# How to define initial state $\rvert \Psi(0) \rangle \equiv \rvert 1, -1 \rangle \otimes \rvert 0 \rangle_{\text{cav}}$ of a system in QuTiP?

Say, we have a $$\require{mhchem}\ce{^87Rb}$$ atom having an electric dipole transition on the $$D_{1}$$ line and we have two hyperfine ground states, one on $$F = 1$$ and one on $$F = 2$$ level. So, we take two pair of states $$|F=2, m=-2\rangle$$ and $$|F=1, m = -1\rangle$$ as the ground state. The details on this can be found here. I need to find time evolution of the probability of being in the initial state $$|\Psi(0)\rangle \equiv | 1, -1 \rangle \otimes | 0 \rangle_{\text{cav}}.$$

I don't understand how to define the initial state in QuTiP. I have gone through the paper 'QuTiP: An open-source Python framework for the dynamics of open quantum systems' by J.R. Johansson, P.D. Nation, Franco Nori. I have found few examples such as cavity in its ground state which coupled to a qubit in a balanced superposition of its ground and excited state $$|\Psi(0)\rangle=\left(|0\rangle_{c}|0\rangle_{q}+|0\rangle_{c}|1\rangle_{q}\right) / \sqrt{2}$$ and atom in excited state $$|\Psi(0)\rangle=\operatorname{tensor}(\text { fock }(\mathrm{N}, 0), \text { fock }(2,1)).$$ But I am still not able to understand how to define the initial state $$|\Psi(0)\rangle \equiv | 1, -1 \rangle \otimes | 0 \rangle_{\text{cav}}$$ in QuTiP.

• @glS, I want to understand how to define the given specific state $|\Psi(0)\rangle \equiv | 1, -1 \rangle \otimes | 0 \rangle_{\text{cav}}$. The dimension of the space is related to the number of cavity fock states and in this case it is $N =2$.