Nature | Vol 577 | 23 January 2020 | 485additional regrowth term in equation ( 3 )) to sustain the SOC state on
even longer timescales^47. It should also be possible to investigate other
observables beyond the mean-field level, including spatio-temporal
correlations in the active and remaining densities. This would make
it possible to determine multiple critical exponents and scaling rela-
tions, helping to answer long-standing questions about the universal or
non-universal aspects of SOC and its relation to other non-equilibrium
universality classes. Additionally, further experiments could explore
the interface between driven–dissipative and isolated quantum systems
governed by competing classical and quantum dynamical rules^48 –^50 ,
ultimately leading to a more complete and quantitative understanding
of non-equilibrium universality.
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availability are available at https://doi.org/10.1038/s41586-019-1908-6.
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abcRydberg number1,00050001,5000.000.020.040.06n^ t(μm–3)Time, t (ms) Avalanche size, sProbability00100 2 304 101 10210 –510 –410 –310 –2Fig. 4 | Observation of power-law distributed excitation avalanches.
a, Evolution of the remaining density for the 66p3/2 state (solid line).
b, Simultaneously measured Rydberg atom number (active component)
integrated over the whole atom cloud showing large f luctuations of the active
density for t ≳ 10 ms (solid line). Each of the 200 plotted values corresponds to a
new realization of the experiment. The dashed lines in a, b are mean-field
predictions, where the effective volume of the atom cloud in b is adjusted for
optimal agreement. c, Probability distribution for the instantaneous number
of Rydberg excitations (avalanche size) for 3,630 experimental runs. To
determine the power-law exponent we truncate the binned data (by eye, to the
region where the log–log slope is approximately constant), in a finite window
indicated by the solid red line and apply a maximum-likelihood estimation. The
power-law exponent α = −1.37(2) is depicted by the black, straight dashed line.
The grey data correspond to a control measurement for resonant excitation
with a short duration laser pulse, which does not exhibit a power-law
distribution. The dashed grey line is a fit to a stretched Poissonian distribution.