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In this paper, the magic wavelength of the 87Sr optical lattice clock is determined by a method that bypasses the need for lattice trap depth modulation. Instead, it relies on an additional AC Stark shift generated by a dipole beam operating near the frequency of the lattice light and oriented perpendicular to the optical lattice. The magic wavelength is inferred by measuring the AC Stark shift induced by the dipole beam as a function of its power under various frequency detunings. The effect of the dipole beam on the external states of the cold ensemble is evaluated through comparative analysis of the radial and axial sideband spectra, both with and without the dipole beam. Variations in density shift resulting from changes in external states are evaluated using comprehensive numerical calculations. By avoiding trap depth modulation, this method effectively suppresses the influence of the density shift, thereby offering a promising avenue for accurately determining the magic wavelength. [ABSTRACT FROM AUTHOR]

In this paper, the magic wavelength of the 87Sr optical lattice clock is determined by a method that bypasses the need for lattice trap depth modulation. Instead, it relies on an additional AC Stark shift generated by a dipole beam operating near the frequency of the lattice light and oriented perpendicular to the optical lattice. The magic wavelength is inferred by measuring the AC Stark shift induced by the dipole beam as a function of its power under various frequency detunings. The effect of the dipole beam on the external states of the cold ensemble is evaluated through comparative analysis of the radial and axial sideband spectra, both with and without the dipole beam. Variations in density shift resulting from changes in external states are evaluated using comprehensive numerical calculations. By avoiding trap depth modulation, this method effectively suppresses the influence of the density shift, thereby offering a promising avenue for accurately determining the magic wavelength.

For the trapped pre-cooled atoms in an optical dipole trap (ODT), the magic-wavelength ODT can eliminate the differential light shift of the transition between two atomic states, so that the transition frequency between the two states is the same as that of atoms in the free space, which is of great significance for improving the experimental repetition rate and reducing the atomic decoherence in the fields of cold atom physics, quantum optics, and precision measurement. Here we calculate the dynamic polarizabilities of cesium 6S ground state and 7P excited state by using the multi-level model for the ODT with laser wavelength from 1200 to 2000 nm. The magic wavelengths of ODT are obtained for the linearly and circularly polarized laser beams at the intersection of dynamic polarizabilities of two atomic states. Furthermore, we analyze the robustness of the magic trapping conditions and the feasibility of the experimental operation near the telecom C-band wavelength.

For the first time, we experimentally determine the infrared magic wavelength for the ^40 Ca ^+ $4s{\,^2}{S_{1/2}} \to 3d{\,^2}{D_{5/2}}$ 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 (‘Dirac–Fock plus core polarization’ method) but also more precise by a factor of about 300. Using this measured magic wavelength, we also derive the differential static polarizability to be −44.32(32) a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of ^40 Ca ^+ optical clock.

In this work, we present a scheme of a two-photon interaction to calculate magic wavelengths for the 6 2 S 1 2 − 5 2 D 3 2 , 5 2 clock transitions of Ba + ion employing the relativistic coupled-cluster method. These magic wavelengths can be essential inputs to achieve better accuracy in the future ionic clock experiments. In this paper, we further show an application of a two-photon interaction to the spin-mixing processes, | 0 , 0 〉 ↔ | + 1 , − 1 〉 and | 0 , 0 〉 ↔ | − 1 , + 1 〉 , of an ultra-cold spin-1 mixture of 137 Ba + ions and 87 Rb atoms. We determine the protocols for selecting these spin-mixing oscillations by changing the strength and frequencies of the externally applied magnetic field and laser beams, respectively. [ABSTRACT FROM AUTHOR]

Light shift in a state due to the applied laser in an atomic system vanishes at tune-out wavelengths ( λ T s). Similarly, differential light shift in a transition vanishes at the magic wavelengths ( λ m a g i c s). In many of the earlier studies, values of the electric dipole (E1) matrix elements were inferred precisely by combining measurements and calculations of λ m a g i c . Similarly, the λ T values of an atomic state can be used to infer the E1 matrix element, as it involves dynamic electric dipole (α) values of only one state whereas the λ m a g i c values require evaluation of α values for two states. However, both the λ m a g i c and λ T values depend on angular momenta and their magnetic components (M) of states. Here, we report the λ m a g i c and λ T values of many S 1 / 2 and D 3 / 2 , 5 / 2 states, and transitions among these states of the Mg + , Ca + , Sr + and Ba + ions that are independent of M values. It is possible to infer a large number of E1 matrix elements of the above ions accurately by measuring these values and combining with our calculations. [ABSTRACT FROM AUTHOR]

We study the magic wavelength for two-photon 1 S – n S transitions in a hydrogen and deuterium atom, as well as 2 S – n S transitions, where the lower level is the metastable 2 S state. At the magic wavelength, the dynamic Stark shifts of the ground and the excited state of the transition coincide, so that the transition frequency is independent of the intensity of the trapping laser field. Experimentally feasible magic wavelengths of transitions with small slopes in the atomic polarizabilities are determined; these are the most stable magic wavelengths against variations of the laser frequency. We provide data for the magic wavelengths for the 1 S – n S and 2 S – n S transitions in hydrogen and deuterium, with n = 2 , ⋯ , 8 . We also analyze the stability of the elimination of the ac Stark shift at the magic wavelength against tiny variations of the trapping laser frequency from the magic value. [ABSTRACT FROM AUTHOR]

In this work, we present a scheme of a two-photon interaction to calculate magic wavelengths for the 62S12 − 52D32,52 clock transitions of Ba+ ion employing the relativistic coupled-cluster method. These magic wavelengths can be essential inputs to achieve better accuracy in the future ionic clock experiments. In this paper, we further show an application of a two-photon interaction to the spin-mixing processes, |0,0⟩↔|+1,−1⟩ and |0,0⟩↔|−1,+1⟩, of an ultra-cold spin-1 mixture of 137Ba+ ions and 87Rb atoms. We determine the protocols for selecting these spin-mixing oscillations by changing the strength and frequencies of the externally applied magnetic field and laser beams, respectively.

We study the magic wavelength for two-photon 1S–nS transitions in a hydrogen and deuterium atom, as well as 2S–nS transitions, where the lower level is the metastable 2S state. At the magic wavelength, the dynamic Stark shifts of the ground and the excited state of the transition coincide, so that the transition frequency is independent of the intensity of the trapping laser field. Experimentally feasible magic wavelengths of transitions with small slopes in the atomic polarizabilities are determined; these are the most stable magic wavelengths against variations of the laser frequency. We provide data for the magic wavelengths for the 1S–nS and 2S–nS transitions in hydrogen and deuterium, with n=2,⋯,8. We also analyze the stability of the elimination of the ac Stark shift at the magic wavelength against tiny variations of the trapping laser frequency from the magic value.

We report efficient all-optical creation of an ultracold gas of alkaline-earth-metal dimers, ^88 Sr _2 , in their absolute ground state. Starting with weakly bound singlet molecules formed by narrow-line photoassociation in an optical lattice, followed by stimulated Raman adiabatic passage (STIRAP) via a singlet-dominant channel in the $(1){0}_{u}^{+}$ excited potential, we prepare pure samples of more than 5500 molecules in ${X}^{1}{{\Sigma}}_{g}^{+}(v=0,\enspace J=0)$ . We observe two-body collisional loss rates close to the universal limit for both the least bound and most bound vibrational states in ${X}^{1}{{\Sigma}}_{g}^{+}$ . We demonstrate the enhancement of STIRAP efficiency in a magic-wavelength optical lattice where thermal decoherence is eliminated. Our results pave the way for the use of alkaline-earth-metal dimers for high-precision spectroscopy, and indicate favorable prospects for robust quantum state preparation of ultracold molecules involving closed-shell atoms, as well as molecule assembly in deep optical traps tuned to a magic wavelength.

Active clocks could provide better stabilities during initial stages of measurements over passive clocks, in which stabilities become saturated only after long-term measurements. This unique feature of an active clock has led to search for suitable candidates to construct such clocks. The other challenging task of an atomic clock is to reduce its possible systematics. A major part of the optical lattice atomic clocks based on neutral atoms are reduced by trapping atoms at the magic wavelengths of the optical lattice lasers. Keeping this in mind, we find the magic wavelengths between all possible hyperfine levels of the transitions in Rb and Cs atoms that were earlier considered to be suitable for making optical active clocks. To validate the results, we give the static dipole polarizabilities of Rb and Cs atoms using the electric dipole transition amplitudes that are used to evaluate the dynamic dipole polarizabilities and compare them with the available literature values.

• The differential light shift of the transition between two atomic states is eliminated by a magic-wavelength optical dipole trap. • The atomic dynamic polarizabilities are calculated by using the multi-level model. • The magic trapping wavelengths are obtained for the linearly and circularly polarized lights. And the robustness of the magic trapping conditions is analyzed. • A good way to study quantum computing and quantum simulation in ultracold atomic gases. For the trapped pre-cooled atoms in an optical dipole trap (ODT), the magic-wavelength ODT can eliminate the differential light shift of the transition between two atomic states, so that the transition frequency between the two states is the same as that of atoms in the free space, which is of great significance for improving the experimental repetition rate and reducing the atomic decoherence in the fields of cold atom physics, quantum optics, and precision measurement. Here we calculate the dynamic polarizabilities of cesium 6S ground state and 7P excited state by using the multi-level model for the ODT with laser wavelength from 1200 to 2000 nm. The magic wavelengths of ODT are obtained for the linearly and circularly polarized laser beams at the intersection of dynamic polarizabilities of two atomic states. Furthermore, we analyze the robustness of the magic trapping conditions and the feasibility of the experimental operation near the telecom C-band wavelength. [ABSTRACT FROM AUTHOR]

Magic wavelengths for laser trapping of barium atoms in the optical lattices are investigated while considering the optical clock transition at 877 nm between the 6s21S0 state and 6s5d 1D2 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also discussed and analyzed. Some of these magic wavelengths are selected and recommended for the optical lattice trapping laser. [ABSTRACT FROM AUTHOR]

Active clocks could provide better stabilities during initial stages of measurements over passive clocks, in which stabilities become saturated only after long-term measurements. This unique feature of an active clock has led to search for suitable candidates to construct such clocks. The other challenging task of an atomic clock is to reduce its possible systematics. A major part of the optical lattice atomic clocks based on neutral atoms are reduced by trapping atoms at the magic wavelengths of the optical lattice lasers. Keeping this in mind, we find the magic wavelengths between all possible hyperfine levels of the transitions in Rb and Cs atoms that were earlier considered to be suitable for making optical active clocks. To validate the results, we give the static dipole polarizabilities of Rb and Cs atoms using the electric dipole transition amplitudes that are used to evaluate the dynamic dipole polarizabilities and compare them with the available literature values. [ABSTRACT FROM AUTHOR]

The tune‐out and magic wavelengths (TMWs) for the hydrogenlike and screened‐hydrogenlike atoms (Z = 1‐8) are calculated using a variational method. The first three tune‐out wavelengths for each of the nS (n = 1, 2, 3) states and the first three magic wavelengths for each of the 1S‐nS (n = 2, 3) transitions of the hydrogenlike atoms in terms of nuclear charge Z, and the first TMWs for the above mentioned states or transitions of the screened‐hydrogenlike atoms in terms of the screening parameter μ and Z are presented. All the results for the TMWs are reported for the first time in the literature except the magic wavelengths for the hydrogen atom. The magic wavelengths for hydrogen atom are in agreement with the available data. The precise estimation of the TMWs would be helpful for the design of the ion‐trapping experiment of the hydrogenic systems. Our study is expected to be useful for the measurements of the hydrogenic 1S‐2S and 1S‐3S transitions spectroscopy for the improved accuracy. [ABSTRACT FROM AUTHOR]

• Static and dynamic polarizabilities of the 5 s 1/2 , 5 p 1/2 and 5 p /2 3 states are calculated. • Magic wavelengths of the 5 s 1/2 → 5 p 1/2,3/2 transitions are given for linearly and circularly polarized light. • We suggest that the accurate measurement on the magic wavelengths for circularly polarized light could be used to determine the high-precise oscillator strengths of the 5 p 1/2 → 5 d 3/2 , 6 d 3/2 , 7 s 1/2 , 8 s 1/2 and 5 p 3/2 → 5 d 3/2 , 5 d 5/2 , 6 d 5/2 , 7 s 1/2 , 8 s 1/2 transitions. The energy levels and electric dipole matrix elements of Rb atom are calculated using the relativistic configuration interaction with core polarization method. These energy levels and matrix elements are further employed to calculate the electric dipole static and dynamic polarizabilities of the 5 s 1/2 , 5 p 1/2 and 5 p 3/2 states. Finally, the magic wavelengths of the 5 s 1/2 → 5 p 1/2,3/2 transitions are obtained for linearly and circularly polarized light. We suggest that the accurate measurement on the magic wavelengths for circularly polarized light could be used to determine the high-precise oscillator strengths of the 5 p 1/2 → 5 d 3/2 , 6 d 3/2 , 7 s 1/2 , 8 s 1/2 and 5 p 3/2 → 5 d 3/2 , 5 d 5/2 , 6 d 5/2 , 7 s 1/2 , 8 s 1/2 transitions. [ABSTRACT FROM AUTHOR]

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 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. [ABSTRACT FROM PUBLISHER]

State-insensitive dipole trapping of multilevel atoms can be achieved by an appropriate choice of the wavelength of the trapping laser, so that the interaction with the different transitions results in equal AC Stark shifts for the ground and excited states of interest. However, this approach is severely limited by the availability of coherent sources at the required wavelength and of appropriate power. This work investigates state-insensitive trapping of caesium atoms for which the required wavelength of 935.6 nm is inconvenient in terms of experimental realization. Bichromatic state-insensitive trapping is proposed to overcome the lack of suitable laser sources. We first consider pairs of laser wavelengths in the ratio 1:2 and 1:3, as obtained via second- and third-harmonic generation. We found that the wavelength combinations 931.8–1863.6 nm and 927.5–2782.5 nm are suitable for state-insensitive trapping of caesium atoms. In addition, we examine bichromatic state-insensitive trapping produced by pairs of laser wavelengths corresponding to currently available high-power lasers. These wavelength pairs were found to be in the range of 585–588 nm and 623–629 for one laser and 1064–1080 nm for the other. [ABSTRACT FROM PUBLISHER]