Closed Papageno2 closed 6 months ago
For collective spin calculations, if either $Re(\sigma_1^{12})$ or $Im(\sigma_1^{12})$ exceeds 0.5, it implies that the projection of the collective spin exceeds $N/2$ for a system of $N$ spin-1/2 atoms. $$ \begin{align} \langle \hat{J}_x\rangle &= (N/2)(\langle \hat{\sigma}_1^{12}\rangle+\langle \hat{\sigma}_1^{21}\rangle),\ \langle \hat{J}_y\rangle &= (iN/2)(\langle \hat{\sigma}_1^{12}\rangle - \langle \hat{\sigma}_1^{21}\rangle),\ \langle \hat{J}_z\rangle &= (N/2)(2\langle \hat{\sigma}_1^{22}\rangle - 1). \end{align}$$
Hi @Papageno2,
You used the ClusterSpace
which is outdated. Please use the Symbolic Sums and Indices
instead. This should resolve your problem.
The superradiant laser example might be useful for you: https://qojulia.github.io/QuantumCumulants.jl/stable/examples/superradiant_laser_indexed/
Here's some documentation about the symbolic sums: https://qojulia.github.io/QuantumCumulants.jl/stable/symbolic_sums/
Hi @Papageno2, You used the
ClusterSpace
which is outdated. Please use theSymbolic Sums and Indices
instead. This should resolve your problem. The superradiant laser example might be useful for you: https://qojulia.github.io/QuantumCumulants.jl/stable/examples/superradiant_laser_indexed/ Here's some documentation about the symbolic sums: https://qojulia.github.io/QuantumCumulants.jl/stable/symbolic_sums/
Thank you for reminding me about the new API: Sumbolic Sums
and Indices
, now I get the same results for order=2
and order=3
. The inconsistency in results that I previously encountered may be attributed to the instability of the ODE due to the sizable detuned parameter $\Delta$.
I am attempting to solve the Tavis-Cummings model using QuantumCumulants.jl@v0.2.25. When I use order=2, everything appears reasonable. However, when I set order=3, 4, or 5, I obtain results that seem unphysical.
Is it acceptable for ⟨σ_112⟩(t) to exceed 1? (I believe there might be an error.) The results appear significantly different from those obtained with order=2.
The results for
order=2
:The results for
order=3
andorder=4
are the same :