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.
We find a simple solution to the problem of probe laser light shifts in two-photon optical atomic clocks. We show that there exists a magic polarization at which the light shifts of the two atomic states involved in the clock transition are identical. We calculate the differential polarizability as a function of laser polarization for two-photon optical clocks based on neutral calcium and strontium, estimate the magic polarization angle for these clocks, and determine the extent to which probe laser light shifts can be suppressed. We show that the light shift and the two-photon excitation rate…
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…
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…
We predict the possibility of "triply-magic" optical lattice trapping of neutral divalent atoms. In such a lattice, the ${^1}\!S_{0}$ and ${^3}\!P_{0}$ clock states and an additional Rydberg state experience identical optical potentials, fully mitigating detrimental effects of the motional decoherence. In particular, we show that this triply magic trapping condition can be satisfied for Yb atom at optical wavelengths and for various other divalent systems (Ca, Mg, Hg and Sr) in the UV region. We assess the quality of triple magic trapping conditions by estimating the probability of excitation …
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 …
We experimentally investigate the lattice-induced light shift by the electric-quadrupole ($E2$) and magnetic-dipole ($M1$) polarizabilities and the hyperpolarizability in Sr optical lattice clocks. Precise control of the axial as well as the radial motion of atoms in a one-dimensional lattice allows observing the $E2$-$M1$ polarizability difference. Measured polarizabilities determine an operational lattice depth to be $72(2) E_R$, where the total light shift cancels to the $10^{-19}$ level, over a lattice-intensity variation of about 30%. This operational trap depth and its allowable intensit…
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…
Progress in atomic optical clocks with total uncertainty of $10^{-18}$ or below requires a precise estimation of multipolar and higher-order effects due to atom-field interactions. Magnesium is an attractive candidate for optical lattice clocks because it is insensitive to blackbody radiation and has a large quality factor. We employ a combined method of the Dirac-Fock plus core polarization and the relativistic configuration interaction to calculate the dynamic multipolar polarizabilities and the hyperpolarizabilities of the atomic Mg clock. The lattice light shift against variation of the la…
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.
Precision measurements and quantum information processing with cold atoms may benefit from trapping atoms with specially engineered, "magic" optical fields. At the magic trapping conditions, the relevant atomic properties remain immune to strong perturbations by the trapping fields. Here we develop a theoretical analysis of a recently observed magic trapping for especially valuable Zeeman-insensitive clock transitions in alkali-metal atoms. The involved mechanism relies on applying "magic" bias B-field along circularly polarized trapping laser field. We map out these B-fields as a function of …
A microwave atomic clock scheme based on Rb and Cs atoms trapped in optical lattice with magic wavelength for clock transition is proposed. The ac Stark shift of clock transition due to trapping laser can be canceled at some specific laser wavelengths. Comparing with in fountain clock, the cavity related shifts, the collision shift, and the Doppler effect are eliminated or suppressed dramatically in atomic clock when the magic optical lattice is exploited. By carefully analyzing various sources of clock uncertainty, we conclude that a microwave atomic clock with an accuracy of better than $2\t…
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）
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…
We investigate simultaneous state-insensitive trapping of a mixture of two different atomic species, Caesium and Rubidium. The magic wavelengths of the Caesium and Rubidium atoms are different, $935.6$ nm and $789.9$ nm respectively, thus single-frequency simultaneous state-insensitive trapping is not possible. We thus identify bichromatic trapping as a viable approach to tune the two magic wavelengths to a common value. Correspondingly, we present several common magic wavelength combinations appropriate for simultaneous state-insensitive trapping of the two atomic species.
We show that it is possible to significantly reduce quadrupole and tensor polarizability shifts of a clock transition by operating at a judiciously chosen field-insensitive point. In some cases shifts are almost completely eliminated making the transition an effective J = 0 to J = 0 candidate. This significantly improves the feasibility of a recent proposal for clock operation with large ion crystals. For such multi-ion clocks, geometric constraints and selection rules naturally divide clock operation into two categories based on the orientation of the magnetic field. We discuss the limitation…
We report the observation of the higher order frequency shift due to the trapping field in a $^{87}$Sr optical lattice clock. We show that at the magic wavelength of the lattice, where the first order term cancels, the higher order shift will not constitute a limitation to the fractional accuracy of the clock at a level of $10^{-18}$. This result is achieved by operating the clock at very high trapping intensity up to $400 $kW/cm$^2$ and by a specific study of the effect of the two two-photon transitions near the magic wavelength.
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…
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…
We analyze doubly magic trapping of Cs hyperfine transitions including previously neglected contributions from the ground state hyperpolarizability and the interaction of the laser light and a static magnetic field. Extensive numerical searches do not reveal any doubly magic trapping conditions for any pair of hyperfine states. However, including the hyperpolarizability reveals light intensity insensitive traps for a wide range of wavelengths at specific intensities. We then investigate the possibility of using bichromatic trapping light fields. Deploying a bichromatic scheme, we demonstrate d…
A Zeeman-insensitive optical clock atomic transition is engineered when nuclear spins are dressed by a non resonant radio-frequency field. For fermionic species as $^{87}$Sr, $^{171}$Yb, and $^{199}$Hg, particular ratios between the radiofrequency driving amplitude and frequency lead to "magic" magnetic values where a net cancelation of the Zeeman clock shift and a complete reduction of first order magnetic variations are produced within a relative uncertainty below the $10^{-18}$ level. An Autler-Townes continued fraction describing a semi-classical radio-frequency dressed spin is numerically…
It has been proposed to use magnetically trapped atomic ensembles to enhance the interrogation time in microwave clocks. To mitigate the perturbing effects of the magnetic trap, near-magic-field configurations are employed, where the involved clock transition becomes independent of the atom's potential energy to first order. Still, higher order effects are a dominating source for dephasing, limiting the performance of this approach. Here we propose a simple method to cancel the energy dependence to both first and second order, using weak radio-frequency dressing. We give values for dressing fr…
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.
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 present an experimental study of the lattice induced light shifts on the 1S_0-3P_0 optical clock transition (v_clock~518 THz) in neutral ytterbium. The ``magic'' frequency, v_magic, for the 174Yb isotope was determined to be 394 799 475(35)MHz, which leads to a first order light shift uncertainty of 0.38 Hz on the 518 THz clock transition. Also investigated were the hyperpolarizability shifts due to the nearby 6s6p 3P_0 - 6s8p 3P_0, 6s8p 3P_2, and 6s5f 3F_2 two-photon resonances at 759.708 nm, 754.23 nm, and 764.95 nm respectively. By tuning the lattice frequency over the two-photon resonan…
Optical clocks benefit from tight atomic confinement enabling extended interrogation times as well as Doppler- and recoil-free operation. However, these benefits come at the cost of frequency shifts that, if not properly controlled, may degrade clock accuracy. Numerous theoretical studies have predicted optical lattice clock frequency shifts that scale nonlinearly with trap depth. To experimentally observe and constrain these shifts in an $^{171}$Yb optical lattice clock, we construct a lattice enhancement cavity that exaggerates the light shifts. We observe an atomic temperature that is propo…
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 present precise values of the dipole polarizabilities ($α$) of the ground $\rm [4f^{14}6s] ~ ^2S_{1/2}$ and metastable $\rm [4f^{14} 5d] ~ ^2D_{3/2}$ states of Yb$^+$, that are %vital {\bf important} in reducing systematics in the clock frequency of the $\rm[4f^{14}6s] ~ ^2S_{1/2} \rightarrow [4f^{14}5d] ~ ^2D_{3/2}$ transition. The static values of $α$ for the ground and $\rm [4f^{14} 5d] ~ ^2D_{3/2}$ states are estimated to be $9.8(1) \times 10^{-40} \,\,\rm Jm^2V^{-2}$ and $17.6(5) \times 10^{-40}\,\, \rm Jm^2V^{-2}$, respectively, while the tensor contribution to the $\rm [4f^{14} 5d] ~…
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…
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…
We report on the direct optical production and spectroscopy of $^1\mathrm{S}_0\mbox{-}^3\mathrm{P}_0$ molecules with large binding energy using the clock transition of $^{171}\mathrm{Yb}$, and on the observation of the associated orbital Feshbach resonance near $1300\,\mathrm{G}$. We measure the magnetic field dependence of the closed-channel dimer and of the open-channel pair state energy via clock-line spectroscopy in a deep optical lattice. In addition, we show that the free-to-bound transition into the dimer can be made first-order insensitive to the trap depth by choice of the lattice wav…
Realization of a fast triple-magic all-optical qutrit in strontium-88
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Fakultät für Physik, Ludwig-Maximilians-Universität（路德维希-马克西米利安大学物理学院）
We carry out relativistic many-body calculations of the static and dynamic dipole polarizabilities of the ground $6s^2 ^1S_0$ and the first excited $6s6p ^3P^o_0$ states of Yb. With these polarizabilities, we compute several properties of Yb relevant to optical lattice clocks operating on the $6s^2 ^1S_0 - 6s6p ^3P^o_0$ transition. We determine (i) the first four {\em magic} wavelengths of the laser field for which the frequency of the clock transition is insensitive to the laser intensity. While the first magic wavelength is known, we predict the second, the third and the forth magic waveleng…
The energy levels and electric dipole ($E1$) matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic $E1$, magnetic dipole ($M1$) and electric quadrupole ($E2$) polarizabilities as well as the hyperpolarizabilities of the $2s^2~^1S_0$ and $2s2p~^3P_0$ states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of $2s^2~^1S_0 \rightarrow 2s2p~^3P_0$ clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock trans…
We analyze the AC Stark shift of the Cs microwave atomic clock transition theoretically and experimentally. Theoretical and experimental data are in a good agreement with each other. Results indicate the absence of a magic wavelength at which there would be no differential shift of the clock states having zero projections of the total angular momentum.
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 wavelengt…
Controlling light shifts in chip-scale atomic beam clocks
National Institute of Standards and Technology（美国国家标准与技术研究院）；University of Colorado Boulder（科罗拉多大学博尔德分校）；Infleqtion（英飞格蒂昂）；HRL Laboratories（HRL实验室）；DARPA（美国国防部高级研究计划局）
The light-induced frequency shift due to the hyperpolarizability (i.e. terms of second-order in intensity) is studied for a forbidden optical transition, $J$=0$\to$$J$=0. A simple universal dependence on the field ellipticity is obtained. This result allows minimization of the second-order light shift with respect to the field polarization for optical lattices operating at a magic wavelength (at which the first-order shift vanishes). We show the possibility for the existence of a magic elliptical polarization, for which the second-order frequency shift vanishes. The optimal polarization of the…
The progress in optical clock with uncertainty at a level of $10^{-18}$ requires unprecedented precision in estimating the contribution of multipolar and higher-order effects of atom-field interactions. Current theoretical and experimental results of dynamic multipolar polarizabilities and hyperpolarizabilities at the magic wavelength for the Sr clock differ substantially. We develop a combined approach of the Dirac-Fock plus core polarization (DFCP) and relativistic configuration interaction (RCI) methods to calculate dynamic multipolar polarizabilities and hyperpolarizabilities of the Sr ato…
We present a scheme for entangling the atoms of an optical lattice to reduce the quantum projection noise of a clock measurement. The divalent clock atoms are held in a lattice at a ``magic'' wavelength that does not perturb the clock frequency -- to maintain clock accuracy -- while an open-shell J=1/2 ``head'' atom is coherently transported between lattice sites via the lattice polarization. This polarization-dependent ``Archimedes' screw'' transport at magic wavelength takes advantage of the vanishing vector polarizability of the scalar, J=0, clock states of bosonic isotopes of divalent atom…
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 demonstrate single-atom resolved imaging with a survival probability of $0.99932(8)$ and a fidelity of $0.99991(1)$, enabling us to perform repeated high-fidelity imaging of single atoms in tweezers for thousands of times. We further observe lifetimes under laser cooling of more than seven minutes, an order of magnitude longer than in previous tweezer studies. Experiments are performed with strontium atoms in $813.4~\text{nm}$ tweezer arrays, which is at a magic wavelength for the clock transition. Tuning to this wavelength is enabled by off-magic Sisyphus cooling on the intercombination li…
We propose a new class of atomic microwave clocks based on the hyperfine transitions in the ground state of aluminum or gallium atoms trapped in optical lattices. For these elements magic wavelengths exist at which both levels of the hyperfine doublet are shifted at the same rate by the lattice laser field, cancelling its effect on the clock transition. Our analysis of various systematic effects shows that, while offering an improved control over systematic errors, the accuracy of the proposed microwave clock is competitive to that of the state-of-the-art primary frequency standard.
We report calculations designed to assess the ultimate precision of an atomic clock based on the 578 nm $6 ^1S_0 --> 6 ^3P^o_0$ transition in Yb atoms confined in an optical lattice trap. We find that this transition has a natural linewidth less than 10 mHz in the odd Yb isotopes, caused by hyperfine coupling. The shift in this transition due to the trapping light acting through the lowest order AC polarizability is found to become zero at the magic trap wavelength of about 752 nm. The effects of Rayleigh scattering, higher-order polarizabilities, vector polarizability, and hyperfine induced e…
Experiments involving optical traps often require careful control of the ac Stark shifts induced by strong confining light fields. By carefully balancing light shifts between two atomic states of interest, optical traps at the magic wavelength have been especially effective at suppressing deleterious effects stemming from such shifts. Highlighting the power of this technique, optical clocks today exploit Lamb-Dicke confinement in magic-wavelength optical traps, in some cases realizing shift cancellation at the ten parts per billion level. Theory and empirical measurements can be used at varyin…
We consider the frequency shift in optical lattice clocks which arises from the coupling of the electronic motion to the atomic motion within the lattice. For the simplest of 3-D lattice geometries this coupling is shown to only affect clocks based on blue-detuned lattices. We have estimated the size of this shift for the prospective strontium lattice clock operating at the 390 nm blue-detuned magic wavelength. The resulting fractional frequency shift is found to be on the order of $10^{-18}$ and is largely overshadowed by the electric quadrupole shift. For lattice clocks based on more complex…
We report an s-wave collisional frequency shift of an atomic clock based on fermions. In contrast to bosons, the fermion clock shift is insensitive to the population difference of the clock states, set by the first pulse area in Ramsey spectroscopy, θ_1. The fermion shift instead depends strongly on the second pulse area θ_2. It allows the shift to be canceled, nominally at θ_2 = π/2, but correlations shift the null to slightly larger θ_2. The shift applies to optical lattice clocks and increases with the spatial inhomogeneity of the clock excitation field, naturally large at optical frequenci…
We report on the spectroscopy of the $5s^2 {}^1S_0 (F=9/2) \to 5s5p {}^3P_0 (F=9/2)$ clock transition of ${}^{87}{\rm Sr}$ atoms (natural linewidth of 1 mHz) trapped in a one-dimensional optical lattice. Recoilless transitions with a linewidth of 0.7 kHz as well as the vibrational structure of the lattice potential were observed. By investigating the wavelength dependence of the carrier linewidth, we determined the magic wavelength, where the light shift in the clock transition vanishes, to be $813.5\pm0.9$ nm.
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 have experimentally demonstrated that magnetic-field-insensitive coherent-population-trapping (CPT) resonances are generated between the ground hyperfine levels on the $D_1$ line of $^{133}$Cs using a two-photon $Λ$ scheme excited by lin || lin polarizations. The frequency shift of the CPT resonance is 0.04 Hz for the deviation of 1 $μ$T at a "magic" magnetic field of 139 $μ$T and is 50 times smaller than that of the conventional clock transition at a typical bias magnetic field for the clock operation. The amplitude of the CPT spectrum excited by lin || lin polarizations is enhanced as the…
We address the problem of the lattice Stark shifts in the Sr clock caused by the multipolar $M1$ and $E2$ atom-field interactions and by the term nonlinear in lattice intensity and determined by the hyperpolarizability. We have developed an approach to calculate hyperpolarizabilities for atoms and ions based on a solution of the inhomogeneous equation which allows to effectively and accurately carry out complete summations over intermediate states. We applied our method to the calculation of the hyperpolarizabilities for the clock states in Sr. We also carried out an accurate calculation of th…
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…
