Small documentation updates

Author: mabuni1998

.gitignore

@@ -0,0 +1 @@
+Manifest.toml

README.md

@@ -37,7 +37,7 @@ Finally, we can define an initial two-photon Gaussian wavepacket state with view
 
 ```julia
 ξfun(t1,t2,σ1,σ2,t0) = sqrt(2/σ1)* (log(2)/pi)^(1/4)*exp(-2*log(2)*(t1-t0)^2/σ1^2)*sqrt(2/σ2)* (log(2)/pi)^(1/4)*exp(-2*log(2)*(t2-t0)^2/σ2^2)
-ψ_cw = twophoton(bw,ξfun,times,1,1,5)
+ψ_cw = twophoton(bw,ξfun,1,1,5)
 psi = fockstate(bc,0) ⊗ ψ_cw
 dt = times[2] - times[1]
 H = im*sqrt(1/dt)*(adw-wda)

docs/.gitignore

@@ -1,2 +1,3 @@
 build/
 site/
+Manifest.toml

docs/src/theoreticalbackground.md

@@ -10,7 +10,7 @@ $$\begin{equation*}
     \ket{\psi} = W^\dagger(\xi) \ket{0} = \int_{t_0}^{t_{end}} \mathrm{d}t \ \xi(t) w^\dagger(t) \ket{\emptyset}
 \end{equation*}$$
 
-here $W^\dagger(\xi)$ creates a photon with the wavefunction $\xi(t)$. $w^\dagger(t)$ is the creation operator for a photon at time $t$, and it obeys the commutation relation: $\left[w(t),w(t')\right ] = \delta(t-t')$. The probability of observing a photon at time $t$ is given by: $\bra{0} w(t) \ket{\psi} = |\xi(t)|^2$. The wavefunction $\xi(t)$ thus describes the temporal distribution of the photon.
+here $W^\dagger(\xi)$ creates a photon with the wavefunction $\xi(t)$. $w^\dagger(t)$ is the creation operator for a photon at time $t$, and it obeys the commutation relation: $\left[w(t),w(t')\right ] = \delta(t-t')$. The probability of observing a photon at time $t$ is given by: $\bra{\psi} w^\dagger(t) w(t) \ket{\psi} = |\xi^{(1)}(t)|^2$. The interpretation of the wavefunction $\xi^{(1)}(t)$. The wavefunction $\xi(t)$ thus describes the temporal distribution of the photon.
 
 The heart of the photon time-binning is discretizing the continuous fock state into time-bins of width $\Delta t$. The interaction with the emitter/cavity is then assumed to span only one time-bin at a time, corresponding to a spectrally flat interaction between the waveguide and emitter/cavity. We thus discretize the annihilation and creation operators by taking[^1]:
 

docs/src/tutorial.md

@@ -18,7 +18,7 @@ bc = FockBasis(1)
 nothing #hide
 ```
 
-Next, we want to create the Hamiltonian for the system. The interaction between the waveguide and cavity is at timestep k given by[^1] $$H_k = i \hbar \sqrt{\gamma / \Delta t}( a^\dagger w_k - a w_k^\dagger)$$, where $$a$$ ($$a^\dagger$$) is the cavity annihilation (creation) operator, $$w_k$$($$w_k^\dagger$$) is the waveguide annihilation (creation) operator, $$\gamma$$ is the leakage rate of the cavity, and `\Delta t = times[2]-times[1]` is the width of the time-bin. `WaveguideQED.jl` follows the same syntax as [`QuantumOptics.jl`](https://qojulia.org/), and operators are defined from a basis. Operators of different Hilbert spaces are then combined using ⊗ (``\otimes``) or `tensor`:
+Next, we want to create the Hamiltonian for the system. The interaction between the waveguide and cavity is at timestep k given by[^1] $$H_k = i \hbar \sqrt{\gamma / \Delta t}( a^\dagger w_k - a w_k^\dagger)$$, where $$a$$ ($$a^\dagger$$) is the cavity annihilation (creation) operator, $$w_k$$($$w_k^\dagger$$) is the waveguide annihilation (creation) operator, $$\gamma$$ is the leakage rate of the cavity, and $$\Delta t = \mathrm{times[2]}-\mathrm{times[1]}$$ is the width of the time-bin. `WaveguideQED.jl` follows the same syntax as [`QuantumOptics.jl`](https://qojulia.org/), and operators are defined from a basis. Operators of different Hilbert spaces are then combined using ⊗ (`\otimes`) or `tensor`:
 
 ```@example tutorial
 a = destroy(bc)
@@ -77,7 +77,7 @@ nothing #hide
 ```
 ![alt text](scat_onephoton.svg)
 
-We see that the wavefunction has changed after the interaction with the cavity. More specifically, we see how the pulse gets absorbed into the cavity leading and a corresponding phase change of the wave. This phase change also leads to destructive interference between the photon being emitted from the cavity and the reflection of the incoming photon. This leads to a dip in the photon wavefunction after the interaction.
+We see that the wavefunction has changed after the interaction with the cavity. More specifically, we see how the pulse gets absorbed into the cavity leading to a phase change in the wavefunction. This phase change also leads to destructive interference between the photon being emitted from the cavity and the reflection of the incoming photon. This leads to a dip in the photon wavefunction after the interaction.
 
 ## Expectation values
 

src/WaveguideQED.jl

@@ -22,7 +22,6 @@ include("WaveguideOperator.jl")
 include("CavityWaveguideOperator.jl")
 include("WaveguideInteraction.jl")
 include("solver.jl")
-#include("should_upstream.jl")
 include("detection.jl")
 include("plotting.jl")
 include("precompile.jl")