‘Coherent evolution of superexchange interaction in seconds long optical clock spectroscopy’ dataset

 

Description of the data and file structure

All experimental data presented in “Coherent evolution of superexchange interaction in seconds long optical clock spectroscopy” in both the main text and supplementary materials is provided. Each folder provided in ‘paper_data.zip’ is labelled by figure name and contains the data for each figure. Here we go folder-by-folder and specifically annotate each dataset.

 

Fig 2:

(B) plot_fig_2b.py is the Python script to plot the data in Fig.2(B).

Left panel: ‘dark_times’ are the Ramsey interferometer dark times in seconds.  ‘C_’ are the Ramsey fringe contrasts. A detailed explanation of Ramsey spectroscopy is provided in the main text of our manuscript. Our method of determining these contrasts is in the section ‘Ellipse fitting analysis’ in the Supplemental materials. ‘C_errs’ are one standard deviation error bars for the ‘C_’ measurements.

Upper right panel: P1_2s.csv are the excitation fractions in region P1 for 2 second Ramsey spectroscopy dark time. Details of regions P1 and P2 are provided in ‘Ellipse fitting analysis’ of the manuscript. ‘P2_2s.csv’ are the excitation fractions in region P2 for 2 second Ramsey spectroscopy dark time.

Bottom right panel: P1_16s.csv is the excitation fractions in region P1 for 16 second Ramsey spectroscopy dark time. P2_16s.csv is the excitation fractions in region P2 for 16 second Ramsey spectroscopy dark time.

(C) plot_fig_2c.py is the python script to plot the data in Fig.2(C).

‘Fig_2c.csv’ is the data for Fig.2(C). Each grid point corresponds to a quality factor Q as defined in the caption of Fig. 2.  The grid corresponds to the transverse and vertical optical lattice confinement depths detailed in the paper figure.

Fig3:

(A) ‘fig3a_measurement_resubmission.csv’. Left column are measurement dark times in units of second. Middle column are Ramsey fringe contrasts. Right column are one standard deviation error bars for Ramsey fringe contrasts.

‘fig3a_theory_resubmission’. First column are dark times for theoretical simulation in units of second. Second column are theoretically calculated Ramsey contrasts using the numerically solved many-body Hamiltonian described in the Supplementary materials. Third and fourth column are error bands stemming from the uncertainty on the temperature and T2.

(B) ‘fig3b_measurement_resubmission.csv’. Left column are measurement dark times in units of second. Middle column are Ramsey fringe contrasts. Right column are one standard deviation error bars for Ramsey fringe contrasts.

‘fig3b_theory_resubmission’. First column are dark times for theoretical simulation in units of second. Second column are theoretically calculated Ramsey contrasts using the numerically solved many-body Hamiltonian described in the Supplementary materials. Third and fourth column are error bands stemming from the uncertainty on the temperature and T2.

(C) ‘fig3c_measurement.csv’. Left column are perpendicular trap depths in units of the lattice photon recoil energy. Middle column is the measured oscillation frequency in Hz. Right column is the one standard deviation frequency error in the oscillation frequency.

‘fig3c_2site_model.csv’. Left column are perpendicular trap depths in units of the lattice photon recoil energy. Right column are the modelled oscillation frequencies as explained in the ‘Heuristic averaging of superexchange dynamics’ section of the supplemental materials.

‘fig3c_full_sim.csv’. Left column are perpendicular trap depths in units of the lattice photon recoil energy. Middle column are the fit results obtained from the full theoretical simulations used in panel (A) and (B) analysis. Right column are one standard deviation error.

(D) ‘fig3d_measurement.csv’. First column are the scaled dark times for Ramsey spectroscopy measurements. Sequentially in each column from left to right, we scan the transverse confinement and provide the Ramsey fringe contrast and the one standard deviation uncertainty in contrast. The top row of each column provides a label for additional clarity.

‘fig3d_simulation.csv’ First column are rescaled dark times. Second column are modelled contrast decay using the theoretical model described in the ‘General averaging’ section of the supplemental materials.

Fig4:

(B) ‘plot_fig_4b.py’ is the python script to plot the data in Fig.4(B). ‘Pulse_0.csv’, ‘Pulse_1.csv’, ‘Pulse_2.csv’, ‘Pulse_3.csv’ are the Ramsey spectroscopy data with tunable clock pulse areas as described in the caption of Fig. 4. First row are dark times in units of seconds. Second row are Ramsey fringe contrasts. Third row are one standard deviation uncertainty in contrast.

(D) ‘plot_fig_4d.py’ is the python script to plot the data in Fig.4(D). ‘-24.csv’ to ‘+12.csv’ are experimental positions of atoms in units of microns. First row are dark times in units of seconds. Second row are Ramsey fringe contrasts. Third row are one standard deviation uncertainty in contrast. Data are offset in contrast for clarity when plotting.

(E) ‘fig4e_measurement.csv’ Left column are experimental positions of atoms in units of microns. Middle column is the measured oscillation frequency in Hz. Right column is the one standard deviation frequency error in the oscillation frequency.

‘fig4e_simulation.csv’ Left column are positions of atoms in units of microns. Middle column are oscillation frequencies from heuristic superexchange simulation. Right column are one standard deviation in oscillation frequencies.

S1:

(A) ‘plot_fig_S1A.py’ is the python script to plot the data in Fig.S1(A). ‘dark_times_S1_a.csv’ are the dark times in units of seconds. ‘N_S1_a.csv’ are the atom numbers as a function of dark time.

(B) ‘plot_fig_S1B.py’ is the python script to plot the data in Fig.S1(B). ‘dark_times_S1_b.csv’ are the dark times in units of seconds. ‘Ns_S1_b.csv’ are the atom numbers as a function of dark time. ‘Ns_errs_S1_b.csv’ are the one standard deviation errors in atom numbers as a function of dark time.

S2:

The ‘x’ and ‘y’ data for each panel in Fig. S2 are provided. The last three numbers in each measurement (e.g. ‘404010’ ) refer to the transverse and vertical trap depths respectively in units of the lattice photon recoil energy. As seen in Fig. S2, there is a small anharmonic correction and the corrected trap depths are provided in the manuscript. ‘x_data_.csv’ refers to the clock laser frequency in Hz.  ‘y_data_.csv’ refers to the excitation fraction of the atomic ensemble.

S3:

‘fig_s3_measurement.csv’ Left column are perpendicular trap depths in units of the lattice photon recoil energy. Middle column is the measured oscillation frequency in Hz. Right column is the one standard deviation frequency error in the oscillation frequency.

‘fig_s3_model.csv’ Left column are perpendicular trap depths in units of the lattice photon recoil energy. Right column are the modelled oscillation frequency in Hz.

S4:

‘plot_fig_s4.py’ is the python script to plot the data in Fig. S4. ’14.csv’ is the measurement at 14 px radius. Top row are the dark times in units of seconds. Second row are Ramsey fringe contrasts. Third row are one standard deviation uncertainty in contrast.

’48.csv’ is the measurement at 48 px radius. Top row are the dark times in units of seconds. Second row are Ramsey fringe contrasts. Third row are one standard deviation uncertainty in contrast.

S5:

In panels a-e, we vary the perpendicular trap depth. For a given trap depth (i.e. 19.6 Er), we theoretically model Ramsey fringe contrast decay as a function of temperature. (e.g. 19.6 Er, 200 nK): ‘datContTempV19d6T200.csv’. Left column are the dark times in units of seconds. Right column are Ramsey fringe contrasts. These are overlayed with experimental measurements (e.g. 19.6 Er, 200 nK): ‘datContTempV19d6experiment.csv’. Left column are the dark times in units of seconds. Middle column are Ramsey fringe contrasts. Right column are Ramsey fringe contrast error bars (one standard deviation).

S6:

(B) ‘plot_fig_s6.py’ is the python script to plot the data in Fig. S6(B). ‘Vz_X.csv’ are coherence time measurements where X is the vertical trap depth in units of the lattice photon recoil energy. First row is the trap depth. Second row is the coherence time in units of seconds. Third row is the coherence time error bar (one standard deviation).

‘plot_fig_s6_inset.py’ is the python script to plot the data in Fig. S6(B) inset. ‘Vz_NX.csv’ are atom lifetime measurements where X is the vertical trap depth in units of the lattice photon recoil energy. First row is the trap depth. Second row is the atom lifetime in units of seconds. Third row is the atom lifetime error bar (one standard deviation).

(C) ‘plot_fig_S6c_1.py’ is the python script to plot the upper left figure in in Fig. S6(C). ‘Vz_perp_X.csv’ are coherence time measurements where X is the perpendicular trap depth in units of the lattice photon recoil energy. First row is the trap depth. Second row is the coherence time in units of seconds. Third row is the coherence time error bar (one standard deviation).

‘plot_fig_S6c_2.py’ is the python script to plot the upper right figure. ‘Vz_perp_X.csv’ are coherence time measurements where X is the perpendicular trap depth in units of the lattice photon recoil energy. First row is the trap depth. Second row is the coherence time in units of seconds. Third row is the coherence time error bar (one standard deviation).

‘plot_fig_S6c_3.py’ is the python script to plot the lower left figure. ‘Vz_perp_X.csv’ are atom lifetime measurements where X is the perpendicular trap depth in units of the lattice photon recoil energy. First row is the trap depth. Second row is the atom lifetime in units of seconds. Third row is the atom lifetime error bar (one standard deviation).

‘plot_fig_S6c_4.py’ is the python script to plot the lower right figure. ‘Vz_perp_X.csv’ are atom lifetime measurements where X is the perpendicular trap depth in units of the lattice photon recoil energy. First row is the trap depth. Second row is the atom lifetime in units of seconds. Third row is the atom lifetime error bar (one standard deviation).

Access information

The link to this data will be provided in the citations section of our published manuscript. All questions may be directed to the paper’s corresponding authors.

Code/Software

• Theory code - A Mathematica notebook is provided containing sample code used to numerically solve the full many-body Hamiltonian in Fig 3.
• Data code - Camera images are processed using ‘image_processing/absorption imaging.py’ code. We use this absorption imaging procedure to extract the atom number and excitation fraction values in the provided data.