03_Rydberg_state_prep.jl

# for ordered state preparation task

using Bloqade
using PythonCall
using KrylovKit
using SparseArrays

plt = pyimport("matplotlib.pyplot");

# scanning the detuning

nsites = 9
atoms = generate_sites(ChainLattice(), nsites, scale = 5.72)

# testing higher "pulse area" Rabi parameter and longer detuning scan
# From authors experince with state prepartion in dissipative QD and 
# Littlewood et al work on ARP on interacting systems

Ω = 2π * 8
Δ_step = 30

Δ = LinRange(-2π * 12, 2π * 12, Δ_step);


# density profile

density_g = zeros(Δ_step, nsites)

for ii in 1:Δ_step
    h_ii = rydberg_h(atoms; Δ = Δ[ii], Ω) # create the Rydberg Hamiltonian
    h_m = mat(h_ii) # convert the Hamiltonian into a matrix
    vals, vecs, info = KrylovKit.eigsolve(h_m, 1, :SR) # find the ground state eigenvalue and eigenvector
    g_state = ArrayReg(vecs[1]) # creates the initial state with all atoms in ``| 0 \rangle`` state

    for jj in 1:nsites
        density_g[ii, jj] = rydberg_density(g_state, jj) # measure the density of Rydberg excitations on each site
    end
end







# plotting for negative detuning

fig, ax = plt.subplots(figsize = (10, 4))
ax.bar(1:nsites, density_g[1, :])
ax.set_xticks(1:nsites)
ax.set_xlabel("Sites")
ax.set_ylabel("Rydberg density")
ax.set_title("Density Profile: 1D Chain, Δ = -2π * 12 MHz")
fig

# plotting for negative detuning

fig, ax = plt.subplots(figsize = (10, 4))
ax.bar(1:nsites, density_g[30, :])
ax.set_xticks(1:nsites)
ax.set_xlabel("Sites")
ax.set_ylabel("Rydberg density")
ax.set_title("Density Profile: 1D Chain, Δ = 2π * 12 MHz")
fig

# order parameter

order_para = map(1:Δ_step) do ii
    return sum(density_g[ii, 1:2:nsites]) - sum(density_g[ii, 2:2:nsites])
end

fig, ax = plt.subplots(figsize = (10, 4))
ax.plot(Δ / 2π, order_para)
ax.set_xlabel("Δ/2π (MHz) ")
ax.set_ylabel("Order parameter")
fig

# preparation of ordered states in 1D (increased the time more than 50% to test, increased the pulse area)

total_time = 3.0+2.0;
Ω_max = 2π * 6;
Ω = piecewise_linear(clocks = [0.0, 0.1, 2.1, 2.2, total_time], values = [0.0, Ω_max, Ω_max, 0, 0]);

U1 = -2π * 12;
U2 = 2π * 12;
Δ = piecewise_linear(clocks = [0.0, 0.6, 2.1, total_time], values = [U1, U1, U2, U2]);

fig, (ax1, ax2) = plt.subplots(ncols = 2, figsize = (12, 4))
Bloqade.plot!(ax1, Ω)
ax1.set_ylabel("Ω/2π (MHz)")
Bloqade.plot!(ax2, Δ)
ax2.set_ylabel("Δ/2π (MHz)")
fig

nsites = 9
atoms = generate_sites(ChainLattice(), nsites, scale = 5.72)

h = rydberg_h(atoms; Δ, Ω)

reg = zero_state(9);
prob = SchrodingerProblem(reg, total_time, h);
integrator = init(prob, Vern8());


##

densities = []
for _ in TimeChoiceIterator(integrator, 0.0:1e-3:total_time)
    push!(densities, rydberg_density(reg))
end
D = hcat(densities...);


##

fig, ax = plt.subplots(figsize = (10, 4))
shw = ax.imshow(real(D), interpolation = "nearest", aspect = "auto", extent = [0, total_time, 0.5, nsites + 0.5])
ax.set_xlabel("time (μs)")
ax.set_ylabel("site")
ax.set_xticks(0:0.2:total_time)
ax.set_yticks(1:nsites)
bar = fig.colorbar(shw)
fig

bitstring_hist(reg; nlargest = 20)

# Emulation in the Blockade subspace