Documen a ion and No a ion Summa y
The iles con ain da a su icien o ep oduce all he plo s in he publica ion1. Fu he
ques ions and eques s should be sen o he con ac pe son o his eco d.
The da ase s use he .jld ile o ma om he JLD package o he Julia p og amming language.
The iles’ naming con en ion is in ended o be sel -explana o y. Each ile con ains se en en ies:
1. “ps” = pa ame e s (d, ∆ , N , N1, N2, Ns, Ni ,a ol, ol):
d= numbe o spa ial dimensions (= 2 o all he iles);
∆ = imes ep size;
N = numbe o imes eps;
N1, N2= numbe o si es on he espec i e axis on each o he wo subla ices (= 10,10
o all he iles);
Ns= numbe o “ eplicas” on each la ice si e (= 1 o all he iles);
Ni = maximum numbe o i e a ions o he implici sol e be o e h owing an e o ;
a ol = absolu e ole ance (= 10−8 o all he iles);
ol = ela i e ole ance (= 10−6 o all he iles).
2. “cs” = coupling cons an s (ω0, κ, ∆, g, λ):
ω0= ca i y equency (= 1 o all he iles);
κ= pho on-loss a e (= 0 o all he iles);
∆ = a omic equency/de uning (= −0.1 o all he iles);
g= ligh -ma e in e ac ion coupling;
λ= Rydbe g in e ac ion coupling.
3. “D” = pho on p opaga o s D[1: 2,1: 2,1: 2,1: N ,1: N ]:
The i s index de e mines he ype o he p opaga o : D[1, . . .]↔F, D[2, . . .]↔ρ. The
second and hi d indices co espond o he ield ypes, wi h 1 ↔ϕ, 2 ↔π. Finally, he
las wo indices co espond o empo al a gumen s. Fo example,
D[1,1,2, n , n′
] = Fϕπ(n ·∆ , n′
·∆ ).
4. “Se” = spin Se[1: 3,1: N ] on he “e en” subla ice (subla ice Ain he pape ’s no a ion):
The i s index co esponds o he spin componen s {1,2,3}↔{x, y, z}and he second
index is he empo al a gumen . Fo example,
Se[2, n ] = ⟨ˆsy
A(n ·∆ )⟩.
5. “So” = spin So[1: 3,1: N ] on he “odd” subla ice (subla ice Bin he pape ’s no a ion):
Same no a ions.
1A. N. Mikhee , H. Hosseinabadi, J. Ma ino, “P e he maliza ion o ligh and ma e in ca i y-coupled Rydbe g
a ays”, a Xi :2504.06267 [cond-ma .s a -mech].
6. “phi” = pho on ield expec a ion alue phi[1: 2,1: N ]:
The i s index de e mines he ield ype, wi h 1 ↔ϕ, 2 ↔π, while he second index is
he empo al a gumen . Fo example,
phi[2, n ] = ⟨ˆπ(n ·∆ )⟩.
7. “P” = Hubba d–S a ono ich ield p opaga o P[1: 2,1: 2,1: 2,1: N1,1: N2,1: N ,1: N ]:
The i s index de e mines he ype o he p opaga o : P[1, . . .]↔Fχχ,P[2, . . .] = ρχχ.
The second and hi d indices co espond o he subla ice labels, wi h 1 ↔A, 2 ↔B.
The nex wo indices (n1and n2) label momen um a gumen s, wi h a con en ion ha
−Ni/2≤ni≤Ni/2−1. He e, nico esponds o one o he basis ec o s Gi, spanning he
educed B illouin zone. Finally, he las wo indices co espond o empo al a gumen s.
Fo example,
P[1,1,2, n1, n2, n , n′
] = Fχχ
AB,k(n ·∆ , n′
·∆ ),wi h k= Gx
1n1
N1
+Gx
2n2
N2
,Gy
1n1
N1
+Gy
2n2
N2!T
.
