arXiv subjects

Sukhjit Singh

Publications and source records attributed to Sukhjit Singh.

At least 19 recordsLinked to original sources

arXiv2022

Accurate determination of quadrupole polarizabilities of the excited states of alkali-metal atoms

The scalar and tensor components of the electric quadrupole (E2) polarizabilities of the first two excited states of all the alkali-metal atoms are determined. To validate the calculations, we have evaluated the ground state E2 polarizabilities of these atoms and compared them with the literature values. We could not find the ground state E2 polarizability value for Fr in the literature to compare with our result. The dominant parts of these quantities are estimated by combining the precisely calculated E2 transition matrix elements of many low-lying transitions with the experimental energies, while the other contributions are estimated using lower-order methods. Our estimated values for the ground states of the above atoms are in good agreement with the literature values suggesting that our estimated E2 polarizabilities for the excited states of the alkali atoms, which were not known earlier except for the Li atom, are also quite accurate. These reported E2 polarizabilities could be useful in guiding many precision measurements in the alkali atoms.

physics.atom-ph↗

arXiv2022

Tune-out and magic wavelengths, and electric quadrupole transition properties of the singly charged alkaline-earth metal ions

In continuation to our earlier reported data on the electric dipole (E1) matrix elements and lifetimes of the metastable states of the alkaline earth ions in [Atomic Data and Nuc. Data Tables {\bf 137} (2021) 101381], we present here the tune-out and magic wavelengths of the Mg$^+$, Ca$^+$, Sr$^+$ and Ba$^+$ alkaline earth-metal ions by determining dynamic E1 polarizabilities. Furthermore, we have evaluated the electric quadrupole (E2) matrix elements of a large number of forbidden transitions using an all-order relativistic many-body method and compare them with the previously reported values for a few selective transitions. Compilation of both the E1 and E2 transition matrix elements, will now provide a more complete knowledge about the transition properties of the considered singly charged alkaline earth-metal ions. Similarly, the listed precise values of tune-out and magic wavelengths due to the dominant E1 polarizabilities can be helpful to conduct experiments using the above ions with reduced systematics. Therefore, all these data will be immensely useful for various applications for carrying out the high-precision experiments and laboratory simulations in atomic physics, and interpreting transition lines in the astrophysical observations.

physics.atom-ph↗

arXiv2021

Bohr's Phenomenon for Some Univalent Harmonic Functions

In 1914 Bohr proved that there is an $r_0 \in(0,1)$ such that if a power series $\sum_{m=0}^\infty c_m z^m$ is convergent in the open unit disc and $|\sum_{m=0}^\infty c_m z^m|<1$ then, $\sum_{m=0}^\infty |c_m z^m|<1$ for $|z|<r_0$. The largest value of such $r_0$ is called the Bohr radius. In this article, we find Bohr radius for some univalent harmonic mappings having different dilatations and in addition, also compute Bohr radius for the functions convex in one direction.

math.CV↗

arXiv2020

van der Waals coefficients of the multi-layered MoS$_2$ with alkali metals

The van der Waals coefficients and the separation dependent retardation functions of the interactions between the atomically thin films of the multi-layered transition metal molybdenum disulfide (MoS$_2$) dichalcogenides with the alkali atoms are investigated. First, we determine the frequency-dependent dielectric permittivity and intrinsic carrier density values for different layers of MoS$_2$ by adopting various fitting models to the recently measured optical data reported by Yu and co-workers [Sci. Rep. {\bf 5}, 16996 (2015)] using spectroscopy ellipsometry. Then, dynamic electric dipole polarizabilities of the alkali atoms are evaluated very accurately by employing the relativistic coupled-cluster theory. We also demonstrate the explicit change in the above coefficients for different number of layers. These studies are highly useful for the optoelectronics, sensing and storage applications using layered MoS$_2$.

cond-mat.mtrl-sci↗

arXiv2019

An Alternative Approach to Convolutions of Harmonic Mappings

Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic mappings. So, researchers started exploring properties of convolutions of some specific univalent harmonic mappings and while doing so, they have mostly used well known Cohn's rule or/and Schur-Cohn's algorithm, which involves computations that are very cumbersome. The main objective of this article is to present an alternative approach, which requires very less computational efforts and allows us to prove more general results. Most of the earlier known results follow as particular cases of the results proved herein.

math.CV↗

arXiv2018

Higher-component quadrupole polarizabilities: Estimations for the clock states of the alkaline earth-metal ions

Derivations for the higher tensor components of the quadrupole polarizabilities are given and their values for the metastable states of the Ca$^+$, Sr$^+$ and Ba$^+$ alkaline earth-metal ions are estimated. We also give the scalar quadrupole polarizabilities of the ground and metastable states of these ions to compare our results with the previously available theoretical and experimental results. Reasonably good agreement between our calculations with the previous values of scalar quadrupole polarizabilities demonstrate their correctness. The reported scalar and tensor quadrupole polarizabilities could be very useful to estimate the uncertainties due to the gradient of the electric fields in the clock frequencies of the above alkaline earth-metal ions when accuracies of these frequency measurements attain below 10$^{-19}$ precision level.

physics.atom-ph↗

arXiv2017

Annexing magic and tune-out wavelengths to the clock transitions of the alkaline-earth metal ions

We present additional magic wavelengths ($λ_{\rm{magic}}$) for the clock transitions in the alkaline-earth metal ions considering circular polarized light aside from our previously reported values in [J. Kaur et al., Phys. Rev. A {\bf 92}, 031402(R) (2015)] for the linearly polarized light. Contributions from the vector component to the dynamic dipole polarizabilities ($α_d(ω)$) of the atomic states associated with the clock transitions play major roles in the evaluation of these $λ_{\rm{magic}}$, hence facilitating in choosing circular polarization of lasers in the experiments. Moreover, the actual clock transitions in these ions are carried out among the hyperfine levels. The $λ_{\rm{magic}}$ values in these hyperfine transitions are estimated and found to be different from $λ_{\rm{magic}}$ for the atomic transitions due to different contributions coming from the vector and tensor part of $α_d(ω)$. Importantly, we also present $λ_{\rm{magic}}$ values that depend only on the scalar component of $α_d(ω)$ for their uses in a specially designed trap geometry for these ions so that they can be used unambiguously among any hyperfine levels of the atomic states of the clock transitions. We also present $α_d(ω)$ values explicitly at the 1064 nm for the atomic states associated with the clock transitions which may be useful for creating "high-field seeking" traps for the above ions using the Nd:YAG laser. The tune out wavelengths at which the states would be free from the Stark shifts are also presented. Accurate values of the electric dipole matrix elements required for these studies are given and trends of electron correlation effects in determining them are also highlighted.

physics.atom-ph↗

arXiv2016

Determination of magic wavelengths for the $7s ~ {^2}S_{1/2}-7p ~ {^2}P_{3/2,1/2}$ transitions in Fr atom

Magic wavelengthsfor the $7S_{1/2}-7P_{1/2,3/2}$ transitions in Fr were reported by Dammalapati \textit{et al.} in [Phys. Rev. A 93, 043407 (2016)]. These $λ_{\rm{magic}}$ were determined by plotting dynamic polarizabilities ($α$) of the involved states with the above transitions against a desired range of wavelength. Electric dipole (E1) matrix elements listed in [J. Phys. Chem. Ref. Data 36, 497 (2007)], from the measured lifetimes of the $7P_{1/2,3/2}$ states and from the calculations considering core-polarization effects in the relativistic Hartree-Fock (HFR) method, were used to determine $α$. However, contributions from core correlation effects and from the E1 matrix elements of the $7P-7S$, $7P-8S$ and $7P-6D$ transitions to $α$ of the $7P$ states were ignored. In this work, we demonstrate importance of these contributions and improve accuracies of $α$ further by replacing the E1 matrix elements taken from the HFR method by the values obtained employing relativistic coupled-cluster theory. Our static $α$ are found to be in excellent agreement with the other available theoretical results; whereas substituting the E1 matrix elements used by Dammalapati \textit{et al.} give very small $α$ values for the $7P$ states. Owing to this, we find disagreement in $λ_{\rm{magic}}$ reported by Dammalapati \textit{et al.} for linearly polarized light; especially at wavelengths close to the D-lines and in the infrared region. As a consequence, a $λ_{\rm{magic}}$ reported at 797.75 nm which was seen supporting a blue detuned trap in their work is now estimated at 771.03 nm and is supporting a red detuned trap. Also, none of our results match with the earlier results for circularly polarized light. Moreover, our static values of $α$ will be very useful for guiding experiments to carry out their measurements.

physics.atom-ph↗

arXiv2016

Magnetic sublevel independent magic wavelengths: Application in the Rb and Cs atoms

A generic scheme to trap atoms at the magic wavelengths ($λ_{\rm{magic}}$s) that are independent of vector and tensor components of the interactions of the atoms with the external electric field is presented. The $λ_{\rm{magic}}$s for the laser cooling D2 lines in the Rb and Cs atoms are demonstrated and their corresponding polarizability values without vector and tensor contributions are given. Consequently, these $λ_{\rm{magic}}$s are independent of magnetic sublevels and hyperfine levels of the atomic states involved in the transition, thus, can offer unique approaches to carry out many high precision measurements with minimal systematics. Inevitably, the proposed technique can also be used for electronic or hyperfine transitions in other atomic systems.

physics.atom-ph↗

arXiv2016

Comparing magic wavelengths for the $6s ~ {^2}S_{1/2}-6p ~ {^2}P_{1/2,3/2}$ transitions of Cs using circularly and linearly polarized light

We demonstrate magic wavelengths, at which external electric field produces null differential Stark shifts, for the $6s ~ {^2}S_{1/2}-6p ~ {^2}P_{1/2,3/2}$ transitions in the Cs atom due to circularly polarized light. In addition, we also obtain magic wavelengths using linearly polarized light, in order to verify the previously reported values, and make a comparative study with the values obtained for circularly polarized light. A number of these wavelengths are found to be in the optical region and could be of immense interest to experimentalists for carrying out high precision measurements. To obtain these wavelengths, we have calculated dynamic dipole polarizabilities of the ground, $6p ~{^2}P_{1/2}$ and $6p ~{^2}P_{3/2}$ states of Cs. We use the available precise values of the electric dipole (E1) matrix elements of the transitions that give the dominant contributions from the lifetime measurements of the excited states. Other significantly contributing E1 matrix elements are obtained by employing a relativistic coupled-cluster singles and doubles method. The accuracies of the dynamic polarizabilities are substantiated by comparing the static polarizability values with the corresponding experimental results.

physics.atom-ph↗

arXiv2016

Dispersion coefficients for the interaction of inert gas atoms with alkali and alkaline earth ions and alkali atoms with their singly ionized ions

We report the dispersion coefficients for the interacting inert gas atoms with the alkali ions, alkaline earth ions and alkali atoms with their singly charged ions. We use our relativistic coupled-cluster method to determine dynamic dipole and quadrupole polarizabilities of the alkali atoms and singly ionized alkaline earth atoms, whereas a relativistic random phase approximation approach has been adopted to evaluate these quantities for the closed-shell configured inert gas atoms and the singly and doubly ionized alkali and alkaline earth atoms, respectively. Accuracies of these results are adjudged from the comparison of their static polarizability values with their respective experimental results. These polarizabilities are further compared with the other theoretical results. Reason for the improvement in the accuracies of our estimated dispersion coefficients than the data listed in [At. Data and Nucl. Data Tables 101, 58 (2015)] are discussed. Results for some of the atom-ion interacting systems were not available earlier, these results and the other reported improved results will be very useful for the comprehensive understanding of the collisional physics involving these atom-atom and atom-ion interactions in the cold atom and atom-ion hybrid trapping experiments at the low-temperature regime.

physics.atom-ph↗

arXiv2015

Magic wavelengths in the alkaline earth ions

We present magic wavelengths for the $nS$ - $nP_{1/2,3/2}$ and $nS$ - $mD_{3/2,5/2}$ transitions, with the respective ground and first excited $D$ states principal quantum numbers $n$ and $m$, in the Mg$^+$, Ca$^+$, Sr$^+$ and Ba$^+$ alkaline earth ions for linearly polarized lights by plotting dynamic polarizatbilities of the $nS$, $nP_{1/2,3/2}$ and $mD_{3/2,5/2}$ states of the ions. These dynamic polarizabilities are evaluated by employing a relativistic all-order perturbative method and their accuracies are ratified by comparing their static values with the available high precision experimental or other theoretical results. Moreover, some of the magic wavelengths identified by us in Ca$^+$ concurs with the recent measurements reported in [{\bf Phys. Rev. Lett. 114, 223001 (2015)}]. Knowledge of these magic wavelengths are propitious to carry out many proposed high precision measurements trapping the above ions in the electric fields with the corresponding frequencies.

physics.atom-ph↗

arXiv2014

Systematic Shifts for Ytterbium-ion Optical Frequency Standards

The projected systematic uncertainties of single trapped Ytterbium-ion optical frequency standards are estimated for the quadrupole and octupole transitions which are at wavelengths 435.5 nm and 467 nm, respectively. Finite temperature of the ion and its interaction with the external fields introduce drift in the measured frequency compared to its absolute value. Frequency shifts due to electric quadrupole moment, induced polarization and excess micromotion of the ion depend on electric fields, which are estimated in this article. Geometry of the trap electrodes also result in unwanted electric fields which have been considered in our calculation. Magnetic field induced shift and Stark shifts due to electro-magnetic radiation at a surrounding temperature are also estimated. At CSIR-NPL, we are developing a frequency standard based on the octupole transition for which the systematic uncertainties are an order of magnitude smaller than that using the quadrupole transition, as described here.

physics.atom-ph↗

arXiv2014

Convolution properties of univalent harmonic mappings convex in one direction

Let $\ast$ and $\widetilde {\ast}$ denote the convolution of two analytic maps and that of an analytic map and a harmonic map respectively. Pokhrel [1] proved that if $f = h+\overline{g}$ is a harmonic map convex in the direction of $e^{iγ}$ and $ϕ$ is an analytic map in the class DCP, then $f\widetilde{\ast} ϕ= h\widetilde{\ast}ϕ+ \overline{g\widetilde{\ast}ϕ}$ is also convex in the direction of $e^{iγ}$, provided $f\widetilde{\ast}ϕ$ is locally univalent and sense-preserving. In the present paper we obtain a general condition under which $f\widetilde{\ast} ϕ$ is locally univalent and sense-preserving. Some interesting applications of the general result are also presented.

math.CV↗

arXiv2013

On harmonic convolutions involving a vertical strip mapping

Let f_β= h_β+\bar{g}_βand F_a = H_a +\bar{G}_a be harmonic mappings obtained by shearing of analytic mappings h_β+g_β= 1/(2i\sinβ)log((1 + ze^{iβ})/(1 + ze^{-iβ})), 0<β<πand H_a+G_a = z/(1-z), respectively. Kumar et al. [5] conjectured that if ω(z)=e^{iθ}z^n (θ\in R, n\in N) and ω_a(z)=(a-z)/(1-az), a\in(-1,1) are dilatations of f_βand F_a, respectively, then F_a\ast f_β\in S_H^0 and is convex in the direction of the real axis provided a\in[(n-2)/(n + 2), 1).They claimed to have verified the result for n = 1, 2, 3 and 4 only. In the present paper, we settle the above conjecture in the affirmative for β=π/2 and for all n\in N.

math.CV↗

arXiv2013

An application of Cohn's rule to convolutions of univalent harmonic mappings

Dorff et al. [4], proved that the harmonic convolution of right half-plane mapping with dilatation -z and mapping f_β= h_β+ \bar{g}_β, where f_βis obtained by shearing of analytic vertical strip mapping, with dilatation e^{iθ}z^n; n = 1,2,θ\in R, is in S_H^0 and is convex in the direction of the real axis. In this paper, by using Cohn's rule, we generalize this result by considering dilatations (a-z)/(1-az), a\in (-1,1) and e^{iθ} z^n (n\in N;θ\in R) of right half-plane mapping and f_β, respectively.

math.CV↗

arXiv2013

Linear combinations of univalent harmonic mappings convex in the direction of the imaginary axis

In the present paper, we introduce a family of univalent harmonic functions, which map the unit disk onto domains convex in the direction of the imaginary axis. We find conditions for the linear combinations of mappings from this family to be univalent and convex in the direction of the imaginary axis. Linear combinations of functions from this family and harmonic mappings obtained by shearing of analytic vertical strip maps are also studied.

math.CV↗

arXiv2013

Order of convexity of Integral Transforms and Duality

Recently, Ali et al defined the class $\mathcal{W}_β(α, γ)$ consisting of functions $f$ which satisfy $$\Re e^{iϕ}\left((1-α+2γ)\frac{f(z)}{z}+(α-2γ)f'(z)+γzf''(z)-β\right)>0,$$ for all $z\in E=\left\{z : |z|<1\right\}$ and for $α, γ\geq0$ and $β<1$, $ϕ\in \mathbb{R}$ (the set of reals). For $f\in{\mathcal{W}_β(α, γ)}$, they discussed the convexity of the integral transform $$V_λ(f)(z):=\int_{0}^{1}λ(t)\frac{f(tz)}{t}dt,$$ where $λ$ is a non-negative real-valued integrable function satisfying the condition $\displaystyle\int_{0}^{1}λ(t)dt=1$. The aim of present paper is to find conditions on $λ(t)$ such that $V_λ(f)$ is convex of order $δ$ ($0\leqδ\leq1/2$) whenever $f\in{\mathcal{W}}_β(α, γ)$. As applications, we study various choices of $λ(t)$, related to classical integral transforms.

math.CV↗