nonadiabatic effects leading to a mixed population distribution. By introducing the time delay between the Stokes and pump pulses, nearly complete population transfer is realized in both coupled TLSs.

We analyze two-center interference effects in the yields of ionization of a dissociating hydrogen molecular ion by an ultrashort vuv laser pulse. To this end, we performed numerical simulations of the time-dependent Schrödinger equation for a ${\mathrm{H}}_2{}^{+}$ model ion interacting with two time-delayed laser pulses. The scenario considered corresponds to a pump-probe scheme, in which the first (pump) pulse excites the molecular ion to the first excited dissociative state and the second (probe) pulse ionizes the electron as the ion dissociates. The results of our numerical simulations for the ionization yield as a function of the time delay between the two pulses exhibit characteristic oscillations due to interferences between the partial electron waves emerging from the two protons in the dissociating hydrogen molecular ion. We show that the photon energy of the pump pulse should be in resonance with the ${\sigma }_g-{\sigma }_u$ transition and the pump pulse duration should not exceed 5 fs in order to generate a well-confined nuclear wave packet. The spreading of the nuclear wave packet during the dissociation is found to cause a decrease of the amplitudes of the oscillations as the time delay increases. We develop an analytical model to fit the oscillations and show how dynamic information about the nuclear wave packet, namely, velocity, mean internuclear distance, and spreading, can be retrieved from the oscillations. The predictions of the analytical model are tested well against the results of our numerical simulations.

We use the dynamical invariants associated with the Hamiltonian of an atom in a one dimensional moving trap to inverse engineer the trap motion and perform fast atomic transport without final vibrational heating. The atom is driven nonadiabatically through a shortcut to the result of adiabatic, slow trap motion. For harmonic potentials this only requires designing appropriate trap trajectories, whereas perfect transport in anharmonic traps may be achieved by applying an extra field to compensate the forces in the rest frame of the trap. The results can be extended to atom stopping or launching. The limitations due to geometrical constraints, energies, and accelerations involved are analyzed along with the relation to previous approaches based on classical trajectories or “fast-forward” and “bang-bang” methods, which can be integrated in the invariant-based framework.

Precision measurement of atomic and nuclear polarization is an essential step for beta-asymmetry measurement of radioactive atoms. In this paper, we report the polarization measurement of Rb atoms in an yttrium-aluminum-garnet (YAG) far-off-resonance optical dipole trap. We have prepared a cold cloud of polarized Rb atoms in the YAG dipole trap by optical pumping and achieved an initial nuclear polarization of up to 97.2(5)$\%$. The initial atom distribution in different Zeeman levels is measured by using a combination of microwave excitation, laser pushing, and atomic retrap techniques. The nuclear-spin polarization is further purified to 99.2(2)$\%$ in 10 s and maintained above 99$\%$ because the two-body collision loss rate between atoms in mixed spin states is greater than the one-body trap loss rate. Systematic effects on the nuclear polarization, including the off-resonance Raman scattering, magnetic field gradient, and background gas collisions, are discussed.

We studied the nuclear dynamics in diatomic molecules (N${}_2$, ${\mathrm{O}}_2$, and CO) following their interaction with intense near-IR few-cycle laser pulses. Using Coulomb-explosion imaging in combination with the pump-probe approach, we mapped dissociation pathways of those molecules and their molecular ions. We identified all symmetric and asymmetric breakup channels for molecular ions up to ${\mathrm{N}}_2^{5+}$, ${\mathrm{O}}_2^{4+}$, and CO${}^{4+}$. For each of those channels we measured the kinetic energy release (KER) spectra as a function of delay between the pump and probe pulses. For both ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ the asymmetric (3,1) channel is only observed for short (<20 fs) delays and completely disappears after that. We interpret this observation as a signature of electron localization taking place in dissociating molecular tri-cations when their internuclear separation reaches about 2.5 times the equilibrium bond length. This is a direct confirmation that electron localization plays an essential role in the universal mechanism of enhanced ionization in homonuclear diatomic molecules. Using classical and quantum mechanical simulations of the time-dependent KER spectra, we identify the pathways and intermediate states involved in the laser-induced dissociation of those molecules.

The quantum dynamics of two distant H atoms excited by ultrashort and spatially shaped laser pulses is studied by the numerical solution of the non-Born-Oppenheimer time-dependent Schrödinger equation within a three-dimensional (3D) model, including the internuclear distance $R$ and the two $z$ coordinates of the electrons $z_1$ and $z_2$. The two one-dimensional (1D) H atoms, A and B, are assumed to be initially in their ground states with a large (but otherwise arbitrary) internuclear separation of $R=100$ a.u. (5.29 nm). Two types of a spatial envelope of a laser field linearly polarized along the $z$ axis are considered: (i) a broad Gaussian envelope, such that atom A is excited by the laser field predominantly, and (ii) a narrow envelope, such that practically only atom A is excited by the laser field. With the laser carrier frequency $\omega =1.0$ a.u. and the pulse duration $t_p=5$ fs, in both cases an efficient energy transfer from atom A to atom B has been found. The ionization of atom B achieved mostly after the end of the laser pulse is close to or even higher than that of atom A. It is shown that with a narrow spatial envelope of the laser field, the underlying mechanisms of the energy transfer from A to B and the ionization of B are the Coulomb attraction of the laser driven electron by the proton of atom B and a short-range Coulomb repulsion of the two electrons when their wave functions significantly overlap in the domain of atom B. In the case of a broad Gaussian spatial envelope of the laser field, the opposite process also occurs, but with smaller probability: the energy is transferred from the weakly excited atom B to atom A, and the ionization of atom A is also induced by the electron-electron repulsion in the domain of atom A due to a strong overlap of the electronic wave functions.

We present a theoretical study of transient absorption and reshaping of extreme ultraviolet (XUV) pulses by helium atoms dressed with a moderately strong infrared (IR) laser field. We formulate the atomic response using both the frequency-dependent absorption cross section and a time-frequency approach based on the time-dependent dipole induced by the light fields. The latter approach can be used in cases when an ultrafast dressing pulse induces transient effects, and/or when the atom exchanges energy with multiple frequency components of the XUV field. We first characterize the dressed atom response by calculating the frequency-dependent absorption cross section for XUV energies between 20 and 24 eV for several dressing wavelengths between 400 and 2000 nm and intensities up to 10${}^{12}$ W/cm${}^2$. We find that for dressing wavelengths near 1600 nm, there is an Autler-Townes splitting of the $1s\to 2p$ transition that can potentially lead to transparency for absorption of XUV light tuned to this transition. We study the effect of this XUV transparency in a macroscopic helium gas by incorporating the time-frequency approach into a solution of the coupled Maxwell-Schrödinger equations. We find rich temporal reshaping dynamics when a 61-fs XUV pulse resonant with the $1s\to 2p$ transition propagates through a helium gas dressed by an 11-fs, 1600-nm laser pulse.

Two-electron correlated spectra of nonsequential double ionization below laser-intensity threshold are known to exhibit back-to-back scattering of the electrons, i.e., the anticorrelation of the electrons. Currently, the widely accepted interpretation of the anticorrelation is recollision-induced excitation of the ion plus subsequent field ionization of the second electron. We argue that another mechanism, namely, simultaneous electron emission, when the time of return of the rescattered electron is equal to the time of liberation of the bounded electron (i.e., the ion has no time for excitation), can also explain the anticorrelation of the electrons in the deep, below laser-intensity threshold regime. Our conclusion is based on the results of the numerical solution of the time-dependent Schrödinger equation for a model system of two one-dimensional electrons, as well as on an adiabatic analytic model that allows for a closed-form solution.

We introduce a class of solitonlike entities in spinor three-component Bose-Einstein condensates. These entities generalize well-known solitons. For special values of coupling constants, the system considered is completely integrable and supports $N$ soliton solutions. The one-soliton solutions can be generalized to systems with different values of coupling constants. However, they no longer interact elastically. When two so-generalized solitons collide, a spin component oscillation is observed in both emerging entities. We propose to call these newfound entities oscillatons. They propagate without dispersion and retain their character after collisions. We derive an exact mathematical model for oscillatons and show that the well-known one-soliton solutions are a particular case.

We present the theoretical mean-field zero-temperature phase diagram of a Bose-Einstein condensate (BEC) with dipolar interactions loaded into an optical lattice with a staggered flux. Apart from uniform superfluid, checkerboard supersolid, and striped supersolid phases, we identify several supersolid phases with staggered vortices, which can be seen as combinations of supersolid phases found in earlier work on dipolar BECs and a staggered-vortex phase found for bosons in optical lattices with staggered flux. By allowing for different phases and densities on each of the four sites of the elementary plaquette, more complex phase patterns are found.

We theoretically analyze interference patterns of parametrically driven one-dimensional ultracold atomic gases. By modulating the interaction strength periodically in time, we propose to excite collective modes in a pair of independent one-dimensional gases at energies corresponding to the drive frequency. The excited collective modes lead to spatial oscillations in the correlations of the interference pattern, which can be analyzed to obtain the sound velocity of the collective modes. We discuss both bosonic and fermionic systems and how such experiments could be used to probe spin-charge separation.

We study the winding-number dependence of the stationary states of a Bose-Einstein condensate in a ring-shaped lattice. The system is obtained by confining atoms in a toroidal trap with equally spaced radial barriers. We calculate the energy and angular momentum as functions of the winding number and the barrier height for two quite distinct particle numbers. In both cases we observe two clearly differentiated regimes. For low barriers, metastable vortex states are obtained up to a maximum winding number that depends on the particle number and barrier height. In this regime, the angular momentum and energy show, respectively, almost linear and quadratic dependences on the winding number. For large barrier heights, on the other hand, stationary states are obtained up to a maximum winding number that depends only on the number of lattice sites, whereas energy and angular momentum are shown to be sinusoidal functions of the winding number.

We study the formation of a Bose-Einstein condensate in a cigar-shaped three-dimensional harmonic trap, induced by the controlled addition of an attractive “dimple” potential along the weak axis. In this manner we are able to induce condensation without cooling due to a localized increase in the phase-space density. We perform a quantitative analysis of the thermodynamic transformation in both the sudden and adiabatic regimes for a range of dimple widths and depths. We find good agreement with equilibrium calculations based on self-consistent semiclassical Hartree-Fock theory describing the condensate and thermal cloud. We observe that there is an optimal dimple depth that results in a maximum in the condensate fraction. We also study the nonequilibrium dynamics of condensate formation in the sudden turn-on regime, finding good agreement for the observed time dependence of the condensate fraction with calculations based on quantum kinetic theory.

We study theoretically two spatially separate quasi-one-dimensional atomic Fermi gases in a double-well trap. By tuning independently their spin polarizations, a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid or a Bardeen-Cooper-Schrieffer (BCS) superfluid may be formed in each well. We seek the possibility of creating a spatially tunable atomic Josephson junction between two superfluids, which is supposed to be realizable via building a weak link at given positions of the double-well barrier. We show that within mean-field theory the maximum Josephson current is proportional to the order parameter in two wells. Thus, the spatial inhomogeneity of the FFLO order parameter in one well may be directly revealed through the current measurement with the position-tunable link. We anticipate that this type of Josephson measurement can provide useful evidence for the existence of exotic FFLO superfluids. Possible experimental realizations of the Josephson measurements in atomic Fermi gases are discussed.

A resonant two-level atom doped in a one-dimensional waveguide behaves as a mirror, but this single-atom “mirror” can only reflect single photons perfectly at a specific frequency. For a one-dimensional coupled-resonator waveguide, we propose to extend the perfect-reflection region from a specific frequency point to a wide band by placing many atoms individually in the resonators in a finite coordinate region of the waveguide. Such a doped resonator array promises to control the propagation of a practical photon wave packet with a certain momentum distribution instead of a single photon, which is ideally represented by a plane wave with a specific momentum. The studies based on the discrete-coordinate scattering theory indicate that such a hybrid structure with finite atoms indeed provides a near-perfect reflection for a single photon in a wide band. We also calculated the photon group velocity distribution, which shows that the perfect-reflection wide band exactly corresponds to the stopping light region.

Antirelaxation coatings in atomic vapor cells allow ground-state coherent spin states to survive many collisions with the cell walls. This reduction in the ground-state decoherence rate gives rise to ultranarrow-bandwidth features in electromagnetically induced transparency (EIT) spectra, which can form the basis of, for example, long-time scale slow and stored light, sensitive magnetometers, and precise frequency standards. Here we study, both experimentally and theoretically, how Zeeman EIT contrast and width in paraffin-coated rubidium vapor cells are determined by cell and laser-beam geometry, laser intensity, and atomic density. Using a picture of Ramsey pulse sequences, where atoms alternately spend “bright” and “dark” time intervals inside and outside the laser beam, we explain the behavior of EIT features in coated cells, highlighting their unique characteristics and potential applications.