GoKawiilCooling sequence
The cold-atom apparatus used in this experiment has previously been described in refs. 42,56. To prepare samples of cold 87Sr, the atoms are first collected over 1.5 s in a blue three-dimensional MOT that uses the 1S 0 → 1P 1 transition at 461 nm and a field gradient of 3.5 mT cm−1. Atoms that leak into the metastable 3P 2 manifold are recycled into the MOT using repump lasers at 679 nm and 707 nm. For efficient repumping of 87Sr, frequency sidebands at 585 MHz and 487 MHz are applied to the 707-nm light using an electro-optic modulator to create frequency components near-resonant with transitions from all five hyperfine manifolds of 3P 2 (ref. 57).
When the blue MOT is switched off, the atoms are captured in a red MOT operating on the 1S 0 F = 9/2 to \({}^{3}P_{{1}}\,{F}^{{\prime} }=11/2\) transition at 689 nm, using a field gradient of 390 μT cm−1. Sidebands at 1,463.265 MHz are applied to the 689-nm light using a resonant electro-optic modulator, such that the F = 9/2 to \({F}^{{\prime} }=9/2\) transition stirs the atoms between Zeeman sublevels of the ground state, thus mitigating losses into sublevels where atoms are weakly confined28. During the first 220 ms in the red MOT, an intensity of 1,800I sat is used for each of the six MOT beams, where I sat = 3 μW cm−2 is the saturation intensity of the 689-nm transition. To capture the wide range of Doppler-shifted atoms released from the blue MOT, a sawtooth-wave modulation is applied to the 689-nm light at a sweep frequency of 20 nm and a peak-to-peak sweep range of 6 MHz (ref. 58). For the following 100 nm, while in the ‘narrowband’ red MOT, the sawtooth frequency modulation is switched off and the intensities of the six MOT beams are ramped linearly from 490I sat to 40I sat . To help support the atoms against the force of gravity, a seventh, unbalanced MOT beam—the ‘up’ beam—is introduced in the vertical direction during the narrowband MOT. The up beam is necessary for creating narrowband red MOTs below 100I sat without causing significant atom loss. Upon completion of the narrowband red MOT, the atoms have a temperature of 2 μK and are compressed into a region comparable in size with the optical dipole trap.
Dipole trap and state preparation
Two crossed optical dipole traps, separated vertically by 1 mm, are formed by separate 2.5-W horizontal beams at 1,064 nm with horizontal and vertical 1/e2 radii of 220 μm and 23 μm, respectively, crossed with a shared 840-mW vertical beam at 813 nm with 1/e2 radii of 60 μm in both transverse axes. Overlapping with the top crossed dipole trap, a 4-mW transparency beam at 488 nm, detuned by 25 GHz from the 5s5p 3P 1 → 5s5d 3D 2 transition, is applied with a 1/e2 radius of 40 μm to protect the atoms from scattered 689-nm light after they are loaded into the top crossed dipole trap region.
Immediately after the free-space red MOT stages described above, the dipole trapping beams, the transparency beam and repumpers at 679 nm and 707 nm are switched on; the red MOT is then held for 100 ms in a ‘top-trap loading’ stage, during which the bias magnetic fields, beam intensities and detunings of the red MOT are optimized to load the atoms into the upper of the two dipole traps. During the top-trap loading stage, the red MOT intensity is linearly ramped from 20I sat to 4I sat to steadily reduce the atom temperature. Next, to load the bottom optical dipole trap, the red MOT is released for 3 ms by switching off the 689-nm beams. During this time, the cold atoms already in the top trap are held in place, while the hotter atoms fall towards the bottom trap. While the atoms are falling, the vertical bias magnetic field is stepped such that the zero of the quadrupole magnetic field is close to the bottom dipole trap. After 3 ms of free fall, the red MOT beams are switched back on for 100 ms in a ‘bottom-trap loading’ stage using the same parameters as the top-trap loading stage, except for the different bias magnetic field. All but the hottest atoms in the top trap remain in the top trap during the bottom-trap loading stage, as they are protected by the 488-nm transparency beam against scattered 689-nm light.
After both dipole traps are loaded, the MOT beams are switched off, a horizontal bias field is applied and the trapped atoms are optically pumped into the stretched state M F = 9/2 by applying a horizontal bias field of 38 μT and delivering a 20-ms pulse of circularly polarized light at 689 nm, resonant with the 1S 0 F = 9/2 to 3P 1 \({F}^{{\prime} }\) = 9/2 transition. During the optical pumping, sawtooth-wave frequency modulation is applied to the 689-nm light at a rate of 30 kHz over a range of 6 MHz. Finally, all beams except the dipole trap are switched off, and the bias magnetic field is adiabatically ramped to the final field used for atom interferometry: 31 μT aligned with the linear polarization of the vertical 698-nm clock beam.
Velocity selection on the clock transition
The clock beam at 698 nm propagates vertically upwards through both dipole trap regions with a waist of 600 μm. The clock laser linewidth is verified against an independent cavity-stabilized laser to ensure that it is below 2 Hz before delivery of the light to atoms through an uncompensated 10-m fibre42. Clock spectroscopy sequences are carried out immediately after atoms are released from both dipole traps. The excitation fraction is detected using a 200-μs fluorescence pulse at 461 nm to detect the number of atoms in the ground state 1S 0 , which is followed by 3.5-ms repumping pulses at 679 nm and 707 nm and another 200-μs fluorescence pulse at 461 nm to detect atoms that are in the 3P 0 state after the interferometer sequence. Scattered light from each 461-nm spectroscopy pulse is gathered in separate exposures of an electron-multiplying charge-coupled device (EMCCD) camera (Andor iXon Ultra 897), and a separate EMCCD image without atoms present is used to subtract background counts.
At the maximum available clock power of 640 mW, a Rabi π-pulse time of 44 μs is measured. However, the clock transition was observed to have a peak excitation fraction of 0.3 and a Doppler-broadened linewidth of 60 kHz, which is considerably larger than the 20-kHz Fourier limit. To improve the fidelity of the Rabi pulses in the atom-interferometer sequence, a velocity selection procedure is used. The clock beam is pulsed on for 200 μs at 20 mW, which implements a π pulse that excites the slowest atoms to the upper clock state 3P 0 . The atoms in the ground state are then pushed away using a 500-μs pulse at 461 nm, leaving only the slow atoms in the 3P 0 state to enter the interferometer sequence. After this velocity selection sequence, a resonant, 44-μs Rabi π pulse yielded a peak de-excitation fraction of 90%.
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