Tuning of non-paraxial effects of the Laguerre-Gaussian beam interacting with the two-component Bose-Einstein condensates

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 201

E1E1 PNC transition amplitudes of the hyperfine components for 2S1/2^2S_{1/2} −- 2D3/2^2D_{3/2} transitions of 137^{137}Ba+^{+} and 87^{87}Sr+^{+}

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

Matrix-Based Characterization of the Motion and Wrench Uncertainties in Robotic Manipulators

Characterization of the uncertainty in robotic manipulators is the focus of this paper. Based on the random matrix theory (RMT), we propose uncertainty characterization schemes in which the uncertainty is modeled at the macro (system) level. This is different from the traditional approaches that model the uncertainty in the parametric space of micro (state) level. We show that perturbing the system matrices rather than the state of the system provides unique advantages especially for robotic manipulators. First, it requires only limited statistical information that becomes effective when dealing with complex systems where detailed information on their variability is not available. Second, the RMT-based models are aware of the system state and configuration that are significant factors affecting the level of uncertainty in system behavior. In this study, in addition to the motion uncertainty analysis that was first proposed in our earlier work, we also develop an RMT-based model for the quantification of the static wrench uncertainty in multi-agent cooperative systems. This model is aimed to be an alternative to the elaborate parametric formulation when only rough bounds are available on the system parameters. We discuss that how RMT-based model becomes advantageous when the complexity of the system increases. We perform experimental studies on a KUKA youBot arm to demonstrate the superiority of the RMT-based motion uncertainty models. We show that how these models outperform the traditional models built upon Gaussianity assumption in capturing real-system uncertainty and providing accurate bounds on the state estimation errors. In addition, to experimentally support our wrench uncertainty quantification model, we study the behavior of a cooperative system of mobile robots. It is shown that one can rely on less demanding RMT-based formulation and yet meets the acceptable accuracy.Comment: 15 pages, 11 figure

Angular Momentum Transfer in Interaction of Laguerre-Gaussian Beams with Atoms and Molecules

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 quantitative study on the role of TKI combined with Wnt/β\beta-catenin signaling and IFN-α\alpha in the treatment of CML through deterministic and stochastic approaches

We propose deterministic and stochastic models for studying the pharmacokinetics of chronic myeloid leukemia (CML), upon administration of IFN-$\alpha$ (the traditional treatment for CML), TKI (the current frontline medication for CML) and Wnt/$\beta$-catenin signaling (the state-of-the art therapeutic breakthrough for CML). To the best of our knowledge, no mathematical model incorporating all these three therapeutic protocols are available in literature. Further, this work introduces a stochastic approach in the study of CML dynamics. The key contributions of this work are: (1) Determination of the patient condition, contingent upon the patient specific model parameters, which leads to prediction of the appropriate patient specific therapeutic dosage. (2) Addressing the question of how the dual therapy of TKI and Wnt/$\beta$-catenin signaling or triple combination of all three, offers potentially improved therapeutic responses, particularly in terms of reduced side effects of TKI or IFN-$\alpha$. (3) Prediction of the likelihood of CML extinction/remission based on the level of CML stem cells at detection

Relativistic coupled cluster calculations on hyperfine structures and electromagnetic transition amplitudes of In III

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 figure

Tunable magic wavelengths for trapping with focused Laguerre-Gaussian beam

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 Figure

Precise many-body calculations and hyperfine interaction effect on dynamic polarizabilities at the low-lying energy levels of Y2+^{2+}

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.

The optical manipulation of matter-wave vortices: An analogue of circular dichroism

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.

Density profiles of two-component Bose-Einstein condensates interacting with a Laguerre-Gaussian Beam

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 figure