DOI: 10.5061/dryad.j6q573nrb
title: Data from: A dissipation-induced superradiant transition in a strontium cavity-QED system

description: Driven-dissipative many-body systems are ubiquitous in nature and a
 fundamental resource for quantum technologies. However, they are also
 complex and hard to model since they cannot be described by the standard
 tools in equilibrium statistical mechanics. Probing non-equilibrium
 critical phenomena in pristine setups can illuminate new perspectives on
 such systems. Here we use an ensemble of cold $^{88}$Sr atoms coupled to a
 driven high-finesse cavity to study the cooperative resonance fluorescence
 (CRF) model, a classic driven-dissipative model describing coherently
 driven dipoles superradiantly emitting light. We observe its
 non-equilibrium phase diagram characterized by a second-order phase
 transition. Below a critical drive strength, the atoms quickly reach the
 so-called superradiant steady-state featuring a macroscopic dipole moment;
 above the critical point, the atoms undergo persistent Rabi-like
 oscillations. At longer times, spontaneous emission transforms the
 second-order transition into a discontinuous first-order transition. Our
 observations pave the way for harnessing robust entangled states and
 exploring boundary time crystals in driven-dissipative systems.
description: # A dissipation-induced superradiant transition in a strontium cavity-QED
 system
 [https://doi.org/10.5061/dryad.j6q573nrb](https://doi.org/10.5061/dryad.j6q573nrb) ## Description of the data and file structure Files are named according to the following naming convention: fig`ASSOCIATED SUBFIGURE.csv`. See the explanation below: `[ASSOCIATED SUBFIGURE]` references the subfigure of the manuscript where the data is plotted. This repository contains data from `fig2`, `fig3`, `fig4`, and `fig5`, which are the four figures containing experimental data. All of these figures contain sub-panels which are labeled alphabetically. For example, data from Fig. 2, panel c is referenced by `fig2c`. Data in each file is separated into columns. They represent x, y-coordinate value of each data point or corresponding error bars. They are labeled according to the following naming convention: `[PARAMETER]_[COORDINATE/ERRORBAR]`. See the explanation below: `[PARAMETER]` refers to the parameter distinguishing different traces in a subfigure. For example, data from Fig. 2a is characterized by different atom numbers, so `N=3.4e3`, `N=8.2e3`, and `N=2.1e4` are used to label different datasets with different atom numbers. For completeness, we used `\Omega_d/\Omega_c=1.4`, `$t=9~\mu$s`, `Quench`/`Ramp`, `\Delta_{ca}=0` to represent different Rabi frequencies used, different drive durations, different ways of turning on the drive, and different cavity-atom detunings used in the experiment. For all the simulation results presented in the paper, `[PARAMETER]` is further appended by `_theory`. `[COORDINATE/ERRORBAR]` denotes the x, y-coordinates of the data or the associated error bars. Concretely, 4 types of data are recorded: * *x*: x-coordinate of the data in that trace. * *y*: y-coordinate of the data in that trace. * *x_error*: error bars associated with each x-data point in that trace. * *y_error*: error bars associated with each y-data point in that trace. The data is expressed in the same units present in the figures. For completeness, we describe the units here: * Drive Rabi frequency are recorded in `MHz`. * Normalized Rabi frequency is dimensionless. * Spin projection Jz/(N/2) are normalized to `[-1,1]`. * Fractional transmission are normalized to `[0,1]`. * Drive duration t is recorded in units of `μs`. 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 an `_error` after the measured value. For example, the error bars for y-coordinate data reported as `N=2.1e4_y` are labeled with a header `N=2.1e4_y_error`.