remove Plots.jl

Author: ytdHuang

HierarchicalEOM.jl/cavityQED.qmd

@@ -10,8 +10,7 @@ engine: julia
 ## Package Imports
 ```{julia}
 using HierarchicalEOM
-using LaTeXStrings
-import Plots
+using CairoMakie
 ```
 
 ## Introduction
@@ -53,22 +52,26 @@ N = 3 ## system cavity Hilbert space cutoff
 ωA = 2
 ωc = 2
 g = 0.1
-## operators
+
+# operators
 a_c = destroy(N)
 I_c = qeye(N)
 σz_A = sigmaz()
 σm_A = sigmam()
 I_A = qeye(2)
-## operators in tensor-space
+
+# operators in tensor-space
 a = tensor(a_c, I_A)
 σz = tensor(I_c, σz_A)
 σm = tensor(I_c, σm_A)
-## Hamiltonian
+
+# Hamiltonian
 H_A = 0.5 * ωA * σz
 H_c = ωc * a' * a
 H_int = g * (a' * σm + a * σm')
 H_s = H_A + H_c + H_int
-## initial state
+
+# initial state
 ψ0 = tensor(basis(N, 0), basis(2, 0));
 ```
 
@@ -94,13 +97,19 @@ Before incorporating the correlation function into the HEOMLS matrix, it is esse
 tlist_test = 0:0.1:10;
 Bath_test = Boson_DrudeLorentz_Pade(a + a', Γ, W, kT, 1000);
 Ct = correlation_function(Bath, tlist_test);
-Ct2 = correlation_function(Bath_test, tlist_test);
-Plots.plot(tlist_test, real(Ct), label = "N=20 (real part )", linestyle = :dash, linewidth = 3)
-Plots.plot!(tlist_test, real(Ct2), label = "N=1000 (real part)", linestyle = :solid, linewidth = 3)
-Plots.plot!(tlist_test, imag(Ct), label = "N=20 (imag part)", linestyle = :dash, linewidth = 3)
-Plots.plot!(tlist_test, imag(Ct2), label = "N=1000 (imag part)", linestyle = :solid, linewidth = 3)
-Plots.xaxis!("t")
-Plots.yaxis!("C(t)")
+Ct2 = correlation_function(Bath_test, tlist_test)
+
+# plot
+fig = Figure(size = (500, 350))
+ax = Axis(fig[1, 1], xlabel = L"t", ylabel = L"C(t)")
+lines!(ax, tlist_test, real(Ct2), label = L"$N=1000$ (real part)", linestyle = :solid)
+lines!(ax, tlist_test, real(Ct),  label = L"$N=20$ (real part)", linestyle = :dash)
+lines!(ax, tlist_test, imag(Ct2), label = L"$N=1000$ (imag part)", linestyle = :solid)
+lines!(ax, tlist_test, imag(Ct),  label = L"$N=20$ (imag part)", linestyle = :dash)
+
+axislegend(ax, position = :rt)
+
+fig
 ```
 
 ## Construct HEOMLS matrix
@@ -149,83 +158,102 @@ np_steady_H = expect(a' * a, steady_H)
 plot results
 
 ```{julia}
-p1 = Plots.plot(
-    t_list,
-    [σz_evo_H, ones(length(t_list)) .* σz_steady_H],
-    label = [L"\langle \sigma_z \rangle" L"\langle \sigma_z \rangle ~~(\textrm{steady})"],
-    linewidth = 3,
-    linestyle = [:solid :dash],
-)
-p2 = Plots.plot(
-    t_list,
-    [np_evo_H, ones(length(t_list)) .* np_steady_H],
-    label = [L"\langle a^\dagger a \rangle" L"\langle a^\dagger a \rangle ~~(\textrm{steady})"],
-    linewidth = 3,
-    linestyle = [:solid :dash],
-)
-Plots.plot(p1, p2, layout = [1, 1])
-Plots.xaxis!("t")
+fig = Figure(size = (600, 350))
+
+ax1 = Axis(fig[1, 1], xlabel = L"t")
+lines!(ax1, t_list, σz_evo_H, label = L"\langle \sigma_z \rangle", linestyle = :solid)
+lines!(ax1, t_list, ones(length(t_list)) .* σz_steady_H, label = L"\langle \sigma_z \rangle ~~(\textrm{steady})", linestyle = :dash)
+axislegend(ax1, position = :rt)
+
+ax2 = Axis(fig[2, 1], xlabel = L"t")
+lines!(ax2, t_list, np_evo_H, label = L"\langle a^\dagger a \rangle", linestyle = :solid)
+lines!(ax2, t_list, ones(length(t_list)) .* np_steady_H, label = L"\langle a^\dagger a \rangle ~~(\textrm{steady})", linestyle = :dash)
+axislegend(ax2, position = :rt)
+
+fig
 ```
 
 ## Power spectrum
 
 ```{julia}
 ω_list = 1:0.01:3
 psd_H = PowerSpectrum(M_Heom, steady_H, a, ω_list)
-Plots.plot(ω_list, psd_H, linewidth = 3)
-Plots.xaxis!(L"\omega")
+
+# plot
+fig = Figure(size = (500, 350))
+ax = Axis(fig[1, 1], xlabel = L"\omega")
+lines!(ax, ω_list, psd_H)
+
+fig
 ```
 
 ## Compare with Master Eq. approach
 
 The Lindblad master equations which describes the cavity couples to an extra bosonic reservoir with [Drude-Lorentzian spectral density](https://qutip.org/HierarchicalEOM.jl/stable/bath_boson/Boson_Drude_Lorentz/#Boson-Drude-Lorentz) is given by
 
 ```{julia}
-## Drude_Lorentzian spectral density
+# Drude_Lorentzian spectral density
 Drude_Lorentz(ω, Γ, W) = 4 * Γ * W * ω / ((ω)^2 + (W)^2)
-## Bose-Einstein distribution
+
+# Bose-Einstein distribution
 n_b(ω, kT) = 1 / (exp(ω / kT) - 1)
-## build the jump operators
-jump_op =
-    [sqrt(Drude_Lorentz(ωc, Γ, W) * (n_b(ωc, kT) + 1)) * a, sqrt(Drude_Lorentz(ωc, Γ, W) * (n_b(ωc, kT))) * a', J_pump];
-## construct the HEOMLS matrix for master equation
+
+# build the jump operators
+jump_op = [
+    sqrt(Drude_Lorentz(ωc, Γ, W) * (n_b(ωc, kT) + 1)) * a,
+    sqrt(Drude_Lorentz(ωc, Γ, W) * (n_b(ωc, kT)))     * a',
+    J_pump
+];
+
+# construct the HEOMLS matrix for master equation
 M_master = M_S(H_s)
 M_master = addBosonDissipator(M_master, jump_op)
-## time evolution
+
+# time evolution
 sol_M = HEOMsolve(M_master, ψ0, t_list; e_ops = [σz, a' * a]);
-## steady state
+
+# steady state
 steady_M = steadystate(M_master);
-## expectation value of σz
+
+# expectation value of σz
 σz_evo_M = real(sol_M.expect[1, :])
 σz_steady_M = expect(σz, steady_M)
-## average photon number
+
+# average photon number
 np_evo_M = real(sol_M.expect[2, :])
-np_steady_M = expect(a' * a, steady_M)
-p1 = Plots.plot(
-    t_list,
-    [σz_evo_M, ones(length(t_list)) .* σz_steady_M],
-    label = [L"\langle \sigma_z \rangle" L"\langle \sigma_z \rangle ~~(\textrm{steady})"],
-    linewidth = 3,
-    linestyle = [:solid :dash],
-)
-p2 = Plots.plot(
-    t_list,
-    [np_evo_M, ones(length(t_list)) .* np_steady_M],
-    label = [L"\langle a^\dagger a \rangle" L"\langle a^\dagger a \rangle ~~(\textrm{steady})"],
-    linewidth = 3,
-    linestyle = [:solid :dash],
-)
-Plots.plot(p1, p2, layout = [1, 1])
-Plots.xaxis!("t")
+np_steady_M = expect(a' * a, steady_M);
+```
+
+plot results
+
+```{julia}
+fig = Figure(size = (600, 350))
+
+ax1 = Axis(fig[1, 1], xlabel = L"t")
+lines!(ax1, t_list, σz_evo_M, label = L"\langle \sigma_z \rangle", linestyle = :solid)
+lines!(ax1, t_list, ones(length(t_list)) .* σz_steady_M, label = L"\langle \sigma_z \rangle ~~(\textrm{steady})", linestyle = :dash)
+axislegend(ax1, position = :rt)
+
+ax2 = Axis(fig[2, 1], xlabel = L"t")
+lines!(ax2, t_list, np_evo_M, label = L"\langle a^\dagger a \rangle", linestyle = :solid)
+lines!(ax2, t_list, ones(length(t_list)) .* np_steady_M, label = L"\langle a^\dagger a \rangle ~~(\textrm{steady})", linestyle = :dash)
+axislegend(ax2, position = :rt)
+
+fig
 ```
 
 We can also calculate the power spectrum
 
 ```{julia}
 ω_list = 1:0.01:3
 psd_M = PowerSpectrum(M_master, steady_M, a, ω_list)
-Plots.plot(ω_list, psd_M, linewidth = 3)
-Plots.xaxis!(L"\omega")
+
+# plot
+fig = Figure(size = (500, 350))
+ax = Axis(fig[1, 1], xlabel = L"\omega")
+lines!(ax, ω_list, psd_M)
+
+fig
 ```
 
 Due to the weak coupling between the system and an extra bosonic environment, the Master equation's outcome is expected to be similar to the results obtained from the HEOM method.

Makefile

@@ -6,7 +6,7 @@ include _environment
 default: help
 
 render:
-	${JULIA} --project=@. -e 'import Pkg; Pkg.instantiate(); Pkg.resolve(); Pkg.precompile(); using QuantumToolbox, HierarchicalEOM;'
+	${JULIA} --project=@. -e 'import Pkg; Pkg.resolve(); Pkg.instantiate(); Pkg.precompile(); using QuantumToolbox, HierarchicalEOM;'
 	${JULIA} --project=@. -e 'using QuantumToolbox, HierarchicalEOM;'
 	${QUARTO} render
 

Project.toml

@@ -1,6 +1,5 @@
 [deps]
 CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
 HierarchicalEOM = "a62dbcb7-80f5-4d31-9a88-8b19fd92b128"
-LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
-Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 QuantumToolbox = "6c2fb7c5-b903-41d2-bc5e-5a7c320b9fab"
+QuartoNotebookRunner = "4c0109c6-14e9-4c88-93f0-2b974d3468f4"

README.md

@@ -25,7 +25,7 @@ make render
 or
 ```shell
 source _environment
-julia --project=@. -e 'import Pkg; Pkg.instantiate(); Pkg.resolve(); Pkg.precompile()'
+julia --project=@. -e 'import Pkg; Pkg.resolve(); Pkg.instantiate(); Pkg.precompile()'
 julia --project=@. -e 'using QuantumToolbox, HierarchicalEOM;'
 quarto render
 ```