Datasets for "Prethermalization of light and matter in cavity-coupled Rydberg arrays"

Documentation and Notation Summary The files contain data sufficient to reproduce all the plots in the publication1. Further questions and requests should be sent to the contact person for this record. The datasets use the .jld file format from the JLD package of the Julia programming language. The files’ naming convention is intended to be self-explanatory. Each file contains seven entries: 1. “ps” = parameters (d, ∆t, Nt, N1, N2, Ns, Nit,atol,rtol): d= number of spatial dimensions (= 2 for all the files); ∆t= timestep size; Nt= number of timesteps; N1, N2= number of sites on the respective axis on each of the two sublattices (= 10,10 for all the files); Ns= number of “replicas” on each lattice site (= 1 for all the files); Nit = maximum number of iterations for the implicit solver before throwing an error; atol = absolute tolerance (= 10−8for all the files); rtol = relative tolerance (= 10−6for all the files). 2. “cs” = coupling constants (ω0, κ, ∆, g, λ): ω0= cavity frequency (= 1 for all the files); κ= photon-loss rate (= 0 for all the files); ∆ = atomic frequency/detuning (= −0.1 for all the files); g= light-matter interaction coupling; λ= Rydberg interaction coupling. 3. “D” = photon propagators D[1: 2,1: 2,1: 2,1: Nt,1: Nt]: The first index determines the type of the propagator: D[1, . . .]↔F, D[2, . . .]↔ρ. The second and third indices correspond to the field types, with 1 ↔ϕ, 2 ↔π. Finally, the last two indices correspond to temporal arguments. For example, D[1,1,2, nt, n′ t] = Fϕπ(nt·∆t, n′ t·∆t). 4. “Se” = spin Se[1: 3,1: Nt] on the “even” sublattice (sublattice Ain the paper’s notation): The first index corresponds to the spin components {1,2,3}↔{x, y, z}and the second index is the temporal argument. For example, Se[2, nt] = ⟨ˆsy A(nt·∆t)⟩. 5. “So” = spin So[1: 3,1: Nt] on the “odd” sublattice (sublattice Bin the paper’s notation): Same notations. 1A. N. Mikheev, H. Hosseinabadi, J. Marino, “Prethermalization of light and matter in cavity-coupled Rydberg arrays”, arXiv:2504.06267 [cond-mat.stat-mech]. 6. “phi” = photon field expectation value phi[1: 2,1: Nt]: The first index determines the field type, with 1 ↔ϕ, 2 ↔π, while the second index is the temporal argument. For example, phi[2, nt] = ⟨ˆπ(nt·∆t)⟩. 7. “P” = Hubbard–Stratonovich field propagator P[1: 2,1: 2,1: 2,1: N1,1: N2,1: Nt,1: Nt]: The first index determines the type of the propagator: P[1, . . .]↔Fχχ,P[2, . . .] = ρχχ. The second and third indices correspond to the sublattice labels, with 1 ↔A, 2 ↔B. The next two indices (n1and n2) label momentum arguments, with a convention that −Ni/2≤ni≤Ni/2−1. Here, nicorresponds to one of the basis vectors Gi, spanning the reduced Brillouin zone. Finally, the last two indices correspond to temporal arguments. For example, P[1,1,2, n1, n2, nt, n′ t] = Fχχ AB,k(nt·∆t, n′ t·∆t),with k= Gx 1n1 N1 +Gx 2n2 N2 ,Gy 1n1 N1 +Gy 2n2 N2!T .