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index.jl
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### A Pluto.jl notebook ###
# v0.19.26
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
end
# ╔═╡ 8a91db1a-03f0-11ee-1958-6da2a99c3d9b
begin
using QuantumOptics
using Plots
using LaTeXStrings
using PlutoUI
using Latexify
using LinearAlgebra
end
# ╔═╡ 9642e591-58fb-448a-b653-e144b5b8d8c9
begin
# Parameters (defined below as sliders)
#γ = 2.0
#η = 1.5
#Δ = 0.0
T = [0:0.05:10;]
end
# ╔═╡ b7c0e4d9-4084-4d2c-9104-9adaf6ec5f60
begin
gamma_slider = @bind γ Slider(0:0.1:8, show_value=true, default = 2.)
delta_slider = @bind δ Slider(0:0.1:8, show_value=true, default=0.)
eta_slider = @bind Ω₀ Slider(0:0.1:8, show_value=true, default = 1.5)
md"""
γ: $(gamma_slider)
δ: $(delta_slider)
Ω₀: $(eta_slider)
"""
end
# ╔═╡ 656749ee-3e6b-4aaa-8f20-94c3b6882ad4
begin
# Basis and operators
b1 = SpinBasis(1//2)
sm = sigmam(b1) # matrix |ground><excited|
sp = sigmap(b1) # matrix |excited><ground|
sz = sigmaz(b1) # pauli matrix σ_z
# Deterministic part of the Hamiltonian (ħ=1)
H = 0.5*(δ*sz - Ω₀*(sp + sm) )
# Stochastic part of the Hamiltonian
Hs = 0.5*sqrt(γ)*sz
end
# ╔═╡ 03e32213-b93c-4613-ba9a-091f4ba2f043
# Initial state
ψ0 = spinup(b1)
# ╔═╡ ffe18f08-03d1-4f5a-8c26-18e4d54f0af2
# Average over stochastic Schrödinger equations
fout(t, psi) = (
real(expect(QuantumOptics.projector(spinup(b1)), psi)), real(expect(QuantumOptics.projector(ψ0), psi)),
)
# ╔═╡ f3e152ed-562b-446c-8fbd-5f8a2adc1654
(collect(H))
# ╔═╡ ce6ffcf6-9e09-4c46-bec4-ed4320107fde
begin
# Master equation with dephasing
tout, fout_vals = timeevolution.master(T, ψ0, H, [sz]; rates=[0.25γ], fout=fout)
occ_spinup = first.(fout_vals)
occ_spindown = last.(fout_vals)
end
# ╔═╡ 58603de3-be4f-410d-b163-596d4c8e9f44
begin
plot(tout, occ_spinup, label="", legend=:outerbottom)
#plot!(tout, occ_spindown, label="down")
labelplotfun = @latexrun f(t) = (Ω₀ / sqrt(Ω₀^2 + δ^2))^2*cos(sqrt(Ω₀^2 + δ^2) * t / 2)^2 + (δ/sqrt(Ω₀^2 + δ^2))^2
plot!(tout, f, label=labelplotfun)
#plot!(tout, z_im)
# axis([0, T[end], -1, 1])
yaxis!([0, 1.1])
yticks!(-1:0.2:1)
xlabel!("t (a.u.)")
ylabel!("occupation")
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
QuantumOptics = "6e0679c1-51ea-5a7c-ac74-d61b76210b0c"
[compat]
LaTeXStrings = "~1.3.0"
Latexify = "~0.16.0"
Plots = "~1.38.15"
PlutoUI = "~0.7.51"
QuantumOptics = "~1.0.10"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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