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Applied Physics Letters

Measuring the probe Stark shift by frequency modulation spectroscopy in an 87Sr optical lattice clock

Qinfang Xu, Xiaotong Lu, Jingjing Xia, Yebing Wang, Hong Chang

Published Sep 6, 2021• 12 citations
Publisher

Abstract

In this paper, we demonstrate a frequency modulation technique to accurately measure the probe Stark shift of optical clocks. The effective coupling strength of the probe laser to the clock transition is precisely controlled by this frequency modulation technique, which is different from the traditional method by controlling the effective coupling strength via changing the probe light power. In an 87Sr optical lattice clock, the probe Stark shifts are measured as a function of the square of the bare state coupling strength. The probe Stark shift coefficient of 87Sr is experimentally determined as −6.0(5)×10−7/Hz using this frequency modulation technique. With the help of frequency modulation, the probe light power can be as large as possible without decreasing the measurement precision and the achieved measurement lever arm is improved by more than one order of magnitude compared with previous results.

DOI
10.1063/5.0060277

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In this paper, we demonstrate a frequency modulation technique to accurately measure the probe Stark shift of optical clocks. The effective coupling strength of the probe laser to the clock transition is precisely controlled by this frequency modulation technique, which is different from the traditional method by controlling the effective coupling strength via changing the probe light power. In an 87Sr optical lattice clock, the probe Stark shifts are measured as a function of the square of the bare state coupling strength. The probe Stark shift coefficient of 87Sr is experimentally determined as −6.0(5)×10−7/Hz using this frequency modulation technique. With the help of frequency modulation, the probe light power can be as large as possible without decreasing the measurement precision and the achieved measurement lever arm is improved by more than one order of magnitude compared with previous results.
With the uncertainty of the optical clocks improving to the order of 10-18, the probe light used to detect the clock transition has demonstrated nonnegligible Stark shift, provoking to precisely evaluate this shift. Here, we demonstrate a frequency modulation technique to realize a large measurement lever arm of the probe Stark shift with no cost of the measurement accuracy of the interleaved stabilization method. This frequency-modulated spectrum is theoretical described and experimental verified. The probe Stark shift coefficient of the 87Sr optical lattice clock is experimentally determined as -(45.97+/-3.51) Hz/(W/cm2) using this frequency modulation spectroscopy.
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 We investigate Floquet modulation for measuring the probe-induced AC Stark shift coefficient in optical lattice clocks. Periodic frequency modulation allows a high probe intensity to enlarge the measured frequency difference between the settings at low and high probe power while Bessel function dressing maintains a narrow excitation spectrum. This combination improves sensitivity to the coefficient without sacrificing frequency discrimination. We identify modulation conditions that suppress additional frequency shifts while avoiding strong motional resonances. At the same probe intensities and total measurement time, numerical simulations including preparation time show a lower coefficient uncertainty than conventional Rabi inter-rogation with a single π pulse. At high probe intensities, the Floquet coefficient uncertainty approaches a plateau dominated by Rabi frequency calibration.
A major obstacle for optical clocks is the frequency shift due to black body radiation. We discuss how one can tackle this problem in an optical lattice clock; in our case 87-Sr: firstly, by a measurement of the dc Stark shift of the clock transition and, secondly, by interrogating the atoms in a cryogenic environment. Both approaches rely on transporting ultracold atoms over several cm within a probe cycle. We evaluate this approach of mechanically moving the optical lattice and conclude that it is feasible to transport the atoms over 50 mm within 300 ms. With this transport a dc Stark shift measurement will allow to reduce the contribution of the blackbody radiation to the fractional uncertainty below 2 * 10^-17 at room temperature by improving the shift coefficient known only from atomic structure calculations up to now. We propose a cryogenic environment at 77 K that will reduce this contribution to few parts in 10^-18.
Atomic clocks are based on highly stable and well-characterized atomic transitions, mak-ing precise control and understanding of systematic frequency shifts essential for improved timekeeping performance. This thesis presents an experimental study of light-induced Stark shifts in rubidium and their impact on precision laser spectroscopy relevant to atomic frequency standards, as well as the effects of residual amplitude modulation on the laser lock point and the resulting sensitivity of both short- and long-term stability. A laser-based spectroscopy system was developed to probe rubidium transitions while enabling controlled variation of optical intensity. The optical beam was experimentally characterized through calculations of beam waist and measurements of power to accurately determine the intensity at the interaction region. Frequency shifts arising from the AC Stark effect were measured as a function of optical power, allowing extraction of the differential polarizability between atomic energy levels using a theoretical model relating energy shifts to electric-field intensity. Uncertainty analysis was performed through systematic propagation of experimental errors associated with beam geometry, optical power calibration, and frequency measurements. In addition, residual amplitude modulation generated by electro-optic phase modulation was investigated as a significant source of systematic error in frequency stabilization systems used in atomic clocks. The magnitude and behavior of RAM were experimentally characterized, and its impact on frequency stability was quantified by measuring the sensitivity of the laser lock point to controlled variations in RAM. Potential mitigation strategies were then explored through active pre-compensation of RAM using an amplitude electro-optic modulator in a closed-loop feedback system.
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.