Photoionization cross sections of ultracold 88Sr in 1P1 and 3S1 states at 390 nm and the resulting blue-detuned magic wavelength optical lattice clock constraints
Marcin Witkowski, Sławomir Bilicki, Marcin Bober, Domagoj Kovačić, Vijay Singh, A. Tonoyan, M. Zawada
We present the measurements of the photoionization cross sections of the excited 1P1 and 3S1 states of ultracold 88Sr atoms at 389.889 nm wavelength, which is the magic wavelength of the 1S0-3P0 clock transition. The photoionization cross section of the 1P1 state is determined from the measured ionization rates of 88Sr in the magneto-optical trap in the 1P1 state to be 2.20(50)×10−20 m2, while the photoionization cross section of 88Sr in the 3S1 state is inferred from the photoionization-induced reduction in the number of atoms transferred through the 3S1 state in an operating optical lattice clock to be 1.38(66) ×10−18 m2. Furthermore, the resulting limitations of employing a blue-detuned magic wavelength optical lattice in strontium optical lattice clocks are evaluated. We estimated photoionization induced loss rates of atoms at 389.889 nm wavelength under typical experimental conditions and made several suggestions on how to mitigate these losses. In particular, the large photoionization induced losses for the 3S1 state would make the use of the 3S1 state in the optical cycle in a blue-detuned optical lattice unfeasible and would instead require the less commonly used 3D1,2 states during the detection part of the optical clock cycle.
We present the measurements of the photoionization cross sections of the excited 1P1 and 3S1 states of ultracold 88Sr atoms at 389.889 nm wavelength, which is the magic wavelength of the 1S0-3P0 clock transition. The photoionization cross section of the 1P1 state is determined from the measured ionization rates of 88Sr in the magneto-optical trap in the 1P1 state to be 2.20(50)×10−20 m2, while the photoionization cross section of 88Sr in the 3S1 state is inferred from the photoionization-induced reduction in the number of atoms transferred through the 3S1 state in an operating optical lattice clock to be 1.38(66) ×10−18 m2. Furthermore, the resulting limitations of employing a blue-detuned magic wavelength optical lattice in strontium optical lattice clocks are evaluated. We estimated photoionization induced loss rates of atoms at 389.889 nm wavelength under typical experimental conditions and made several suggestions on how to mitigate these losses. In particular, the large photoionization induced losses for the 3S1 state would make the use of the 3S1 state in the optical cycle in a blue-detuned optical lattice unfeasible and would instead require the less commonly used 3D1,2 states during the detection part of the optical clock cycle.
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.
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 study the influence of ultracold collisions induced by the inhomogeneous excitation on the clock-transition frequency in one- and two-dimensional shallow blue-detuned (BD) 87Sr optical lattice clocks with a magic wavelength of ${\ensuremath{\lambda}}_{b}=389.889$ nm. The minimal lattice potential required to tightly confine atoms in each single lattice site is much larger than that required for a red-detuned (RD) lattice operating at ${\ensuremath{\lambda}}_{r}=813.4$ nm because of the relatively smaller magic wavelength. For a deep optical lattice, the two-body interactions of atoms in a single lattice site mainly contribute to the clock-transition frequency shift, while the intersite collisions primarily affect the collisional shift in a shallow optical lattice. For an effective misalignment angle $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}10$ mrad of the probe beam with respect to the lattice axis, the fractional collisional shifts in both one- and two-dimensional BD lattices are at the ${10}^{\ensuremath{-}16}$ level.
Collisions with background atoms are known to induce a significant shift in the frequency of state-of-the-art optical atomic clocks and contribute to state decoherence in cold atom experiments. The effects of these collisions can be quantified by measuring their cross sections. We experimentally measured the collision cross section between 88Sr−N2 in a Magneto-Optical Trap (MOT). The measurement was carried out by monitoring the atom number loss rate as a function of background pressure of N2 and the cross section thus obtained was 8.1(4)×10−18 m2. The measured collision cross section has been utilized for the determination of C6 coefficient of the ground state (1S0) of 88Sr atom, which can be useful to estimate the relative frequency shift in the clock transition. We also estimate the loss rate induced by the combined effect of the decay of atoms in the long-lived 3P0 state and temperature-induced atomic losses from the capture volume of the MOT. We find that the contribution due to the latter is dominant in comparison to the other atomic loss channels and must be included in the studies that rely on the total loss rate measurement.
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.
We report the measurement of the absolute photoionization cross section for the 5P 3/2 state of 87 Rb at wavelength of 473 nm, which results in the photoelectron energies of 33 meV above the ionization threshold, using cold atoms confined in a vapor-loaded magneto-optical trap. The 87 Rb 5P 3/2 photoionization cross section at 473 nm is determined to be σ PI = 10.5 ± 2.2 Mb. Considering the spatial distribution of the trapped atoms, the average intensity of the ionization laser seen by an atom in the MOT instead of ionizing laser intensity I PI is used in our calculations for the photoionization cross sections. The excited state fraction is also accurately estimated using the latest experimental result.