qojulia / QuantumCumulants.jl

Generalized mean-field equations in open quantum systems
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How to represent the number $N$ of atom in an atomic ensemble with collective spin operators? #203

Closed lilbearx closed 6 months ago

lilbearx commented 6 months ago

Model

I want to study the dynamic evolution of an atomic ensemble with $N$ atoms, and the master equation of the system is: Screenshot from 2024-04-20 11-40-24 where the $\hat{H}$ is: Screenshot from 2024-04-20 11-43-28 So I try to solve it with the QuantumCumulants v0.3.1.

Code

using QuantumCumulants, OrdinaryDiffEq
using ModelingToolkit, DelimitedFiles
using Symbolics

@cnumbers   λ N ξ η;

h = SpinSpace("spinspace")
Jx = Spin(h,"J1",1)
Jy = Spin(h,"J1",2)
Jz = Spin(h,"J1",3)
Jm = Jx - 1im*Jy
Jp = Jx + 1im*Jy

H = -ξ*λ^2/N*(N^2/4-Jz^2)
J = [Jm]
rates = [2*η*λ^2/N]
ops = [Jx]
eqs = meanfield(ops,H,J,rates = rates,order=2)

And the outcome is: Screenshot from 2024-04-20 11-52-08

How to simplify the number $N$ of atom.