refactor: consolidate interaction_picture_A into a single function

docs/src/api.md

@@ -93,15 +93,7 @@ interaction_picture_M_2modes_equal
 ```
 
 ```@docs
-interaction_picture_A_2modes
-```
-
-```@docs
-interaction_picture_A_3modes
-```
-
-```@docs
-interaction_picture_A_4modes
+interaction_picture_A
 ```
 
 ## [Correlations](@id API: Correlations)

docs/src/examples/06-1_interaction-picture__PRA2023_107-013706_fig2.md

@@ -98,7 +98,7 @@ gu_t = u_to_gu(u, T)
 gv_t = v_to_gv(u, T) # identical output mode v(t) = u(t)
 
 # interaction-picture coefficient matrix M(t) for u ↔ v
-A_uv = interaction_picture_A_2modes(gu_t, gv_t)
+A_uv = interaction_picture_A(gu_t, gv_t)
 M_t = interaction_picture_M(A_uv, T)
 
 # constant and time-dependent parameters

docs/src/examples/08-1_pulse-delay__simple.md

@@ -179,7 +179,7 @@ nothing # hide
 
 ````@example 08-1_pulse-delay__simple
 # interaction-picture coefficient matrix M(t) for u ↔ d
-A_ud = interaction_picture_A_2modes(gu_, gin_)
+A_ud = interaction_picture_A(gu_, gin_)
 M_t = interaction_picture_M(A_ud, T)
 
 M_ls = [M(i, j) for i = 1:la for j = 1:la]

docs/src/implementation.md

@@ -121,7 +121,7 @@ A(t) = \frac{1}{2}\begin{bmatrix}
 \end{bmatrix}
 ```
 
-The functions [`interaction_picture_A_2modes`](@ref), [`interaction_picture_A_3modes`](@ref), and [`interaction_picture_A_4modes`](@ref) build the coupling matrices for two, three and four modes. For two equal modes ($u(t) = v(t)$) the analytic solution of $M(t)$ is provided by [`interaction_picture_M_2modes_equal`](@ref).
+The function [`interaction_picture_A`](@ref) builds the coupling matrix for any number of modes. For two equal modes ($u(t) = v(t)$) the analytic solution of $M(t)$ is provided by [`interaction_picture_M_2modes_equal`](@ref).
 
 Using the interaction picture for scattering with a Fock state $| n=20 \rangle$ on a two-level system, is  demonstrated in the example [Interaction Picture Scattering with a Quantum Pulse](examples/06-1_interaction-picture__PRA2023_107-013706_fig2.md). 
 

examples/06-1_interaction-picture__PRA2023_107-013706_fig2.jl

@@ -87,7 +87,7 @@ gu_t = u_to_gu(u, T)
 gv_t = v_to_gv(u, T) # identical output mode v(t) = u(t)
 
 ## interaction-picture coefficient matrix M(t) for u ↔ v
-A_uv = interaction_picture_A_2modes(gu_t, gv_t)
+A_uv = interaction_picture_A(gu_t, gv_t)
 M_t = interaction_picture_M(A_uv, T)
 
 ## constant and time-dependent parameters

examples/08-1_pulse-delay__simple.jl

@@ -177,7 +177,7 @@ nothing # hide
 #
 
 ## interaction-picture coefficient matrix M(t) for u ↔ d
-A_ud = interaction_picture_A_2modes(gu_, gin_)
+A_ud = interaction_picture_A(gu_, gin_)
 M_t = interaction_picture_M(A_ud, T)
 
 M_ls = [M(i, j) for i = 1:la for j = 1:la]

src/QuantumInputOutput.jl

@@ -38,9 +38,7 @@ export SLH, # SLH.jl
     two_time_corr_matrix,
     interaction_picture_M, # interaction picture
     interaction_picture_M_2modes_equal,
-    interaction_picture_A_2modes,
-    interaction_picture_A_3modes,
-    interaction_picture_A_4modes,
+    interaction_picture_A,
     substitute_operators
 
 include("SLH.jl")

src/interaction_picture.jl

@@ -61,88 +61,54 @@ end
 _as_time_function(x) = x isa Function ? x : (_ -> x)
 
 """
-    interaction_picture_A_2modes(g1, g2)
+    interaction_picture_A(gs)
+    interaction_picture_A(g1, g2, gs...)
 
-Coefficient matrix `A(t)` for two virtual modes `(1, 2)`,
+Coefficient matrix `A(t)` for `N` interacting modes with couplings `gs = [g_1, …, g_N]`.
+All couplings may be time-dependent functions or constants.
+
+The anti-Hermitian matrix has entries
 
 ```math
-A(t) = \\frac{1}{2}
-\\begin{bmatrix}
-0 & g_1(t) g_2^*(t) \\\\
--g_1^*(t) g_2(t) & 0
-\\end{bmatrix}
+A_{ij}(t) = \\tfrac{1}{2}\\,g_i(t)\\,g_j^*(t), \\quad i < j,
+\\qquad A_{ji} = -A_{ij}^*,
+\\qquad A_{ii} = 0.
 ```
 
-All couplings may be time-dependent or constant.
-"""
-function interaction_picture_A_2modes(g1, g2)
-    g1f = _as_time_function(g1)
-    g2f = _as_time_function(g2)
-    A(t) = 0.5 * [
-        0 g1f(t) * conj(g2f(t));
-        -conj(g1f(t)) * g2f(t) 0
-    ]
-    return A
-end
-interaction_picture_A_2modes(g_ls) = interaction_picture_A_2modes(g_ls...)
-
-"""
-    interaction_picture_A_3modes(g1, g2, g3)
-
-Coefficient matrix `A(t)` for three interacting modes ordered as `(1, 2, 3)`
+For two modes this gives
 
 ```math
 A(t) = \\frac{1}{2}
 \\begin{bmatrix}
-0 & g_1(t) g_2^*(t) & g_1(t) g_3^*(t) \\\\
--g_1^*(t) g_2(t) & 0 & g_2(t) g_3^*(t) \\\\
--g_1^*(t) g_3(t) & -g_2^*(t) g_3(t) & 0
-\\end{bmatrix}
+0 & g_1(t)\\, g_2^*(t) \\\\
+-g_1^*(t)\\, g_2(t) & 0
+\\end{bmatrix},
 ```
 
-All couplings may be time-dependent or constant.
-"""
-function interaction_picture_A_3modes(g1, g2, g3)
-    g1f = _as_time_function(g1)
-    g2f = _as_time_function(g2)
-    g3f = _as_time_function(g3)
-    A(t) =
-        0.5 * [
-            0 conj(g2f(t)) * g1f(t) g1f(t) * conj(g3f(t));
-            -g2f(t) * conj(g1f(t)) 0 g2f(t) * conj(g3f(t));
-            -conj(g1f(t)) * g3f(t) -conj(g2f(t)) * g3f(t) 0
-        ]
-    return A
-end
-
-"""
-    interaction_picture_A_4modes(g1, g2, g3, g4)
-
-Coefficient matrix `A(t)` for four interacting modes ordered as `(1, 2, 3, 4)`
+and for three modes
 
 ```math
 A(t) = \\frac{1}{2}
 \\begin{bmatrix}
-0 & g_1(t) g_2^*(t) & g_1(t) g_3^*(t) & g_1(t) g_4^*(t) \\\\
--g_1^*(t) g_2(t) & 0 & g_2(t) g_3^*(t) & g_2(t) g_4^*(t) \\\\
--g_1^*(t) g_3(t) & -g_2^*(t) g_3(t) & 0 & g_3(t) g_4^*(t) \\\\
--g_1^*(t) g_4(t) & -g_2^*(t) g_4(t) & -g_3^*(t) g_4(t) & 0
-\\end{bmatrix}
+0 & g_1(t)\\, g_2^*(t) & g_1(t)\\, g_3^*(t) \\\\
+-g_1^*(t)\\, g_2(t) & 0 & g_2(t)\\, g_3^*(t) \\\\
+-g_1^*(t)\\, g_3(t) & -g_2^*(t)\\, g_3(t) & 0
+\\end{bmatrix}.
 ```
-
-All couplings may be time-dependent or constant.
 """
-function interaction_picture_A_4modes(g1, g2, g3, g4)
-    g1f = _as_time_function(g1)
-    g2f = _as_time_function(g2)
-    g3f = _as_time_function(g3)
-    g4f = _as_time_function(g4)
-    A(t) =
-        0.5 * [
-            0 g1f(t) * conj(g2f(t)) g1f(t) * conj(g3f(t)) g1f(t) * conj(g4f(t));
-            -conj(g1f(t)) * g2f(t) 0 g2f(t) * conj(g3f(t)) g2f(t) * conj(g4f(t));
-            -conj(g1f(t)) * g3f(t) -conj(g2f(t)) * g3f(t) 0 g3f(t) * conj(g4f(t));
-            -conj(g1f(t)) * g4f(t) -conj(g2f(t)) * g4f(t) -conj(g3f(t)) * g4f(t) 0
-        ]
+function interaction_picture_A(gs)
+    gfs = _as_time_function.(gs)
+    n = length(gfs)
+    function A(t)
+        g = [gf(t) for gf in gfs]
+        M = zeros(ComplexF64, n, n)
+        for i in 1:n, j in (i+1):n
+            M[i, j] = g[i] * conj(g[j])
+            M[j, i] = -conj(M[i, j])
+        end
+        return 0.5 * M
+    end
     return A
 end
+
+interaction_picture_A(g1, g2, gs...) = interaction_picture_A([g1, g2, gs...])

test/test_interaction_picture.jl

@@ -56,7 +56,7 @@ using Test
     gv_t = v_to_gv(u, T)
 
     # Interaction-picture coefficient matrices
-    A_uv = interaction_picture_A_2modes(gu_t, gv_t)
+    A_uv = interaction_picture_A(gu_t, gv_t)
     M_num = interaction_picture_M(A_uv, T)
     M_ana = interaction_picture_M_2modes_equal(u, T)