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We conduct a theoretical study of the creation and dynamics of vortices in a two-dimensional binary Bose-Einstein condensate with a mass imbalance between the species. To initiate the dynamics, we use one or two rotating paddle potentials in one species, while the other species is influenced only via the interspecies interaction. In both species, the number and the dominant sign of the vortices are determined by the rotation frequency of the paddle potential. Clusters of positive and negative vortices form at a low rotation frequency comparable to that of the trap when using the single paddle potential. In contrast, vortices of the same sign tend to dominate as the rotation frequency of the paddle increases, and the angular momentum reaches a maximum value at a paddle frequency, where the paddle velocity becomes equal to the sound velocity of the condensate. When the rotation frequency is sufficiently high, the rapid annihilation of vortex-antivortex pairs significantly reduces the number of vortices and antivortices in the system. For two paddle potentials rotating in the same direction, the vortex dynamics phenomenon is similar to that of a single paddle. However, when the paddle potentials are rotated in the opposite direction, both positive and negative signed vortices occur at all rotational frequencies. At the low rotation frequencies, the cluster of like-signed vortices produces the $k^{-5/3}$ and $k^{-3}$ power laws in the incompressible kinetic energy spectrum at low and high wavenumbers, respectively, a hallmark of the quantum turbulent flows., Comment: 14 pages, 13 figures

We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with $l$-fold symmetry, ranging from quadrupole ($l=2$) to heptagon modes ($l=7$), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of the collective excitations. The oscillation amplitude of the surface excitations increases exponentially during the modulation. We find that only the $l=6$ mode is unstable due to its emergent coupling with the dipole motion of the cloud. Our experimental results are in excellent agreement with the mean-field framework. Our work opens a new pathway for generating higher-lying collective excitations with applications, such as the probing of exotic properties of quantum fluids and providing a generation mechanism of quantum turbulence., 5 pages, 4 figures

We theoretically investigate the out-of-equilibrium dynamics in a binary Bose-Einstein condensate confined within two-dimensional box potentials. One species of the condensate interacts with a pair of oppositely wound, but otherwise identical Laguerre-Gaussian laser pulses, while the other species is influenced only via the interspecies interaction. Starting from the Hamiltonian, we derive the equations of motion that accurately delineate the behavior of the condensates during and after the light-matter interaction. Depending on the number the helical windings (or the magnitude of topological charge), the species directly participating in the interaction with lasers is dynamically segmented into distinct parts which collide together as the pulses gradually diminish. This collision event generates nonlinear structures in the related species, coupled with the complementary structures produced in the other species, due to the interspecies interaction. The long-time dynamics of the optically perturbed species is found to develop the Kolmogorov-Saffman scaling law in the incompressible kinetic energy spectrum, a characteristic feature of the quantum turbulent state. However, the same scaling law is not definitively exhibited in the other species. This study warrants the usage of Laguerre-Gaussian beams for future experiments on quantum turbulence in Bose-Einstein condensates., Comment: 15 pages, 9 figures

We unravel the ground state properties and the non-equilibrium quantum dynamics of two bosonic impurities immersed in an one-dimensional fermionic environment by applying a quench of the impurity-medium interaction strength. In the ground state, the impurities and the Fermi sea are phase-separated for strong impurity-medium repulsions while they experience a localization tendency around the trap center for large attractions. We demonstrate the presence of attractive induced interactions mediated by the host for impurity-medium couplings of either sign and analyze the competition between induced and direct interactions. Following a quench to repulsive interactions triggers a breathing motion in both components, with an interaction dependent frequency and amplitude for the impurities, and a dynamical phase-separation between the impurities and their surrounding for strong repulsions. For attractive post-quench couplings a beating pattern owing its existence to the dominant role of induced interactions takes place with both components showing a localization trend around the trap center. In both quench scenarios, attractive induced correlations are manifested between non-interacting impurities and are found to dominate the direct ones only for quenches to attractive couplings.

The present paper determines the precise values of magic wavelengths corresponding to the clock transitions ${5}^{2}S\text{--}{4}^{2}D$ of the ${\mathrm{Y}}^{2+}$ ion at the levels of both fine and hyperfine structures due to the external light beams having linear as well as circular polarization. To calculate the dynamic polarizabilities of the associated states of the transitions, we employ the sum-over-states technique, where the dominating and correlation sensitive part of the sum is evaluated using a highly correlated relativistic coupled-cluster theory. The estimated magic wavelengths of the light beams have substantial importance to cool and trap the ion using a blue-detuned trapping scheme. We also present the tune-out wavelengths, which are useful in state-insensitive trapping and cooling. The vector component of a total polarizability, which is induced by a circularly polarized light only, can provide additional magic wavelengths. Considerable effects of hyperfine interaction on the values of polarizabilities and number of magic wavelengths divulge the importance of precise estimations of hyperfine-structure splitting.

We unravel the periodically driven dynamics of two repulsively interacting bosonic impurities within a bosonic bath upon considering either the impact of a finite pulse or a continuous shaking of the impurities harmonic trap. Following a pulse driving of initially miscible components we reveal a variety of dynamical response regimes depending on the driving frequency. At resonant drivings the impurities decouple from their host while if exposed to a high frequency driving they remain trapped in the bosonic gas. For continuous shaking we showcase that in the resonantly driven regime the impurities oscillate back and forth within and outside the bosonic medium. In all cases, the bosonic bath is perturbed performing a collective dipole motion. Referring to an immiscible initial state we unveil that for moderate driving frequencies the impurities feature a dispersive behavior whilst for a high frequency driving they oscillate around the edges of the Thomas-Fermi background. Energy transfer processes from the impurities to their environment are encountered, especially for large driving frequencies. Additionally, coherence losses develop in the course of the evolution with the impurities predominantly moving as a pair., 22 pages, 16 figures

Experiments with vortex beams have shown a surge of interest in controlling cold atoms. Most of the controlling protocols are dominated by circularly polarized light due to its ability to induce vector polarization at atoms, which is impossible for paraxial linearly polarized light. Here we develop a theory for frequency dependent polarizability of an atomic state interacting with a focused linearly polarized vortex beam. The naturally induced spin-orbit coupling in this type of linearly polarized beam produces vector component of the valence polarizability to an atomic state, obeying the total angular momentum conservation of the beam. The theory is employed on $^{87}$Sr$^{+}$ ion to accurately calculate the magic wavelengths for the clock transitions and tune-out wavelengths for the clock states using relativistic coupled-cluster method. The induced vector component in the dynamic polarizability due to the linearly polarized focused vortex beam promotes fictitious magnetic field to the atomic state. We demonstrate that this fictitious magnetic field, depending on the focusing angle and OAM of the beam, improves the flexibility of the coherent heteronuclear spin oscillations in a spin-1 mixture of $^{87}$Rb and $^{23}$Na atoms., Comment: 20 pages, 4 figures

A theory of dynamic polarizability for trapping relevant states of Sr\(^+\) is presented here when the ions interact with a focused optical vortex. The coupling between the orbital and spin angular momentum of the optical vortex varies with focusing angle of the beam and is studied in the calculation of the magic wavelengths for \(5s_{{1}/{2}}\rightarrow 4d_{{3}/{2}, {5}/{2}}\) transitions of Sr\(^+\). The initial state of our interest here is \(5s_{{1}/{2}}\) with \(m_J = -1/2\) of which is different possible trapping state compare to our recent work on Sr\(^+\) [Phys. Rev. A 97, 022511 (2018)]. We find a variation in magic wavelengths and the corresponding polarizabilities with different combinations of orbital and spin angular momentum of the vortex beam. The variation is very significant when the wavelengths of the beam are in the infrared region of the electromagnetic spectrum. The calculated magic wavelengths will help the experimentalists to trap the ion for performing the high-precision spectroscopic measurements.

Here we report on accurate ab initio calculations to study astrophysically important electromagnetic transition parameters among different low-lying states of Sn IV. Our ab initio calculations are based on the sophisticated relativistic coupled-cluster theory, which almost exhausts many important electron correlations. To establish the accuracy of the calculations, we compare our results with the available experiments and estimates the transition amplitudes in length and velocity gauged forms. Most of these allowed and forbidden transition wavelengths lie in the infrared region, and they can be observed in the different cool stellar and interstellar media. For the improvement of uncertainty, we use experimental energies to the estimations of the above transition parameters. The presented data will be helpful to find the abundances of the ion in different astrophysical and laboratory plasma., Comment: 7 pages

We present the theory of microscopic interaction of the spin-orbit coupled focused Laguerre-Gaussian (LG) beam with the two-component Bose-Einstein condensate (BEC), composed of two hyperfine states of $^{87}$Rb in a harmonic trap. We have shown that Raman Rabi frequency distributions over the inter-component coupling identify phase separation coupling strength. A significant enhancement of side-band transitions due to non-paraxial nature of vortex beam is observed for particular values of inter-component coupling around 1.25 and 0.64 in unit of 5.5nm for $10^5$ and $10^6$ number of atoms, respectively. The uncertainty in the estimation of these coupling strengths is improved with the focusing angles of the beam. We discuss an experimental scheme to verify this non-paraxial effect on ultra-cold atoms., Comment: 15 pages, 7 figures, Journal of Physics Communications 2018

We present in this paper a theory of dynamic polarizability for an atomic state due to an external field of non-paraxial Laguerre-Gaussian (LG) beam using the sum-over-states technique. A highly correlated relativistic coupled-cluster theory is used to evaluate the most important and correlation sensitive parts of the sum. The theory is applied on Sr$^+$ to determine the magic wavelengths for $5s_{{1}/{2}}\rightarrow 4d_{{3}/{2}, {5}/{2}}$ transitions. Results show the variation of magic wavelengths with the choice of orbital and spin angular momenta of the incident LG beam. Also, the tunability of the magic wavelengths is studied using the focusing angle of the LG beam and observed its efficiency in the near-infrared region. Evaluations of the wide spectrum of magic wavelengths from infrared to ultra-violet have substantial importance to the experimentalists for carrying out high precision measurements in fundamental physics. These magic wavelengths can be used to confine the atom or ion at the dark central node or at the high-intensity ring of the LG beam., 24 pages, 6 Tables, 5 Figures

Spectroscopic properties, useful for plasma diagnostics and astrophysics, of a few rubidium-like ions are studied here. We choose one of the simplest, but correlationally challenging series where $d-$ and $f-$ orbitals are present in the core and/or valence shells with $4d$ $^2D_{3/2}$ as the ground state. We study different correlation characteristics of this series and make precise calculations of electronic structure and rates of electromagnetic transitions. Our calculated lifetimes and transition rates are compared with other available experimental and theoretical values. Radiative rates of vacuum ultra-violet electromagnetic transitions of the long lived Tc$^{6+}$ ion, useful in several areas of physics and chemistry, are estimated. To the best of our knowledge, there is no literature for most of these transitions., 17 pages, 11 figures

The density profiles of trapped two-component Bose-Einstein condensates (BEC) and its microscopic interaction with Laguerre Gaussian (LG) beam are studied. We consider the $^{87}$Rb BEC in two hyperfine spin components. The wavelength of the LG beam is assumed to be comparable to the atomic de-Broglie wavelength. Competitions between intra- and inter-component interactions produce interesting density structures of the ground state of BEC. We demonstrate vortex-antivortex interference and its dependence on the inter-component interactions and Raman transitions., Comment: 14 pages, 30 figures

The exchange of orbital angular momentum (OAM) between paraxial optical vortex and a Bose-Einstein condensate (BEC) of atomic gases is well known. In this paper, we develop a theory for the microscopic interaction between matter and an optical vortex beyond paraxial approximation. We show how superposition of vortex states of BEC can be created with a focused optical vortex. Since, the polarization or spin angular momentum (SAM) of the optical field is coupled with OAM of the field, in this case, these angular momenta can be transferred to the internal electronic and external center-of-mass (c.m.) motion of atoms provided both the motions are coupled. We propose a scheme for producing the superposition of matter-wave vortices using Gaussian and a focused Laguerre-Gaussian (LG) beam. We study how two-photon Rabi frequencies of stimulated Raman transitions vary with focusing angles for different combinations of OAM and SAM of optical states. We demonstrate the formation of vortex-antivortex structure and discuss interference of three vortex states in a BEC., 15 pages, 7 figures

Isotope shifts (ISs) of ${D}_{1}\phantom{\rule{4.pt}{0ex}}(ns\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}np\phantom{\rule{0.16em}{0ex}}^{2}P_{1/2})$ and ${D}_{2}\phantom{\rule{4.pt}{0ex}}(ns\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}np\phantom{\rule{0.16em}{0ex}}^{2}P_{3/2})$ transitions for the first three elements of the K isoelectronic sequence are calculated with all-order correlated relativistic coupled-cluster theory. To get precise ab initio results, all the orbitals of the reference states have been optimized by a linear regression technique. Some of the important IS estimations reported here were not available in literature. Interesting features of odd-even staggering and magic neutron number effects are also observed in the case of volume shift calculations. Energy-level corrections for a few levels due to a change in the nuclear model from a point nucleus to a Fermi nucleus have been studied with interesting correlation features and compared with other theoretical results available in literature.

Previous studies show that within paraxial limit and electric dipole approximations, the orbital angular momentum (OAM) of a Laguerre–Gaussian (LG) beam rotates the whole atom about the beam axis but does not affect the internal electronic motion. The contribution of the Gaussian part of the LG beam profile to the angular momentum exchange is not usually taken into account. In this paper, we develop a theory which shows that not only the OAM of a LG beam, but also the geometry of the beam cross section, plays an important role in the electronic lowest-order transitions in the interaction of the beam with a trapped Rydberg atom, due to the large span of its electronic wavefunctions. In this interaction, the standard dipole selection rules do not hold and our results show that the otherwise forbidden transitions can become sufficiently probable.