Search

The transformation of a molecular Hamiltonian from the fermionic space to the qubit space results in a series of Pauli strings. Calculating the energy then involves evaluating the expectation values of each of these strings, which presents a significant bottleneck for applying variational quantum eigensolvers (VQEs) in quantum chemistry. Unlike fermionic Hamiltonians, the terms in a qubit Hamiltonian are additive. This work leverages this property to introduce a novel method for extracting information from the partial qubit Hamiltonian, thereby enhancing the efficiency of VQEs. This work introduces the SHARC-VQE (Simplified Hamiltonian Approximation, Refinement, and Correction-VQE) method, where the full molecular Hamiltonian is partitioned into two parts based on the ease of quantum execution. The easy-to-execute part constitutes the Partial Hamiltonian, and the remaining part, while more complex to execute, is generally less significant. The latter is approximated by a refined operator and added up as a correction into the partial Hamiltonian. SHARC-VQE significantly reduces computational costs for molecular simulations. The cost of a single energy measurement can be reduced from $O(\frac{N^4}{\epsilon^2})$ to $O(\frac{1}{\epsilon^2})$ for a system of $N$ qubits and accuracy $\epsilon$, while the overall cost of VQE can be reduced from $O(\frac{N^7}{\epsilon^2})$ to $O(\frac{N^3}{\epsilon^2})$. Furthermore, measurement outcomes using SHARC-VQE are less prone to errors induced by noise from quantum circuits, reducing the errors from 20-40% to 5-10% without any additional error correction or mitigation technique. Additionally, the SHARC-VQE is demonstrated as an initialization technique, where the simplified partial Hamiltonian is used to identify an optimal starting point for a complex problem.

Motivated by the recent realization of space-borne Bose-Einstein Condensate (BEC) under micro-gravity conditions, we extend the understanding of ultracold dipolar bosonic gases by exploring their behavior in a novel trapping configuration known as the ``bubble trap" topology. Utilizing the three-dimensional numerical simulations within the extended Gross-Pitaevskii framework, we unveil diverse ground state phases in such a static curved topology. Subsequently, we investigate the influence of rotation on a dipolar BEC confined to the surface of a spherical bubble. Our findings reveal that the rotation of a bubble trap with certain rotation frequencies can modify the effective local dipole-dipole interaction strength, leading to the induction of supersolidity and the formation of quantum droplets. In addition, we demonstrate that a bubble trap can sustain high circulation and the flow also persists for a longer time. Significantly, adjusting the rf detuning parameter allows the condensate to achieve hypersonic velocity. Finally, we explore the impact of drastic change in the topological nature of the trap on the rotating dipolar BEC, transitioning from a filled shell trap to a bubble trap and vice versa., Comment: 9 pages, 10 figures

We present a theoretical study of a spin-orbit coupled spin-1 Bose-Einstein condensate under the influence of sinusoidally varying magnetic fields. In the ground state of the ferromagnetic spin-1 condensate, we investigate topological excitations in the system arising due to the combined effect of Rashba spin-orbit coupling and an in-plane sinusoidally varying magnetic field. In this work, we offer a comparative study for various choices of magnetic fields in the $x\rm{-}y$ plane. For a fixed field strength, the spin-orbit coupled system sustains a rich variety of exotic vortex structures ranging from vortex-antivortex lattices to vortex clusters as we increase the coupling strength., Comment: 23 pages, 14 figures

H\"uckel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated {\pi}-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over direct mapping and allows quantum simulation of the HMO model for systems with up to 2^N conjugated centers in N qubits. The transformation of the H\"uckel Hamiltonian to qubit space is achieved by two different strategies: a machine-learning-assisted transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated {\pi}-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. The higher excited states of large systems, however, are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C_{60} fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are system-agnostic and hence are easily adaptable to similar problems of different complexity in other fields of research.

Recent experimental realization of the heteronuclear dipolar mixture of Dy and Er atoms opens fascinating prospects for creating intriguing novel phases in dipolar quantum gases. The experimentally measured value of intra-species $s$-wave scattering length of $^{166}$Er condensate in a $^{164}$Dy-$^{166}$Er mixture is larger than its intra-species dipolar length, implies that the $^{166}$Er condensate itself will not be in a regime of dominated dipole-dipole interaction (DDI). However, we find that the presence of $^{164}$Dy atoms with high magnetic moment induces droplet nucleation and supersolidity in $^{166}$Er condensate via the long-range and anisotropic inter-species DDI. Remarkably, we find that the imbalance in the magnetic dipole moment combined with its strong anisotropic coupling led to the emergence of unique ground state phases. The emerging phases include doubly superfluid states, a mixture of insulating droplets and supersolid states, binary supersolids with uniform and alternating domains and a combination of supersolid-superfluid mixed states. We delineate the properties of all these ground state phases and construct a phase diagram. We also explore the dynamical evolution across these phase boundaries via a linear quench of inter-species scattering length. Although we have demonstrated the result for the $^{164}$Dy-$^{166}$Er mixture, our results are generally valid for other dipolar bosonic mixtures of different Dy-Er isotope combinations and may become an important benchmark for future experimental scenarios., Comment: 11 pages, 8 figures

Quantum computing is being extensively used in quantum chemistry, especially in simulating simple molecules and evaluating properties like the ground state energy, dipole moment, etc. The transformation of a molecular Hamiltonian from the fermionic space to the qubit space provides us with a series of Pauli strings and the energy calculation involves the evaluation of the expectation values of all these individual strings. This introduces a major bottleneck for applications of VQEs in quantum chemistry. Unlike the fermionic Hamiltonian, the terms in a qubit Hamiltonian are additive and the present paper exploits this property to describe a new approach for extracting information from the partial qubit Hamiltonian of simple molecules to design more efficient variational quantum eigensolvers. In the partial (qubit) Hamiltonian approach (PHA), the qubit Hamiltonian is studied term-by-term to understand their relative contributions to the overall energy and a partial Hamiltonian is constructed with fewer Pauli strings that can resolve the entire Hamiltonian. With PHA, we can simulate molecules at a much lower computational cost with a truncated Hamiltonian. Additionally, the outcomes of the measurements with PHA quench the error due to noise introduced by the quantum circuits. We have also demonstrated the application of PHA as an initialization technique, where the simple partial Hamiltonian can be used to find a suitable initial state for a more complex system. The results of this study have the potential to demonstrate the potential advancement in the field of quantum computing and its implementation in quantum chemistry.

The growing interest in atomic structures of moderately-stripped alkali-like ions in diagnostic study and modeling of astrophysical and laboratory plasma makes an accurate many-body study of atomic properties inevitable. This work presents transition line parameters in the absence or presence of plasma atmosphere for astrophysically important candidates, Ar$^{7+}$, Kr$^{7+}$, Xe$^{7+}$, and Rn$^{7+}$. We employ relativistic coupled-cluster (RCC) theory, a well-known correlation exhaustive method. In the case of a plasma environment, we use Debye Model. Our calculations agree with experiments available in the literature for ionization potentials, transition strengths of allowed and forbidden selections, and lifetimes of several low-lying states. The unit ratios of length and velocity forms of transition matrix elements are the critical estimation of the accuracy of the transition data presented here, especially for a few presented first time in the literature. We do compare our findings with the available recent theoretical results. Our reported data can be helpful to the astronomer in estimating the density of the plasma environment around the astronomical objects or in the discovery of observational spectra corrected by that environment. The present results should be advantageous in the modeling and diagnostics laboratory plasma, whereas the calculated ionisation potential depression parameters reveal important characteristics of atomic structure.

We examine the quench dynamics of an extended Su-Schrieffer-Heeger(SSH) model involving long-range hopping that can hold multiple topological phases. Using winding number diagrams to characterize the system's topological phases geometrically, it is shown that there can be multiple winding number transition paths for a quench between two topological phases. The dependence of the quench dynamics is studied in terms of the survival probability of the fermionic edge modes and post-quench transport. For two quench paths between two topological regimes with the same initial and final topological phase, the survival probability of edge states is shown to be strongly dependent on the winding number transition path. This dependence is explained using energy band diagrams corresponding to the paths. Following this, the effect of the winding number transition path on transport is investigated. We find that the velocities of maximum transport channels varied along the winding number transition path. This variation depends on the path we choose, i.e., it increases or decreases depending upon the path. An analysis of the coefficient maps, energy spectrum, and spatial structure of the edge states of the final quench Hamiltonian provides an understanding of the path-dependent velocity variation phenomenon., Comment: 9 pages with 9 figures

We investigate the Rayleigh-Taylor instability at the two interfaces in a phase-separated three-component Bose-Einstein condensate in the mean-field framework. The subsequent dynamics in the immiscible three-component condensate has been studied in detail for different cases of instigating the instability in the system. The rotational symmetry of the system breaks when the atom-atom interaction is tuned in such a way that the interface between the components becomes unstable giving rise to non-linear patterns of mushroom shapes which grow exponentially with time. We also identify these non-linear patterns as the solutions of the angular Mathieu equation, representing the normal modes., Comment: 12 pages, 11 figures

The recent realization of binary dipolar BEC [Phys. Rev. Lett. 121, 213601 (2018)] opens new exciting aspects for studying quantum droplets and supersolids in a binary mixture. Motivated by this experiment, we study groundstate phases and dynamics of a Dy-Dy mixture. Dipolar bosonic mixture exhibits qualitatively novel and rich physics. Relying on the three-dimensional numerical simulations in the extended Gross-Pitaevskii framework, we unravel the groundstate phase diagrams and characterize different groundstate phases. The emergent phases include both miscible and immiscible single droplet (SD), multiple droplets (MD), supersolid (SS), and superfluid (SF) states. More intriguing mixed groundstates may occur for an imbalanced binary mixture, including a combination of SS-SF, SS-MD, and SS-SS phases. We observed the dynamical transition from a miscible MD state to an immiscible MD state with multiple domains formed along the axial direction by tuning the inter-species scattering length. Also by linear quenches of intra-species scattering lengths across the aforementioned phases, we monitor the dynamical formation of supersolid clusters and droplet lattices. Although we have demonstrated the results for a Dy-Dy mixture and for a specific parameter range of intra-species and inter-species scattering lengths, our results are generally valid for other dipolar mixtures and may become an important benchmark for future experimental scenarios., Comment: 15 pages, 14 figures

Classical optimizers play a crucial role in determining the accuracy and convergence of variational quantum algorithms. In literature, many optimizers, each having its own architecture, have been employed expediently for different applications. In this work, we consider a few popular optimizers and assess their performance in variational quantum algorithms for applications in quantum chemistry in a realistic noisy setting. We benchmark the optimizers with critical analysis based on quantum simulations of simple molecules, such as Hydrogen, Lithium Hydride, Beryllium Hydride, water, and Hydrogen Fluoride. The errors in the ground-state energy, dissociation energy, and dipole moment are the parameters used as yardsticks. All the simulations were carried out with an ideal quantum circuit simulator, a noisy quantum circuit simulator, and a noisy simulator with noise embedded from the IBM Cairo quantum device to understand the performance of the classical optimizers in ideal and realistic quantum environments. We used the standard unitary coupled cluster (UCC) ansatz for simulations, and the number of qubits varied from two, starting from the Hydrogen molecule to ten qubits, in Hydrogen Fluoride. Based on the performance of these optimizers in the ideal quantum circuits, the conjugate gradient (CG), limited-memory Broyden-Fletcher-Goldfarb-Shanno bound (L_BFGS)B), and sequential least squares programming (SLSQP) optimizers are found to be the best-performing gradient-based optimizers. While constrained optimization by linear approximation (COBYLA) and POWELL perform most efficiently among the gradient-free methods. However, in noisy quantum circuit conditions, Simultaneous Perturbation Stochastic Approximation (SPSA), POWELL, and COBYLA are among the best-performing optimizers.

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

Ionic clocks exhibit as the most promising candidates for the frequency standards. Recent investigations show the profound advantages of interrogating two laser beams with different frequencies in developing the frequency standards. Here we present a scheme of a two-photon mechanism to calculate the dynamic polarizabilities for the clock states, 6$^2$S$_{\frac{1}{2}}$ and 5$^2$D$_{\frac{3}{2}, \frac{5}{2}}$, of Ba$^+$ by employing relativistic coupled-cluster method. We illustrate the Stark-shift cancellation between these clock states at the two-photon magic wavelengths. These magic wavelengths can be essential inputs to achieve better accuracy in the ionic clock experiments. We also calculate the magic wavelengths under the single-photon interaction to serve as the reference and for a comparative study. The calculated single- and two-photon magic wavelengths lie in the optical region and thus are significant for future state-of-the-art experiments. Moreover, as an application of the two-photon polarizabilities, we investigate the impact of these polarizabilities on the spin-mixing processes, $|0,0\rangle$ $\leftrightarrow$ $|+1,-1\rangle$ and $|0,0\rangle$ $\leftrightarrow$ $|-1,+1\rangle$, of an ultra-cold spin-1 mixture of the $^{137}$Ba$^+$ and $^{87}$Rb atoms. We determine the protocols of selecting these spin-mixing oscillations by changing the strength of an externally applied magnetic field and the frequencies of the interrogating laser beams.

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

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

In this paper, we have formulated a theory for the microscopic interaction of the asymmetric Laguerre-Gaussian (aLG) beam with the atomic Bose-Einstein condensate (BEC) in a harmonic trap. Here the asymmetry is introduced to an LG beam considering a complex-valued shift in the Cartesian plane keeping the axis of the beam and its vortex states co-axial to the trap axis of the BEC. Due to the inclusion of the asymmetric nature, multiple quantized circulations are generated in the beam. We show how these quantized circulations are transferred to the BEC resulting in a superposition of matter vortex states. The calculated Rabi frequencies for the dipole as well as quadrupole transitions during the transfer process show distinct variability with the shift parameters of the beam. A significant enhancement of the quadrupole Rabi frequency for higher vorticity states is observed compared to symmetric single orbital angular momentum (OAM) mode beam at a particular range of the shift parameters. We also demonstrate the variation of superposition of matter vortex states and observe its distinct feature compared to the superposition of the LG modes for different shift parameters. The first order spatial correlation of the superposed states supports this feature and highlights asymmetry in degree of transverse coherence along orthogonal directions on the surface., Comment: 11 pages, 10 figures

We examine the dynamics associated with the creation of a vortex in a Bose-Einstein condensate (BEC), from another nonrotating BEC using two-photon Raman transition with Gaussian (G) and Laguerre-Gaussian (LG) laser pulses. In particular, we consider BEC of Rb atoms at their hyperfine ground states confined in a quasi two dimensional harmonic trap. Optical dipole potentials created by G and LG laser pulses modify the harmonic trap in such a way that density profiles of the condensates during the Raman transition process depend on the sign of the generated vortex. We investigate the role played by the Raman coupling parameter manifested through dimensionless peak Rabi frequency and intercomponent interaction on the dynamics of the population transfer process and on the final population of the rotating condensate. During the Raman transition process, the two BECs tend to have larger overlap with each other for stronger intercomponent interaction strength., Comment: 11 pages, 6 figures

The present work determines the precise values of magic wavelengths corresponding to the clock transitions 5$^2S$-4$^2D$ of Y$^{2+}$ ion both at the levels of 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., Comment: 25 Pages and three figures, Accepted in Phys. Rev. A

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

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 \textbf{97}, 022511 (2018)]. We find 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 electromagnetic spectrum. The calculated magic wavelengths will help the experimentalists to trap the ion for performing the high precision spectroscopic measurements., Comment: 12 Pages, 8 figures

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 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., Comment: 24 pages, 6 Tables, 5 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

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., Comment: 17 pages, 11 figures

Transfer mechanism of orbital angular moment(OAM) of light to trapped ground-state atoms under paraxial approximation is well known. Here we show how optical OAM of a Laguerre-Gaussian(LG) beam under paraxial approximation can be transferred to trapped Rydberg atoms. Optical OAM is shown to be transferable to a Rydberg electronic state in dipole transition. The Gaussian part of the profile of the LG beam, which is generally neglected , is found to have an important effect on the OAM transfer to the Rydberg atoms. Numerical calculations are calculated based on this theory for Rubidium Rydberg atoms trapped in a harmonic potential. Our results exhibit the mixing of final states of different parities., Comment: 16 pages, 1 figure

This work presents precise calculations of important electromagnetic transition amplitudes along with detail of their many-body correlations using relativistic coupled cluster method. Studies of hyperfine interaction constants, useful for plasma diagnostic, with this correlation exhaustive many-body approach are another important area of this work. The calculated oscillator strengths of allowed transitions, amplitudes of forbidden transitions and lifetimes are compared with the other theoretical results wherever available and they show a good agreement. Hyperfine constants of different isotopes of W VI, presented in this paper will be helpful to get accurate picture of abundances of this element in different astronomical bodies., Comment: 15 pages, 1 figure

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., Comment: 15 pages, 7 figures

The transfer of orbital angular momentum from an optical vortex to an atomic Bose-Einstein condensate changes the vorticity of the condensate. The spatial mismatch between initial and final center-of-mass wavefunctions of the condensate influences significantly the two-photon optical dipole transition between corresponding states. We show that the transition rate depends on the handedness of the optical orbital angular momentum leading to optical manipulation of matter-wave vortices and circular dichroism-like effect. Based on this effect, we propose a method to detect the presence and sign of matter-wave vortex of atomic superfluids. Only a portion of the condensate is used in the proposed detection method leaving the rest in its initial state., Comment: Accepted in Phys. Rev. A

In this paper, we have calculated parity nonconserving electric dipole transition amplitudes of the hyperfine components for the transitions between the ground and first excited states of $^{137}$Ba$^{+}$ and $^{87}$Sr$^{+}$ using sum-over-states technique. The results are presented to extract the constants associated with the nuclear spin dependent amplitudes from experimental measurements. The wavefunctions to calculate the most dominant part of the sums are constructed using highly correlated coupled-cluster theory based on the Dirac-Coulomb-Gaunt Hamiltonian.

Exchange of orbital angular momentum between Laguerre-Gaussian beam of light and center-of-mass motion of an atom or molecule is well known. We show that orbital angular momentum of light can also be transferred to the internal electronic or rotational motion of an atom or a molecule provided the internal and center-of-mass motions are coupled. However, this transfer does not happen directly to the internal motion, but via center-of-mass motion. If atoms or molecules are cooled down to recoil limit then an exchange of angular momentum between the quantized center-of-mass motion and the internal motion is possible during interaction of cold atoms or molecules with Laguerre-Gaussian beam. The orientation of the exchanged angular momentum is determined by the sign of the winding number of Laguerre-Gaussian beam. We have presented selective results of numerical calculations for the quadrupole transition rates in interaction of Laguerre-Gaussian beam with an atomic Bose-Einstein condensate to illustrate the underlying mechanism of light orbital angular momentum transfer. We discuss how the alignment of diatomic molecules will facilitate to explore the effects of light orbital angular momentum on electronic motion of molecules., Comment: Accepted in Phys. Rev. A

Hyperfine constants and anomalies of ground as well as few low lying excited states of $^{113,115,117}$In III are studied with highly correlated relativistic coupled-cluster theory. The ground state hyperfine splitting of $^{115}$In III is estimated to be 106.8 GHz. A shift of almost 1.9 GHz of the above frequency has been calculated due to modified nuclear dipole moment. This splitting result shows its applicability as communication band and frequency standards at $10^{-11}$ sec. Correlations study of hyperfine constants indicates a few distinct features of many-body effects in the wave-functions in and near the nuclear region of this ion. Astrophysically important forbidden transition amplitudes are estimated for the first time in the literature to our knowledge. The calculated oscillator strengths of few allowed transitions are compared with recent experimental and theoretical results wherever available., Comment: 11 pages, 4 figures

This work presents accurate {\it ab initio} investigations of various spectroscopic properties of a few Li-like ions in presence of a plasma environment within the Debye screening potential. The coupled-cluster theory in the relativistic framework has been employed to compute ionization potentials, excitation energies, electric dipole oscillator strengths, and electric quadrupole transition probabilities of Li-like C$^{3+}$, N$^{4+}$, and O$^{5+}$ ions. The unretarded Breit interaction has been implemented to increase the accuracy of the calculations. The effects of ion density and temperature on the ionization potentials, excitation energies, electric dipole oscillator strengths, and electric quadrupole transition probabilities have been investigated in the plasma environment. It is found that the plasma screening leads to a sharp decrease in the ionization potential as the screening strength increases. With increasing strength, the oscillator strengths associated with 2$s ^{2}S_{1/2}$$\rightarrow2 p ^{2}P_{1/2, 3/2}$ transitions increase, whereas the transition probabilities associated with 3$d ^2D_{3/2, 5/2}$$\rightarrow2 s ^2S_{1/2}$ transitions decrease., Comment: 20 pages, 4 figures

In this paper, we have studied electron correlation and Gaunt interaction effects in ionization potentials (IPs) and hyperfine constants A of 2p$^2P_{1/2}$ and 2p$^2P_{3/2}$ states along with the fine structure splitting (FSS) between them for boron isoelectronic sequence using relativistic coupled-cluster (RCC) method. The range of atomic number Z has been taken from 8 to 21. Gaunt contributions are presented at both Dirac-Fock (DF) and coupled-cluster (CC) levels of calculations. The Gaunt corrected correlated results of the IPs and the FSS are compared with the results of NIST. Important correlation contributions like core correlation, core polarisation, pair correlation etc. are studied for hyperfine constants A. Many distinct features of correlation and relativistic effects are observed in these studies. With best of our knowledge, within Gaunt limit, most of the hyperfine constants are presented for the first time in the literature., Comment: 5 figures, submitted to Phy. Rev. A

Relativistic coupled-cluster (RCC) calculations have been performed to estimate the electromagnetic forbidden transition probabilities, oscillator strengths and lifetimes of many low-lying states of five times ionized molybdenum (Mo VI). Contributions from the Breit interaction up to the first order of perturbation have been examined. Our results are in good agreement with the available other reported theoretical and experimental results. A long lifetime about 4.9854 s of the first excited state, 4d $^2D_{5/2}$, has been predicted which can be a very useful criteria in the doping process of thin films. Correlations trends from various RCC terms to the transition amplitude calculations are discussed., Comment: 14 pages, submitted to J. Phys. B

This work presents accurate {\it ab initio} determination of the magnetic dipole (M1) and electric quadrupole (E2) hyperfine structure constants for the ground and a few low-lying excited states in $^{67}$Zn$^{+}$, which is one of the interesting systems in fundamental physics. The coupled-cluster (CC) theory within the relativistic framework has been used here in this calculations. Long standing demands for a relativistic and highly correlated calculations like CC can be able to resolve the disagreements among the lifetime estimations reported previously for a few low-lying states of Zn$^{+}$. The role of different electron correlation effects in the determination of these quantities are discussed and their contributions are presented., Comment: 9 pages, 1 figure. submitted to J. Phys. B Fast Track

The astrophysically important electric quadrupole (E2) and magnetic dipole (M1) transitions for the low-lying states of triply ionized titanium (Ti IV) are calculated very accurately using a state-of-art all-order many-body theory called Coupled Cluster (CC) theory in the relativistic frame-work. Different many-body correlations of the CC theory has been estimated by studying the core and valence electron excitations to the unoccupied states. The calculated excitation energies of different states are in very good agreement with the measurements. Also we compare our calculated electric dipole (E1) transition amplitudes of few transitions with recent many-body calculations by different groups. We have also carried out the calculations for the lifetimes of the low-lying states of Ti IV. A long lifetime is found for the first excited 3d$^{2}D_{5/2}$ state, which suggested that Ti IV may be one of the useful candidates for many important studies. Most of the results reported here are not available in the literature, to the best of our knowledge., Comment: 15 pages submitted to J. Phys. B

In this work, the {\it ab initio} calculations have been carried out to study the oscillator strengths corresponding to `forbidden transitions' of astrophysically important electromagnetic transitions of singly ionized zinc, Zn II. Many important electron correlations are considered to all-orders using the relativistic coupled-cluster theory. Calculated ionization potentials are compared with the experimental values, wherever available. To our knowledge, oscillator strengths of magnetic dipole and electric quardupole transitions are estimated for the first time. The transitions span in the range of ultraviolet, visible, and near infrared regions and are important for astrophysical observations., Comment: 9 pages

This work presents accurate ab initio determination of the hyperfine splitting for the ground state and few low-lying excited states of 113Cd+; important candidates for the frequency standard in the microwave region, using coupled-cluster theory (CC) in the relativistic framework. The calculated hyperfine splitting are well in agreement with recent experimental results. We have also carried out the lifetimes of the 5p2P1=2 and 5p2P3=2 states, which are in well agreement with recent experimental result (Moehring et al., PRA 73 023413, 2006). The roles of different electron correlation effects in the determination of these quantities are discussed and their contributions are presented in the CC terms., Comment: 8 pages, 1 figure

Accurate {\it ab initio} calculations have been carried out to study the valence electron removal energies and oscillator strengths of astrophysically important electromagnetic transitions of quadruply ionized vanadium, $V^{4+}$. Many important electron correlations are considered to all-orders using the relativistic coupled-cluster theory. Calculated ionization potentials and fine structure splittings are compared with the experimental values, wherever available. To our knowledge, oscillator strengths of electric dipole transitions are predicted for the first time for most of the transitions. The transitions span in the range of ultraviolet, visible and near infrared regions and are important for astrophysical observations., Comment: Submitted in Astrophysical J

Electric quadrupole (E2) and magnetic dipole (M1) transition amplitudes among the low-lying states of quadruply ionized vanadium V$^{4+}$, important in various field of experimental and astrophysics are presented very accurately. Most of these results are reported for the first time in the literature. Relativistic coupled-cluster theory with single, double and leading triple excitations has been employed for these calculations. Estimation of different correlation effects arising through the above formalism have been highlighted by studying core and valence electrons excitations to the excited states. The lifetime of the first excited $D$- state is found to be long., Comment: 16 pages in pdf output

Ab initio calculations have been carried out to study the magnetic dipole and electric quadrupole hyperfine structure constants of $^{205}$Pb$^+$. Many-body effects have been considered to all orders using the relativistic coupled-cluster theory in the singles, doubles and partial triples approximation. The trends of these effects are found to be different from atomic systems that have been studied earlier., Comment: 4 tables

Relativistic coupled-cluster(RCC) theory has been employed to calculate the life time of the $6 ^2P_{3/2}$ state of single ionized lead($^{207}Pb$) to an accurac y of 3% and compared with the corresponding value obtained using second order r elativistic many-body perturbation theory(RMBPT). This is one of the very few ap plications of this theory to excited state properties of heavy atomic systems. C ontributions from the different electron correlation effects are given explicitl y.