https://doi.org/10.5061/dryad.7h44j100j

This repository contains the data (both experimental and from simulations) plotted in the associated manuscript.

Description of the data and file structure

Files are named according to the following naming convention: [ASSOCIATED FIGURE]_[DATA SOURCE]_[DESCRIPTION OF DATA].csv. See the explanation below:

• [ASSOCIATED FIGURE] references the figure of the manuscript where the data is plotted. This repository contains data from fig2, fig3, fig4, and figed4, which are the four figures containing experimental data. All of these figures contain sub-panels which are labeled alphabetically. For example, data from Fig. 3, panel f is referenced by fig3f.
• [DATA SOURCE] specifies whether the data is derived from raw experimental data (expt) or from theoretical simulations (simideal or simfull). Note that many figure panels feature data from multiple sources. For clarity, we have uploaded data from different sources as separate files. We use two different models to simulate our system (see manuscript for a detailed description of how the models are defined).
  • simideal refers to so-called "ideal" simulations as described in the paper, which ignore single-particle dissipation and motion of our atoms along the cavity axis.
  • simfull refers to "full" simulations of the experiment, which attempt to capture all technical details of the experiment.
• [DESCRIPTION OF DATA] is meant to be a short semantic identifier describing the type of data included in the file. We define the identifiers here:
  • Files labeled with timetraces contain time dynamics of the order parameter Δ_BCS. The first column is time expressed in μs. The remaining columns describe Δ_BCS for different values of our control parameters (χN, δ_s, φ₀). We indicate the value of any scanned parameters in the header text: for example, the header chiN_0.109_MHz indicates that this column was taken at χN = 2π * 0.109 MHz.
    • timestraces_finesample files represent simulation data with a parameter sweep finer than what is realized in the experiment. These files are larger due to the many parameter values simulated.
  • Files labeled with oscfreqs or oscamps measure the oscillation frequency or amplitude of Δ_BCS. These values are plotted against the relevant control parameter in the first column.
  • Files labeled with avggap measure the average value of Δ_BCS at long times (as defined in the manuscript), plotted against the relevant control parameter.
  • Files labeled with lifetime measure the 1/e coherence time of Δ_BCS.
  • Files labeled with PSDs describe the power spectra of Δ_BCS.
  • Files labeled with peaktrough_times measure the detected time positions of the first peak and trough of curves in Extended Data Fig. 4.
  • Files labeled with higgsfreqs measure the oscillation frequency of transient "Higgs"-like behavior in Extended Data Fig. 4, plotted against the control parameter φ₀. These frequencies are inferred from the peak and trough times from peaktrough_times files.
    • higgsfreqs_gap files also report the Higgs oscillation frequency, this time plotted against the quantity 2Δ_∞ as defined in the manuscript.

The data is expressed in the same units present in the figures. For completeness, we describe the units here:

• Time values are written in units of μs, indicated by the header label "Time_us".
• Frequency values are expressed in MHz and represent cycles/sec as opposed to angular units. These column headings are typically written like "fosc_MHz".
• The control parameter φ₀, representing an initial phase spread of the atomic ensemble as defined in the manuscript, is reported in units of π as indicated in the header phi0_pi. For example, a reported value of 0.418 indicates that φ₀ = 0.418π.
• Plots of the order parameter Δ_BCS are typically unitless and normalized to the initial value.
  • The exception to this is in Extended Data Fig. 4a (figed4a), which plots Δ_BCS as a frequency in MHz.
  • Data representing oscillation amplitudes in time traces of Δ_BCS are also unitless and are normalized in the same way as Δ_BCS itself.
• The power spectral densities (PSDs) from fig3d are expressed in arbitrary units.

Below, we describe how error bars are reported:

• All error bars represent the standard error of the mean for the relevant quantity.
• Error bars are reported a separate column and are typically indicated in the header with a d in front of the measured value. For example, the error bars for oscillation frequencies reported as foscs_MHz are labeled with a header dfoscs_MHz.
• For some traces, we provide both statistical error bars and uncertainties to systematic corrections. These are reported as separate columns and are indicated by, for example, dfoscs_stat_MHz and dfoscs_sys_MHz respectively.
• For some traces, we allow for asymmetric error bars. These are expressed with l or r characters, representing left-hand and right-hand errors respectively. For example: dfl_MHz, dfr_MHz.