To add example for time dependent coupling to a bath

[x94dai]

It seems one cannot construct an annealing object with time-dependent coupling to a bach in the same way as constant coupling. The following code block for example gives an error. It will be useful to have an example that desmonstrates using TimeDependentCoupling.

Δ = 0.1
H = DenseHamiltonian([(s)->2*s-1, (s)->1.0], [σz, Δ * σx], unit=:ħ)
η = 0.001
fc = 4 * 2 * π
T = 20
bath = Ohmic(η, fc, T)
coupling = TimeDependentCoupling([(s)->s], [σz], unit=:ħ)
u0 = PauliVec[3][1]
annealing = Annealing(H, u0, coupling=coupling, bath=bath)

MethodError: Cannot `convert` an object of type TimeDependentCoupling to an object of type OpenQuantumBase.AbstractCouplings
Closest candidates are:
  convert(::Type{T}, ::T) where T at essentials.jl:171

Stacktrace:
 [1] Interaction(::TimeDependentCoupling, ::OhmicBath) at C:\Users\x35dai\.julia\packages\OpenQuantumBase\Pk0vX\src\coupling\interaction.jl:16
 [2] Annealing(::DenseHamiltonian{Complex{Float64}}, ::Array{Complex{Float64},1}; coupling::TimeDependentCoupling, bath::OhmicBath, interactions::Nothing, annealing_parameter::Function) at C:\Users\x35dai\.julia\packages\OpenQuantumBase\Pk0vX\src\annealing\annealing_type.jl:33
 [3] top-level scope at In[11]:8

[neversakura]

You are right, the documentation on this part is a little bit unclear. Currently, there are two objects TimeDepedentCoupling and TimeDependentCouplings. You will need to define each time-dependent coupling operator first and combine them into a TimeDepependentCouplings object.

For your example, the code should be

Δ = 0.1
H = DenseHamiltonian([(s)->2*s-1, (s)->1.0], [σz, Δ * σx], unit=:ħ)
η = 0.001
fc = 4 * 2 * π
T = 20
bath = Ohmic(η, fc, T)
coupling = TimeDependentCoupling([(s)->s], [σz], unit=:ħ)
couplings = TimeDependentCouplings(coupling)
u0 = PauliVec[3][1]
annealing = Annealing(H, u0, coupling=couplings, bath=bath)

I will add some additional tutorials/documentation on this.

[x94dai]

That was a really quick reply! Thanks. It seems pretty straightforward.