Three earlier relativistic coupled-cluster (RCC) calculations of dipole polarizability ($α_d$) of the Cd atom are not in good agreement with the available experimental value of $49.65(1.65) \ e a_0^3$. Among these two are finite-field approaches in which the relativistic effects have been included approximately, while the other calculation uses a four component perturbed RCC method. However, another work adopting an approach similar to the latter perturbed RCC method gives a result very close to that of experiment. The major difference between these two perturbed RCC approaches lies in their implementation. To resolve this ambiguity, we have developed and employed the relativistic normal coupled-cluster (RNCC) theory to evaluate the $α_d$ value of Cd. The distinct features of the RNCC method are that the expression for the expectation value in this approach terminates naturally and that it satisfies the Hellmann-Feynman theorem. In addition, we determine this quantity in the finite-field approach in the framework of A four-component relativistic coupled-cluster theory. Considering the results from both these approaches, we arrive at a reliable value of $α_d=46.02(50) \ e a_0^3$. We also demonstrate that the contribution from the triples excitations in this atom is significant.
Experimental results and high-level quantum chemical ab initio calculations of the static polarizability $α_0=α(ω=0)$ of the cadmium ${^1S_0}$ state are still in marked disagreement. Here we analyze this discrepancy by using experimentally determined dipole oscillator strength distributions (DOSD). It will be shown that within this procedure the experimentally determined static polarizability $α_0$ will shift from $49.7 \pm 1.6~$au to considerably lower values. We now conclude an experimentally determined polarizability of $α_0=47.5 \pm 2.0~$au in much better agreement with the latest calculat…
Using a long-range polarization potential for HeH$^{+}$, we can obtain an empirical value for the Boltzmann constant $k_{B}$ with an order of magnitude greater precision than the previous best experimental value based on the dipole polarizability of $^{4}$He. We find that relativistic and QED effects of order $α_{\rm FS}^{3}$ in the fine structure constant are crucial in the quadrupole polarizability in order to fit the dipole polarizbility with this precision using the polarization potential. By calculating finite-mass corrections for $^{3}$He, we also present theoretical values for the dipol…
We present electric dipole polarizabilities ($α_d$) of the alkali-metal negative ions, from H$^-$ to Fr$^-$, by employing four-component relativistic many-body methods. Differences in the results are shown by considering Dirac-Coulomb (DC) Hamiltonian, DC Hamiltonian with the Breit interaction, and DC Hamiltonian with the lower-order quantum electrodynamics interactions. At first, these interactions are included self-consistently in the Dirac-Hartree-Fock (DHF) method, and then electron correlation effects are incorporated over the DHF wave functions in the second-order many-body perturbation …
The static dipole polarizabibility for the $1sσ$ electron state of the $\mathrm{H}_{2}^{+}$ hydrogen molecular ion is calculated within Born-Oppenheimer approximation. The variational expansion with randomly chosen exponents has been used for numerical studies. The results obtained for the dipole polarizability are accurate to the nine digits.
High precision measurement of the static dipole polarizability of cesium
用激光冷却和发射的铯原子在电场中的飞行时间测量了铯原子6S_1/2标量偶极极化率α_0。我们发现α_0 = 6.611+-0.009 x 10^-39 C m^2/V= 59.42+-0.08 x 10^-24 cm^3 = 401.0+-0.6 a_0^3。0.14%的不确定度比之前的测量提高了14倍。6P_1/2和6P_3/2寿命以及6S_1/2铯-铯分散系数C_6的值使用Derevianko和Porsev的程序[Phys.Rev.A65，053403（2002）]从α_0确定。
The static dipole polarizability for the hydrogen molecular ions H$_2^+$, HD$^+$, and D$_2^+$ are calculated. These new data for polarizability takes into account the leading order relativistic corrections to the wave function of the three-body system resulted from the Breit-Pauli Hamiltonian of $mα^4$ order. Our study covers a wide range of rotational ($L=0-5$) and vibrational ($v=0-10$) states, which are of practical interest for precision spectroscopy of the hydrogen molecular ions.
The perturbed relativistic coupled-cluster (PRCC) theory is applied to calculate the electric dipole polarizabilities of alkaline Earth metal atoms. The Dirac-Coulomb-Breit atomic Hamiltonian is used and we include the triple excitations in the relativistic coupled-cluster (RCC) theory. The theoretical issues related to the triple excitation cluster operators are described in detail and we also provide details on the computational implementation. The PRCC theory results are in good agreement with the experimental and previous theoretical results. We, then, highlight the importance of consideri…
Nonrelativistic and relativistic coupled-cluster calculations extrapolated to the complete basis set limit including excitations up to the quintuple level (CCSDTQP) were carried out to accurately determine the static electric dipole polarizability of the closed-shell palladium atom. The resulting value of $α$ = 26.14(10) a.u. implies that palladium has the smallest dipole polarizability of all known elemental metal atoms due to its unique 4d$^{10}$5s$^0$ configuration. Relativistic effects are found to be already sizeable ($Δ_Rα$= +1.86~a.u.) compared to electron correlation ($Δ_Cα$= +5.06~a.u…
$^{129}$Xe is an important candidate for the searches of electric dipole moments due to violations of time-reversal and parity violations in diamagnetic atoms. In view of the similarities between the electric dipole moment and the polarizability from the point of view of many-body theory, we have performed rigorous calculations of the ground state polarizability of $^{129}$Xe using a self consistent relativistic coupled-cluster method and the relativistic normal coupled-cluster method. The discrepancy between the results from these two methods is two percent, but each of them differs from the …
We develop a method based on the relativistic coupled-cluster theory to incorporate a perturbative interaction to the no-pair Dirac-Coulomb atomic Hamiltonian. The method is general and suitable to incorporate any perturbation Hamiltonian in a many electron atom or ion. Using this perturbed relativistic coupled-cluster (PRCC) theory we calculate the electric dipole polarizability, $α$, of Neon. The linearized PRCC results are in very good agreement with the experimental value. However, the results of the nonlinear PRCC shows larger uncertainty but it is consistent with the observations from ea…
The dynamic electric dipole polarizability function for the magnesium atom is formed by assembling the atomic electric dipole oscillator strength distribution from combinations of theoretical and experimental data for resonance oscillator strengths and for photoionization cross sections of valence and inner shell electrons. Consistency with the oscillator strength (Thomas-Reiche-Kuhn) sum rule requires the adopted principal resonance line oscillator strength to be several percent lower than the values given in two critical tabulations, though the value adopted is consistent with a number of th…
The non-relativistic static and dynamic dipole polarizabilities of hydrogen atom experiencing a cylindrical confinement are investigated. Two methods based on B-Splines are used for the computations of the energies and wavefunctions. The first method is a variational based method while the second one proceeds by a fit of the non-separable Coulomb potential in the product form. The computed energies compare very well with previous computations. They converge, as well as the dipole polarizability, to the exact unconfined free atom values. The fit approach is found to be advantageous, as it helps…
A model for positron binding to polar molecules is considered by combining the dipole potential outside the molecule with a strongly repulsive core of a given radius. Using existing experimental data on binding energies leads to unphysically small core radii for all of the molecules studied. This suggests that electron-positron correlations neglected in the simple model play a large role in determining the binding energy. We account for these by including polarization potential via perturbation theory and non-perturbatively. The perturbative model makes reliable predictions of binding energies…
We calculate ground-state energies and densities of a helium atom confined in an impenetrable spherical box within density functional theory. These calculations are performed by variationally solving Kohn-Sham equation with the ground-state orbital expanded in terms of Slater-type orbitals. Using the ground-state densities we then calculate static linear polarizability and nonlinear hyperpolarizability and study their variation with the radius of confinement. We find that polarizability decreases monotonically with decreasing confinement radius and the hyperpolarizability not only decreases bu…
Dipolar atoms have unique properties, making them interesting for laser cooling and quantum simulations. But, due to relatively large orbital momentum in the ground state these atoms may have large dynamic tensor and vector polarizabilities in the ground state. This enables the formation of spin-dependent optical traps. In this paper real part of tensor and vector dynamic polarizability was experimentally measured and compared to theoretical simulation. For an optical dipole trap operating around 532.07 nm tensor, polarizability was found to be $ - 145 \pm 53\,\,{\rm{a}}{\rm{.u}}{\rm{.}}$ and …
We have developed a Fock-space relativistic coupled-cluster theory based method for the calculation of electric dipole polarizability of one-valence atoms and ions. We employ this method to compute the ground-state and spin-orbit coupled excited state electric dipole polarizability of Al and In. To check the quality of many-electron wavefunctions, we also compute the excitation energies of some low-lying states of Al and In. The effects of Breit interaction and QED corrections from the Uehling potential and the self-energy are included to improve the accuracy of $α$ further. Our recommended va…
We compute the ground-state electric dipole polarizability of group-IIIA ions using the perturbed relativistic coupled-cluster (PRCC) theory. To account for the relativistic effects and QED corrections, we use the Dirac-Coulomb-Breit Hamiltonian with the corrections from the Uehling potential and the self-energy. The effects of triple excitations are considered perturbatively in the PRCC. Our PRCC results for $α$ are good in agreement with the previous theoretical results for all the ions. From our computations we find that the nonlinear terms in PRCC have significant contributions and must be…
In this study, accurate static dipole polarizability and hyperpolarizability are calculated for Al$^+$ ground state 3s$^{2}$ $^{1}$S$_{0}$ and excited state $3s3p$ $^{3}$P$_{J}$ with $J$=0, 1, 2. The finite-field computations use energies obtained with the relativistic configuration interaction approach and the relativistic coupled-cluster approach. Excellent agreement with previously recommended values is found for the dipole polarizability of Al$^{+}$ ground state 3s$^{2}$ $^{1}$S$_{0}$ and excited state $3s3p$ $^{3}$P$_{0}$ as well as the hyperpolarizability of the ground state 3s$^{2}$ $^{…
We employ a fully relativistic coupled-cluster theory to calculate the ground-state electric dipole polarizability and electron correlation energy of superheavy elements Cn, Nh$^+$ and Og. To assess the trend of electron correlation as function of $Z$, we also calculate the correlation energies for three lighter homologs--Zn, Cd and Hg; Ga$^+$, In$^+$ and Tl$^+$; Kr, Xe and Rn--for each superheavy elements. The relativistic effects and quantum electrodynamical corrections are included using the Dirac-Coulomb-Breit Hamiltonian with the corrections from the Uehling potential and the self-energy.…
We use perturbed relativistic coupled-cluster (PRCC) theory to compute the electric dipole polarizabilities $α$ of Zn, Cd and Hg. The computations are done using the Dirac-Coulomb-Breit Hamiltonian with Uehling potential to incorporate vacuum polarization corrections. The triple excitations are included perturbatively in the PRCC theory, and in the unperturbed sector, it is included non-perturbatively. Our results of $α$, for all the three elements, are in excellent agreement with the experimental data. The other highlight of the results is the orbital energy corrections from Breit interaction…
Fock-space perturbed relativistic coupled-cluster calculations of electric dipole polarizability and nuclear spin-dependent parity non-conservation in Cs
We present revised measurements of the static electric dipole polarizabilities of K, Rb, and Cs based on atom interferometer experiments presented in [Phys. Rev. A 2015, 92, 052513] but now re-analyzed with new calibrations for the magnitude and geometry of the applied electric field gradient. The resulting polarizability values did not change, but the uncertainties were significantly reduced. Then we interpret several measurements of alkali metal atomic polarizabilities in terms of atomic oscillator strengths $f_{ik}$, Einstein coefficients $A_{ik}$, state lifetimes $τ_{k}$, transition dipole…
The QED contribution to the dipole polarizability of the $^4$He atom was computed, including the effect of finite nuclear mass. The computationally most challenging contribution of the second electric-field derivative of the Bethe logarithm was obtained using two different methods: the integral representation method of Schwartz and the sum-over-states approach of Goldman and Drake. The results of both calculations are consistent, although the former method turned out to be much more accurate. The obtained value of the electric-field derivative of the Bethe logarithm, equal to $0.048\,557\,2(14…
We use perturbed relativistic coupled-cluster (PRCC) theory to calculate the electric dipole polarizability of noble gas atoms Ar, Kr, Xe and Rn. We also provide a detailed description of the nonlinear terms in the PRCC theory and consider the Dirac-Coulomb-Breit atomic Hamiltonian for the calculations. We find that the largest contribution from Breit interaction to the electric dipole polarizability is 0.1%, in the case of Rn. As we go from Ar to Rn, based on the pattern in the random phase approximation effects, the contraction of the outermost $p_{1/2}$ due to relativistic corrections is di…
Ultracold atoms confined in a dipole trap are submitted to a potential whose depth is proportional to the real part of their dynamic dipole polarizability. The atoms also experience photon scattering whose rate is proportional to the imaginary part of their dynamic dipole polarizability. In this article we calculate the complex dynamic dipole polarizability of ground-state erbium, a rare-earth atom that was recently Bose-condensed. The polarizability is calculated with the sum-over-state formula inherent to second-order perturbation theory. The summation is performed on transition energies and…
To operate an optical lattice clock at a fractional uncertainty below $10^{-17}$, one must typically consider not only electric-dipole (E1) interaction between an atom and the lattice light field when characterizing the resulting lattice light shift of the clock transition but also higher-order multipole contributions, such as electric-quadrupole (E2) and magnetic-dipole (M1) interactions. However, strongly incompatible values have been reported for the E2-M1 polarizability difference of the clock states $(5s5p)\,{}^{3}\mathrm{P}_{0}$ and $(5s^2)\,{}^{1}\mathrm{S}_{0}$ of strontium [Ushijima e…
The efficiency of optical trapping of ultracold atoms depend on the atomic dynamic dipole polarizability governing the atom-field interaction. In this article, we have calculated the real and imaginary parts of the dynamic dipole polarizability of dysprosium in the ground and first excited level. Due to the high electronic angular momentum of those two states, the polarizabilities possess scalar, vector and tensor contributions that we have computed, on a wide range of trapping wavelengths, using the sum-over-state formula. Using the same formalism, we have also calculated the $C_6$ coefficien…
We present precise values of electric polarizabilities for the ground state of Zn due to second-order dipole and quadrupole interactions, and due to third-order dipole-quadrupole interactions. These quantities are evaluated in the linear response theory framework by employing a relativistic version of the normal coupled-cluster (NCC) method. The calculated dipole polarizability value is compared with available experimental and other theoretical results including those are obtained using the ordinary coupled-cluster (CC) methods in both finite-field and expectation value evaluation approaches. …
We apply relativistic many-body methods to compute static differential polarizabilities for transitions inside the ground-state hyperfine manifolds of monovalent atoms and ions. Knowing this transition polarizability is required in a number of high-precision experiments, such as microwave atomic clocks and searches for CP-violating permanent electric dipole moments. While the traditional polarizability arises in the second-order of interaction with the externally-applied electric field, the differential polarizability involves additional contribution from the hyperfine interaction of atomic el…
The finite field calculations are performed for two heavy frequency-standard candidates In$^+$ and Sr. The progressive hierarchy of electron correlations is implemented by the relativistic coupled-cluster and configuration interaction methods combined with basis set of increasing size. The dipole polarizabilities, dipole hyperpolarizabilities, quadrupole moments, and quadrupole polarizabilities are recommended for the ground state 5s$^2$ $^1S_0$ and low-lying states 5s5p $^3P^{\rm o}_{0,1,2}$ of In$^+$ and Sr. Comparative study of the fully and scalar relativistic electron correlation calculat…
We characterize the anisotropic differential ac-Stark shift for the Dy $626$ nm intercombination transition, induced in a far-detuned $1070$ nm optical dipole trap, and observe the existence of a "magic polarization" for which the polarizabilities of the ground and excited states are equal. From our measurements we extract both the scalar and tensorial components of the dynamic dipole polarizability for the excited state, $α_E^\text{s} = 188 (12)\,α_\text{0}$ and $α_E^\text{t} = 34 (12)\,α_\text{0}$, respectively, where $α_\text{0}$ is the atomic unit for the electric polarizability. We also p…
Ab Initio Calculations of the Static and Dynamic Polarizability of BaOH
University of Groningen（格罗宁根大学）；Nikhef, National Institute for Subatomic Physics（尼霍夫国家亚原子物理研究所）；Indian Institute of Technology Bombay（孟买印度理工学院）；Comenius University（科米纽斯大学）
We measured the ground state electric dipole polarizability of sodium, potassium, and rubidium using a Mach-Zehnder atom interferometer with an electric field gradient. We find alpha_Na=24.11(2)_stat(18)_sys x 10^-24 cm^3, alpha_K=43.06(14)(33), and alpha_Rb=47.24(12)(42). Since these measurements were all performed in the same apparatus and subject to the same systematic errors we can present polarizability ratios with 0.3% precision. We find alpha_Rb/alpha_Na=1.959(5), alpha_K/alpha_Na=1.786(6), and alpha_Rb/alpha_K=1.097(5). We combine our ratio measurements with the higher precision measur…
The second-order Stark effect for a planar Dirac one-electron atom in the ground state is analyzed within the framework of the Rayleigh-Schrödinger perturbation theory, with the use of the Sturmian series expansion of the generalized Dirac-Coulomb Green function. A closed-form analytical expression for the static dipole polarizability of that system is found. The formula involves a generalized hypergeometric function ${}_{3}F_{2}$ with the unit argument. Numerical values of the polarizabilities for relativistic planar hydrogenic atoms with atomic numbers $1\leqslant Z\leqslant68$ are provided …
We report a measurement of the dynamical polarizability of dysprosium atoms in their electronic ground state at the optical wavelength of 1064 nm, which is of particular interest for laser trapping experiments. Our method is based on collective oscillations in an optical dipole trap, and reaches unprecedented accuracy and precision by comparison with an alkali atom (potassium) as a reference species. We obtain values of 184.4(2.4) a.u. and 1.7(6) a.u. for the scalar and tensor polarizability, respectively. Our experiments have reached a level that permits meaningful tests of current theo- reti…
We present mean-field calculations of azimuthally averaged retarded dipole-dipole interactions in a Bose-Einstein condensate induced by a laser, at both long and short wavelengths. Our calculations demonstrate that dipole-dipole interactions become significantly stronger at shorter wavelengths, by as much as 30-fold, due to retardation effects. This enhancement, along with inclusion of the dynamic polarizability, indicate a method of inducing long-range interatomic interactions in neutral atom condensates at significantly lower intensities than previously realized.
We report theoretical determination of the dipole polarizability of the neon atom, including its frequency dependence. Corrections for the relativistic, quantum electrodynamics, finite nuclear mass, and finite nuclear size effects are taken into account. We obtain the value $α_0=2.66080(36)$ for the static polarizability, and $α_2=2.850(7)$ and $α_4=4.932(14)$ for the first two polarizability dispersion coefficients (Cauchy moments); all values are in atomic units (a.u.). In the case of static polarizability, our result agrees with the best experimental determination [C. Gaiser and B. Fellmuth…
We use the perturbed relativistic coupled-cluster theory to compute the static electric dipole polarizabilities of the singly ionized alkali atoms, namely, Na$^+$, $^+$, Rb$^+$, Cs$^+$ and Fr$^+$. The computations use the Dirac-Coulomb-Breit Hamiltonian with the no-virual-pair approximation and we also estimate the correction to the static electric dipole polarizability arising from the Breit interaction.
Sturmian basis set for the Dirac equation with finite nuclear size: Application to polarizability, Zeeman and hyperfine splitting, and vacuum polarization
We have carried out a detailed and systematic study of the correlation energies of inert gas atoms Ne, Ar, Kr and Xe using relativistic many-body perturbation theory and relativistic coupled-cluster theory. In the relativistic coupled-cluster calculations, we implement perturbative triples and include these in the correlation energy calculations. We then calculate the dipole polarizability of the ground states using perturbed coupled-cluster theory.
We report on measurements of the anisotropic dynamical polarizability of Dy near the 626-nm intercombination line, employing modulation spectroscopy in a one-dimensional optical lattice. To eliminate large systematic uncertainties resulting from the limited knowledge of the spatial intensity distribution, we use K as a reference species with accurately known polarizability. This method can be applied independently of the sign of the polarizability, i.e., for both attractive and repulsive optical fields on both sides of a resonance. By variation of the laser polarization we extract the scalar a…
Accurate values for atomic dipole matrix elements are useful in many areas of physics, and in particular for interpreting experiments such as atomic parity violation. Obtaining accurate matrix element values is a challenge for both experiment and theory. A new technique that can be applied to this problem is tune-out spectroscopy, which is the measurement of light wavelengths where the electric polarizability of an atom has a zero. Using atom interferometry methods, tune-out wavelengths can be measured very accurately. Their values depend on the ratios of various dipole matrix elements and are…
Tune-out wavelength for the thulium atom near 576 nm
Russian Quantum Center（俄罗斯量子中心）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；PN Lebedev Institute RAS（俄罗斯科学院P.N.列别捷夫物理研究所）；Bauman Moscow State Technical University（鲍曼莫斯科国立技术大学）；National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)（国立研究核大学MEPhI（莫斯科工程物理学院））
