Optical lattice clocks of fermionic strontium offer a versatile platform for probing fundamental physics and developing quantum technologies. The bivalent electronic structure of strontium gives rise to a doubly forbidden atomic transition that is accessible due to hyperfine mixing in fermionic strontium-87, thus resulting in a submillihertz natural linewidth. Currently, the most accurate optical lattice clocks operate on this narrow transition by tightly trapping strontium-87 atoms in a optical lattice at 813 nm. Magic wavelengths occur where the Stark shifts of both the ground and excited states are equal, thus eliminating any position- and intensity-dependent broadening of the corresponding transition. Theoretical calculations of the electronic structure of strontium-87 have also predicted another magic wavelength of the clock transition at 497.01(57) nm. In this work, we experimentally measure the magic wavelength to be 497.4364(4) nm. Compared to the 813-nm magic wavelength, 497 nm is closer to the strong 461-nm dipolar transition of strontium, resulting in an order-of-magnitude increase in atomic polarizability and deeper traps with less optical power. The proximity to the 461-nm transition also leads to an enhanced sensitivity of 334(10) Hz/(nm E R ) at the magic wavelength.
Optical lattice clocks of fermionic strontium offer a versatile platform for probing fundamental physics and developing quantum technologies. The bivalent electronic structure of strontium gives rise to a doubly forbidden atomic transition that is accessible due to hyperfine mixing in fermionic strontium-87, thus resulting in a submillihertz natural linewidth. Currently, the most accurate optical lattice clocks operate on this narrow transition by tightly trapping strontium-87 atoms in a optical lattice at 813 nm. Magic wavelengths occur where the Stark shifts of both the ground and excited states are equal, thus eliminating any position- and intensity-dependent broadening of the corresponding transition. Theoretical calculations of the electronic structure of strontium-87 have also predicted another magic wavelength of the clock transition at 497.01(57) nm. In this work, we experimentally measure the magic wavelength to be 497.4364(4) nm. Compared to the 813-nm magic wavelength, 497 nm is closer to the strong 461-nm dipolar transition of strontium, resulting in an order-of-magnitude increase in atomic polarizability and deeper traps with less optical power. The proximity to the 461-nm transition also leads to an enhanced sensitivity of 334(10) Hz/(nm E R ) at the magic wavelength.
We report the experimental measurement of a magic wavelength at 476.823 62(8) nm for the ${}^{88}\mathrm{Sr}\phantom{\rule{0.2em}{0ex}}5{s}^{2}{\phantom{\rule{0.1em}{0ex}}}^{1}{\mathrm{S}}_{0}\ensuremath{\rightarrow}5s5p{\phantom{\rule{0.1em}{0ex}}}^{3}{\mathrm{P}}_{0}$ clock transition. The magic wavelength is determined through an ac Stark shift spectroscopy of atoms in an optical dipole trap. The value is in reasonable agreement with the theoretical prediction, differing by 0.061(54) nm. This magic wavelength, being shorter than the commonly used one at 813 nm, will be important for applications such as Bragg-pulse matter-wave interferometry involving both clock states. This work also paves the way for quantum simulation with a shorter lattice constant.
State-of-the-art optical clocks based on neutral atoms have already surpassed the world's best microwave atomic clocks in both accuracy and stability, paving the way to high-precision measurements of elementary aspects of nature, like the search for the drift of fundamental constants or the application of relativistic geodesy.These clocks operate with ensembles trapped in an optical lattice.Normally, high-power trapping laser fields induce a large AC Stark shift on the clock's transition frequency, as the clock states have different polarizabilities.A key feature of lattice clocks is the magic wavelength, for which the atomic polarizabilities of the clock states are equal, therefore compensating a differential frequency shift on the clock transition.In the periodic potential of the optical lattice, the energy spectrum of motional states features a band structure, analogous to electrons in a crystalline structure well-known from solid state physics.Within this band structure, atoms can tunnel between adjacent lattice sites.As a consequence from tunneling motion, the clock transition experiences a frequency shift and a broadening, which becomes pronounced in the shallow lattice regime.This work presents the first demonstration of a 24 Mg optical lattice clock including the precise determination of the frequency of the clock transition, its magic wavelength and its second-order Zeeman shift.Furthermore, the effect of tunneling in an optical lattice for magnesium has been extensively studied via optical spectroscopy of Bloch bands and substantiated with theoretical models, that were initially developed for a strontium optical lattice clock.Measuring lattice light induced frequency shifts of the clock transition for various lattice wavelengths and intensities, yielded a value of the magic wavelength of the 1 S 0 → 3 P 0 clock transition in 24 Mg of 468.463(207) nm.This value is in well agreement with a recent theoretical calculation of 468.45(23) nm, using a refined atomic structure model.The experimental value for the magic wavelength was independently verified with optical spectroscopy of Bloch bands carried out on the clock transition.Here, the AC Stark modified band structure is directly probed by a single frequency scan of the carrier resonance, featuring an asymmetric line shape, that is strongly dependent on the lattice wavelength.This technique demonstrates a novel method for the determination of the magic wavelength and could also be applied to other atomic species.In bosonic isotopes of alkaline earth(-like) elements, like 24 Mg, optical dipole excitation of the spin-forbidden 1 S 0 → 3 P 0 clock transition can be enhanced, e.g. by applying an external magnetic field.While these bosons are insensitive to first-order Zeeman shifts, the second-order Zeeman effect displays a dominant contribution to the clock's error budget.In this thesis, the magnetic polarizability β is measured to be -206.6(2.0)MHz/T 2 , consistent with a theoretical calculation, and the clock transition frequency was found to be 655 058 646 691(101) kHz.
The optical lattice clock with neutral atoms occupies an outstanding position in the research field of atomic clocks, demonstrating the great potential of its performance (like the uncertainty and the stability). At present, the optical lattice clock has realized a 10-18 level of its uncertainty. In this paper, we present the realization of loading bosonic atoms 88Sr (strontium, alkaline-earth metals) into a one-dimensional (1D) optical lattice in our laboratory. The optical lattice where the atoms are trapped can make the energy level shift, called Stark shift. But there is the special optical lattice operating at the “magic” wavelength for clock transitions (5s2) 1S0-(5s5p) 3P0, which can make the same Stark light-shift for both of them, indicating a zero light-shift relative to the clock. In our experiment, Sr atoms are cooled in a two-stage cooling and its temperature can be as low as 2 μK. Then these cold atoms are confined in the Lamb-Dicke region by the lattice laser output from an amplified diode laser operating at the “magic” wavelength, 813 nm. Experimentally, it is straightforward to provide 850 mW of lattice power focused to a 38 μm beam radius. After the cold atoms have trapped in the optical lattice, the lifetime of atoms in 1D optical lattice is measured to be 270 ms. The temperature and the number are about 3.5 μK and 1.2×105 respectively. Besides, effects of the power of the lattice laser on both the number and temperature are analyzed. The number changes linearly with the laser power, while there is no obvious influence on the temperature by the power. This original and special approach for atoms trapped in the optical lattice can provide a long interrogation time for probing the clock transition. Furthermore, it may be the foundation for developing our optical lattice clock of strontium atoms.
We report on the magic wavelength measurement of our optical lattice clock based on fermion strontium atoms at the National Institute of Metrology (NIM). A Ti:sapphire solid state laser locked to a reference cavity inside a temperature-stabilized vacuum chamber is employed to generate the optical lattice. The laser frequency is measured by an erbium fiber frequency comb. The trap depth is modulated by varying the lattice laser power via an acousto-optic modulator. We obtain the frequency shift coefficient at this lattice wavelength by measuring the differential frequency shift of the clock transition of the strontium atoms at different trap depths, and the frequency shift coefficient at this lattice wavelength is obtained. We measure the frequency shift coefficients at different lattice frequencies around the magic wavelength and linearly fit the measurement data, and the magic wavelength is calculated to be 368554672(44) MHz.
We demonstrate a spin-polarized clock transition spectrum of the 87Sr optical lattice clock. The clock transition 5s2 1S05s5p 3P0 of isotope 87Sr has a hyperfine structure due to non-zero nuclear spin, inducing ten -polarized transitions from each individual mF state under the condition of a bias magnetic field along the probing polarization axis. In this experiment, atoms are driven to a certain mF state by a circular-polarization pump light to maximize the atomic population, which is beneficial to the stability and uncertainty evaluation of the optical lattice clock. After two stages cooling and trapping, about 3.5106 atoms are trapped in the red magneto-optical trap with a temperature of 3.9 K. A grating-feedback external cavity diode laser with a tapered amplifier is used to build the optical lattice with a magic-wavelength of 813.426 nm. Both waists of the counter-propagating lattice beam along the horizontal direction are overlapped to form a one-dimensional (1D) optical lattice. The lifetime of the atoms trapped in the 1D optical lattice is 1600 ms. The clock laser at 698 nm is a grating-feedback diode laser, which is locked to an ultra-low expansion cavity by the Pound-Drever-Hall technique to stabilize the frequency and phase. As a result, the linewidth of clock laser is narrowed to Hz level. By the normalized shelving method, we obtain a resolved sideband spectrum of 87Sr 5s2 1S05s5p 3P0 transition. According to the spectrum, the lattice temperature along the longitudinal direction is approximately 4.2 K. After that a linewidth of 6.7 Hz of the degenerate clock transition is obtained at a probing time of 150 ms by utilizing a three-dimensional (3D) bias magnetic field, which is used to eliminate the stray magnetic fields. Then a small bias magnetic field of 300 mGs is applied along the polarization axis of the lattice light to achieve the spectrum of Zeeman magnetic sublevels of the clock transition. Furthermore, the mF=+9/2 and mF=-9/2 magnetic sublevels are picked to be respectively pumped by the +-polarized and --polarized light at 689 nm, a variable liquid crystal wave plate is employed to switch on both polarizations. Finally, the spin polarized clock transition spectrum is obtained at the interrogating pulse of 150 ms, and the linewidths of the mF=+9/2, mF=-9/2 magnetic sublevel transitions are 6.8 Hz and 6.2 Hz respectively.
We optically excite the electronic state 3s3p ^{3}P_{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 468.46(21) 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 develop a high-precision relativistic structure model for magnesium, give an improved theoretical value for the blackbody radiation shift, and discuss a clock based on bosonic magnesium.