The magic wavelength for an optical lattice for hydrogen atoms that cancels the lowest order AC Stark shift of the 1S-2S transition is calculated to be 513 nm. The magnitude of AC Stark shift $ΔE=-1.19$ kHz/(10kW/cm$^2$) and the slope $dΔE/dν= -27.7$ Hz/(GHz $\cdot$ 10 kW/cm$^2$) at the magic wavelength suggests that a stable and narrow linewidth trapping laser is necessary to achieve a deep enough optical lattice to confine hydrogen atoms in a way that gives a small enough light shift for the precision spectroscopy of the 1S-2S transition.
Recently, we studied the magic wavelength for the atomic hydrogen 1S-2S transition [A.K., Phys. Rev. A 92, 042507 (2015)]. An explicit summation over virtual atomic states of the discrete part of the hydrogen spectrum was performed to evaluate the atomic polarizability. In this paper, we supplement the contribution of the continuum part of the spectrum and add the reduced-mass correction. The magic wavelength, at which the lowest-order ac Stark shifts of the 1S and 2S states are equal, is found to be equal to 514.6 nm. The ac Stark shift at the magic wavelength is -221.6 Hz / (kW/cm^2), and th…
In a standing wave of light, a difference in spatial distributions of multipolar atom-field interactions may alter the definition of the magic wavelength to minimize the uncertainty of optical lattice clocks. We show that the magic wavelength can be determined so as to eliminate the spatial mismatch in electric dipole, magnetic dipole, and electric quadrupole interactions for specific combinations of standing waves. Experimental prospects of such lattices used with a blue magic wavelength are discussed.
Light at a magic-zero wavelength causes zero energy shift for an atom. We measured the longest magic-zero wavelength for ground state potassium atoms to be $λ_\textrm{zero}=768.971(1)$ nm, and we show how this provides an improved experimental benchmark for atomic structure calculations. This $λ_\textrm{zero}$ measurement determines the ratio of the potassium atom D1 and D2 line strengths with record precision. It also demonstrates a new application for atom interferometry, and we discuss how decoherence will fundamentally limit future measurements of magic-zero wavelengths.
We demonstrate experimentally the existence of magic wavelengths and determine the ratio of the oscillator strengths for a single trapped ion. For the first time, two magic wavelengths for the 40Ca+ clock-transition are measured simultaneously with high precision, giving Lamda|mj|=1/2 = 395.7992(7) nm and Lamda|mj|=3/2 = 395.7990(7) nm. By tuning a laser to an intermediate wavelength between two transitions (4s1/2-4p1/2 and 4s1/2-4p3/2) of 40Ca+, the sensitivity of the clock transition Stark shift to the oscillator strengths for the resonance transition has been greatly enhanced. With the meas…
We demonstrate an atom interferometer operating on the $^1S_0-{}^3P_0$ clock transition of $^{87}$Sr atoms in a "magic" optical guide, where the light shift perturbations of the guiding potential are canceled. As a proof-of-principle demonstration, a Mach-Zehnder interferometer is set horizontally to map the acceleration introduced by the focused optical guide. This magic guide interferometer on the clock transition is applicable to atomic elements where magic wavelengths can be found. Possible applications of the magic guide interferometer, including a hollow-core fiber interferometer and gra…
Extending the search for the magic wavelengths using the circularly polarized light in rubidium [Phys. Rev. A 86, 033416 (2012)], we pursue here to look for the magic wavelengths in the $ns-np_{1/2,3/2}$ transitions of Li, Na and K alkali atoms. These wavelengths for all possible sub-levels are given and compared with the corresponding wavelengths due to the linearly polarized light. We have also mentioned explicitly the dynamic polarizabilities at few important wave lengths. The present study suggests that it is possible to carry out state insensitive trapping of different alkali atoms using …
We calculate and measure the magic wavelengths for the $6s^2{}\,^1S_0-6s6p\,{}^3P_1$ intercombination transition of the neutral ytterbium atom. The calculation is performed with the \textit{ab initio} configuration interaction (CI) + all-order method. The measurement is done with laser spectroscopy on cold atoms in an optical dipole trap. The magic wavelengths are determined to be 1035.68(4) nm for the $π$ transition ($Δm = 0$) and 1036.12(3) nm for the $σ$ transitions ($|Δm| = 1$) in agreement with the calculated values. Laser cooling on the narrow intercombination transition could achieve be…
The dynamic polarizabilities of the atomic states with angular momentum $j> \frac12$ are sensitive to the angle between the quantization axis $\hat{e}_z$ and the polarization vector $\hat{\mathbfε}$ owing to the contribution of anisotropic tensor polarizabilities. The magic wavelength, at which the differential Stark shift of an atomic transition nullifies, depends on this angle. We identified the magic wavelengths for the $4s_{\frac12}\to3d_{\frac32,\frac52}$ transitions of Ca$^{+}$ ions at different angles between $\hat{e}_z$ and $\hat{\mathbfε}$ in the case of linearly polarized light. We f…
For the first time, we experimentally determine the infrared magic wavelength for the $^{40}$Ca$^{+}$ $4s\, ^{2}\!S_{1/2} \rightarrow 3d\,^{2}\!D_{5/2}$ electric quadrupole transition by observation of the light shift canceling in $^{40}$Ca$^{+}$ optical clock. A "magic" magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9)~nm, which is not only in good agreement with theoretical predictions but also more precise by a factor…
Magic wavelength at 477 nm for the strontium clock transition
Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学学院南洋量子中心）；MajuLab, International Joint Research Unit IRL 3654, CNRS, Université Côte d’Azur, Sorbonne Université, National University of Singapore, Nanyang Technological University, Singapore（MajuLab，国际联合研究单位IRL 3654，法国国家科学研究中心，蔚蓝海岸大学，索邦大学，新加坡国立大学，南洋理工大学，新加坡）
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 tunabili…
We theoretically study dynamic scalar polarizabilities of the ground and select long-lived excited states of dysprosium, a highly magnetic atom recently laser cooled and trapped. We demonstrate that there are a set of magic wavelengths of the unpoarized lattice laser field for each pair of states which includes the ground state and one of these excited states. At these wavelengths, the energy shift due to laser field is the same for both states, which can be useful for resolved sideband cooling on narrow transitions and precision spectroscopy. We present an analytical formula which, near reson…
The dynamic dipole polarizabilities of the low-lying states of Ca$^{+}$ for linearly and circularly polarized light are calculated by using relativistic configuration interaction plus core polarization (RCICP) approach. The magic wavelengths, at which the two levels of the transitions have the same ac Stark shifts, for $4s$-$4p_{j,m}$ and $4s$-$3d_{j,m}$ magnetic sublevels transitions are determined. The present magic wavelengths for linearly polarized light agree with the available results excellently. The polarizability for the circularly polarized light has the scalar, vector and tensor com…
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 hig…
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 have calculated ac polarizabilities of the $2 \ ^3S$ and $2 \ ^1S$ states of both $^4$He and $^3$He in the range 318 nm to 2.5 $μ$m and determined the magic wavelengths at which these polarizabilities are equal for either isotope. The calculations, only based on available ab initio tables of level energies and Einstein A coefficients, do not require advanced theoretical techniques. The polarizability contribution of the continuum is calculated using a simple extrapolation beyond the ionization limit, yet the results agree to better than 1% with such advanced techniques. Several promising ma…
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 experim…
A large-scale full-configuration-interaction calculation based on Dirac-Coulomb-Breit (DCB) Hamiltonian is performed for the $2\,^1S_0$ and $2\,^3S_1$ states of helium. The operators of the normal and specific mass shifts are directly included in the DCB framework to take the finite nuclear mass correction into account. High-accuracy energies and matrix elements involved n (the main quantum number) up to 13 are obtained from one diagonalization of Hamiltonian. The dynamic dipole polarizabilities are calculated by using the sum rule of intermediate states. And a series of magic wavelengths with…
Motivated by recent direct measurement of the forbidden $2\,^3S_1\rightarrow3\,^3S_1$ transition in helium [K. F. Thomas et al., Phys. Rev. Lett. 125, 013002(2020)], where the ac Stark shift is one of the main systematic uncertainties, we propose a dichroic two-photon transition measurement for $2\,^3S_1\rightarrow3\,^3S_1$ which could effectively suppress the ac Stark shift by utilizing magic wavelengths: one magic wavelength is used to realize state-insensitive optical trapping, the other magic wavelength is used as one of the two lasers driving the two-photon transition. Carrying out calcul…
We report loading of laser-cooled caesium atoms into a hollow-core photonic-bandgap fiber and confining the atoms in the fiber's 7 $μm$ diameter core with a magic-wavelength dipole trap at $\sim$935 nm. The use of the magic wavelength removes the AC-Stark shift of the 852nm optical transition in caesium caused by the dipole trap in the fiber core and suppresses the inhomogeneous broadening of the atomic ensemble that arises from the radial distribution of the atoms. This opens the possibility to continuously probe the atoms over time scales of a millisecond -- approximately 1000 times longer t…
We present a continuous-wave, 810 nm laser with watt-level powers. Our system is based on difference-frequency generation of 532 nm and 1550 nm fiber lasers in a single pass through periodically poled lithium niobate (PPLN). We measure the broadband spectral noise and residual intensity noise to be compatible with off-resonant dipole trapping of ultracold atoms. Given the large bandwidth of the fiber amplifiers, the output can be optimized for a range of wavelengths, including the strontium clock-magic wavelength of 813 nm. Furthermore, with the exploration of more appropriate nonlinear crysta…
High precision spectroscopy on the $2 \ ^3 S \rightarrow 2 \ ^1 S$ transition is possible in ultracold optically trapped helium but the accuracy is limited by the ac-Stark shift induced by the optical dipole trap. To overcome this problem, we have built a trapping laser system at the predicted magic wavelength of 319.8 nm. Our system is based on frequency conversion using commercially available components and produces over 2 W of power at this wavelength. With this system, we show trapping of ultracold atoms, both thermal ($\sim0.2 \ \mathrm{μK}$) and in a Bose-Einstein condensate, with a trap…
Magic wavelengths for laser trapping of boson isotopes of alkaline-earth Sr, Ca and Mg atoms are investigated while considering terahertz clock transitions between the $^{3}P_{0}, ^{3}P_{1}, ^{3}P_{2}$ metastable triplet states. Our calculation shows that magic wavelengths of trapping laser do exist. This result is important because those metastable states have already been used to realize accurate clocks in the terahertz frequency domain. Detailed discussions for magic wavelength for terahertz clock transitions are given in this paper.
We present an optical approach to compensating for spatially varying ac-Stark shifts that appear on atomic ensembles subject to strong optical control or trapping fields. The introduction of an additional weak light field produces an intentional perturbation between atomic states that is tuned to suppress the influence of the strong field. The compensation field suppresses sensitivity in one of the transition frequencies of the trapped atoms to both the atomic distribution and motion. We demonstrate this technique in a cold rubidium ensemble and show a reduction in inhomogeneous broadening in …
The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the $7s~^2S_{1/2}$, $7p~^2P_{1/2, 3/2}$ and $8s~^{2}S_{1/2}$ levels of the $7s~^{2}S_{1/2}-7p~^{2}P_{1/2,3/2}$ and $7s~^{2}S_{1/2}-8s~^{2}S_{1/2}$ transitions, respectively. Wavelengths in the ultraviolet, visible and near infrared region is identified that are suitable for cooling and trapping. Magic wavelengths between 600-700~nm and 700…
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. …
Extensive calculations of the electric-dipole matrix elements in alkali-metal atoms are conducted using the relativistic all-order method. This approach is a linearized version of the coupled-cluster method, which sums infinite sets of many-body perturbation theory terms. All allowed transitions between the lowest ns, np_1/2, np_3/2 states and a large number of excited states are considered in these calculations and their accuracy is evaluated. The resulting electric-dipole matrix elements are used for the high-precision calculation of frequency-dependent polarizabilities of the excited states…
Magic wavelengths, for which there is no differential ac Stark shift for the ground and excited state of the atom, allow trapping of excited Rydberg atoms without broadening the optical transition. This is an important tool for implementing quantum gates and other quantum information protocols with Rydberg atoms, and reliable theoretical methods to find such magic wavelengths are thus extremely useful. We use a high-precision all-order method to calculate magic wavelengths for the $5s-18s$ transition of rubidium, and compare the calculation to experiment by measuring the light shift for atoms …
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…
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 …
In experiments with trapped atoms, atomic energy levels are shifted by the trapping optical and magnetic fields. Regardless of this strong perturbation, precision spectroscopy may be still carried out using specially crafted, "magic" trapping fields. Finding these conditions for particularly valuable microwave clock transitions in alkalis has so far remained an open challenge. Here I demonstrate that the microwave clock transitions for alkalis may be indeed made impervious to both trapping laser intensity and fluctuations of magnetic fields. I consider driving multiphoton transitions between t…
We experimentally and theoretically determine the magic wavelength of the (5$s^2$)$^{1}S_{0}$$-$(5$s$5$p$)$^{3}P_{0}$ clock transition of $^{111}$Cd to be 419.88(14) nm and 420.1(7) nm. To perform Lamb-Dicke spectroscopy of the clock transition, we use narrow-line laser cooling on the $^{1}S_{0}$$-$$^{3}P_{1}$ transition to cool the atoms to 6 $μ$K and load them into an optical lattice. Cadmium is an attractive candidate for optical lattice clocks because it has a small sensitivity to blackbody radiation and its efficient narrow-line cooling mitigates higher order light shifts. We calculate th…
Improvements in both theory and frequency metrology of few-electron systems such as hydrogen and helium have enabled increasingly sensitive tests of quantum electrodynamics (QED), as well as ever more accurate determinations of fundamental constants and the size of the nucleus. At the same time advances in cooling and trapping of neutral atoms have revolutionized the development of increasingly accurate atomic clocks. Here, we combine these fields to reach the highest precision on an optical tranistion in the helium atom to date by employing a Bose-Einstein condensate confined in a magic wavel…
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…
We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped $^{87}$Rb atoms. Recent progress in metrology exploits so-called "magic wavelengths," whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkalis, due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achi…
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 tota…
We propose blue-detuned optical traps that are suitable for trapping of both ground state and Rydberg excited atoms. Addition of a background compensation field or suitable choice of the trap geometry provides a magic trapping condition for ground and Rydberg atoms at the trap center. Deviations from the magic condition at finite temperature are calculated. Designs that achieve less than 200 kHz differential trap shift between Cs ground and 125s Rydberg states for 10 μK Cs atoms are presented. Consideration of the trapping potential and photoionization rates
Magic-wavelength matter-wave interferometry with optical clock states
Nanyang Technological University（南洋理工大学）；CNRS（法国国家科学研究中心）；Université Côte d’Azur（蔚蓝海岸大学）；Sorbonne Université（索邦大学）；National University of Singapore（新加坡国立大学）；Center for Quantum Technologies（量子技术中心）
Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of large extent of Ry electron wave function on trapping potentials. We find that when the Ry orbit lies outside inflection points in laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron AC polarizability of Ry electron is modulated by intensity landscape and can accept both positive and negative values. We apply these insights to determining magic wavelengths for Ry-ground-state transitions for alkali atoms trapped in infr…
We present the measurements of the photoionisation cross sections of the excited $^1$P$_1$ and $^3$S$_1$ states of ultracold $^{88}$Sr atoms at 389.889 nm wavelength, which is the magic wavelength of the $^{1}$S$_{0}$-${}^{3}$P${}_{0}$ clock transition. The photoionisation cross section of the $^1$P$_1$ state is determined from the measured ionisation rates of $^{88}$Sr in the magneto-optical trap in the $^1$P$_1$ state to be 2.20(50)$\times$10$^{-20}$ m$^2$, while the photoionisation cross section of $^{88}$Sr in the $^3$S$_1$ state is inferred from the photoionisation-induced reduction in th…
Using first-principles calculations, we identify "magic-zero" optical wavelengths, λ_zero, for which the ground-state frequency-dependent polarizabilities of alkali-metal atoms vanish. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. We discuss the use of magic-zero wavelengths for sympathetic cooling in two-species mixtures of alkalis with group-II and other elements of interest. Special cases in which these wavelengths coincide with s…
We optically excite the electronic state $3s3p~^3P_{0}$ in $^{24}$Mg atoms, laser-cooled and trapped in a magic-wavelength lattice. An applied magnetic field enhances the coupling of the light to the otherwise strictly forbidden transition. We determine the magic wavelength, the quadratic magnetic Zeeman shift and the transition frequency to be 468.463(207)$\,$nm, -206.6(2.0)$\,$MHz/T$^2$ and 655 058 646 691(101)$\,$kHz, respectively. These are compared with theoretical predictions and results from complementary experiments. We also developed a high-precision relativistic structure model for m…
Using first-principles calculations, we identify magic wavelengths for the 2s-2p and 2s-3p transitions in lithium. The ns and np atomic levels have the same ac Stark shifts at the corresponding magic wavelength, which facilitates state-insensitive optical cooling and trapping. Tune-out wavelengths for which the ground-state frequency-dependent polarizability vanishes are also calculated. Differences of these wavelengths between 6Li and 7Li are reported. Our approach uses high-precision, relativistic all-order methods in which all single, double, and partial triple excitations of the Dirac-Fock…
D1 magic wavelengths have been predicted for the alkali atoms but are not yet observed to date. We experimentally confirm a D1 magic wavelength that is predicted to lie at 615.87 nm for $^{23}$Na, which we then use to trap and image individual atoms with 80.0(6)% efficiency and without having to modulate the trapping and imaging light intensities. We further demonstrate that the mean loading efficiency remains as high as 74.2(7)% for a 1D array of eight atoms. Leveraging on the absence of trap intensity modulation and lower trap depths afforded by the D1 light, we achieve an order-of-magnitude…
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 substan…
Optical trapping of molecules with long coherence times is crucial for many protocols in quantum information and metrology. However, the factors that limit the lifetimes of the trapped molecules remain elusive and require improved understanding of the underlying molecular structure. Here we show that measurements of vibronic line strengths in weakly and deeply bound $^{88}$Sr$_2$ molecules, combined with \textit{ab initio} calculations, allow for unambiguous identification of vibrational quantum numbers. This, in turn, enables the construction of refined excited potential energy curves that in…
We demonstrate a versatile, rotational-state dependent trapping scheme for the ground and first excited rotational states of $^{23}$Na$^{40}$K molecules. Close to the rotational manifold of a narrow electronic transition, we determine tune-out frequencies where the polarizability of one state vanishes while the other remains finite, and a magic frequency where both states experience equal polarizability. The proximity of these frequencies of only 10 GHz allows for dynamic switching between different trap configurations in a single experiment, while still maintaining sufficiently low scattering…
We develop a theoretical understanding of trapping divalent Rydberg atoms in optical lattices. Because the size of the Rydberg electron cloud can be comparable to the scale of spatial variations of laser intensity, we pay special attention to averaging optical fields over the atomic wavefunctions. Optical potential is proportional to the ac Stark polarizability. We find that in the independent particle approximation for the valence electrons, this polarizability breaks into two contributions: the singly ionized core polarizability and the contribution from the Rydberg electron. Unlike the usua…
The circular polarized laser beam of the ``magic'' wavelength may be used for mixing the $^3P_1$ state into the long-living metastable state $^3P_0$, thus enabling the strictly forbidden $^1S_0$$-$$^3P_0$ ''clock'' transition in even isotopes of alkaline-earth-like atoms, without change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the line width of the "clock" transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on ato…
The zero crossing of the dynamic differential scalar polarizability of the $S_{1/2}-D_{5/2}$ clock transition in $^{138}$Ba$^+$ has been determined to be $459.1614(28)\,$THz. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ($\gtrsim 700\,$nm). In particular it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.
In ponderomotive spectroscopy an amplitude-modulated optical standing wave is employed to probe Rydberg-atom transitions, utilizing a ponderomotive rather than a dipole-field interaction. Here, we engage nonlinearities in the modulation to drive dipole-forbidden transitions up to the fifth order. We reach transition frequencies approaching the sub-THz regime. We also demonstrate magic-wavelength conditions, which result in symmetric spectral lines with a Fourier-limited feature at the line center. Applicability to precision measurement is discussed.
After pumped from $5s_{1/2}$ ground state to $6p_{1/2}$ state, the population inversion between $6s_{1/2}$ and $5p_{1/2,3/2}$ will be established for Rubidium four-level active optical clock. In this paper, we calculate AC Stark shift due to lattice trapping laser which dominates the frequency shift of clock transition in lattice trapped Rubidium four-level active optical clock. Several magic wavelengths are found that can form desired optical lattice trapping potential. By choosing a proper intensity and linewidth of trapping laser, the fractional frequency uncertainty of clock transition due…
We carry out a systematic study of the static and dynamic polarizabilities of the potassium atom using a first-principles high-precision relativistic all-order method in which all single, double, and partial triple excitations of the Dirac-Fock wave functions are included to all orders of perturbation theory. Recommended values are provided for a large number of electric-dipole matrix elements. Static polarizabilities of the 4s, 4p_j, 5s, 5p_j, and 3d_j states are compared with other theory and experiment where available. We use the results of the polarizability calculations to identify magic …
