# 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 $N =2$.
• yea but what that means depends on the context. That state can be for example qutip.tensor(qutip.basis(2, 0), qutip.basis(2, 1), qutip.basis(5, 0)), or something completely different, depending on how you model the different spaces and the conventions you use