Negative photon number with a coherent driving about quantumcumulants.jl HOT 5 OPEN

Hi @eric940109

Yes QuantumCumulants is usually well suited for this problem (depending on the parameter regime).
I think in your case the mistake is that the Hamiltonian is not hermitian (which is unphysical).
For a real eta (eta = 1) the drive term needs to be eta (a' + a) or i eta (a' - a).

from quantumcumulants.jl.

Hi @ChristophHotter

Thanks a lot for your comment! After correcting the drive term, the negative photon numbers seem to still remain. Does this mean my setting of parameters are out of the reasonable parameter regime?

The code and typical results are attached.

M = 2 #order
@cnumbers N Δc Δs g κ γ12 η γ22
hf = FockSpace(:cavity)
ha1 = NLevelSpace(:atom, 2)
ha = ClusterSpace(ha1, N, M)
h = tensor(hf, ha);

@qnumbers a::Destroy(h)
σ(i, j, k) = Transition(h, :σ, i, j)[k]

#Hamiltonian
H = Δc*a'*a + Δs*sum(σ(2,1,i)*σ(1,2,i) for i = 1:M) + g*sum(a'*σ(1,2,i) + a*σ(2,1,i) for i=1:M) + η*(a'+a)

#Collapse operators
J = [a;[σ(1,2,i) for i = 1:M];[σ(2,2,i) for i = 1:M]]
rates = [κ;[γ12 for i = 1:M];[γ22 for i = 1:M]]

#Derive equation
eqs = meanfield([σ(2,2,1)],H,J;rates = rates, order = 2)
eqs_c = complete(eqs, order = 2)

using OrdinaryDiffEq, ModelingToolkit
@named sys = ODESystem(eqs_c)
u0 = zeros(ComplexF64, length(eqs_c))
u0[1] = 1.0
ps = [N, Δc, Δs, g, κ, γ12, η, γ22] #N Δc Δs g κ γ12 η γ22
p0 = [1e14, 0.0, 0.0, 2*π*0.022, 2*π*0.18e6, 1e4, 1e5, 2*π*0.42e6]
prob0 = ODEProblem(sys, u0, (0.0, 8e-5), ps.=>p0)
alg = RK4()
sol0 = solve(prob0, alg)
t0 = sol0.t
q = real.(sol0[a'*a])
using Plots
plot(t0,q)```

Best wishes,
Eric

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The program itself seems fine.
I think the problem is your parameter set, you have very small and very large numbers at the same time, which is usually hard to solve numerically.

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I just saw this again. You could also try to reduce the tolerance of the numerics with e.g. sol0 = solve(prob0, Tsit5(); abstol=1e-10, reltol=1e-10.

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@ChristophHotter Thanks a lot for your reply! I will have it a go!

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