when discussing a quantum harmonic oscillator I understand that the annihilation and creation operators are interpreted as removing or adding a photon to your oscillator. However, for a spin-1 system I do not understand the concept. I ask this because I have encountered a Spin-1 system driven by an external drive where there are spin raising and lowering operators involved.


1 Answer 1


The operators do not have a physical interpretation in the sense that they are not hermitian and thus do not correspond to physical observables.

In the same spirit at your interpretation of the harmonic oscillator raising and lowering operators, the operators $\hat L_\pm$ raise and lower the projection $m\hbar$ of $\hat L_z$.

Much like $\hat x\sim \hat a^\dagger +\hat a$ will change $\vert n\rangle$ to $\sqrt{n+1}\vert n+1\rangle+\sqrt{n}\vert n-1\rangle$, $\hat L_x\sim \hat L_++\hat L_-$ will change $\vert \ell m\rangle$ to a combination of $\vert \ell, m+1\rangle$ and $\vert \ell, m-1\rangle$. Thus your external field will allow your system to transition (after short times) from $\vert \ell,m\rangle$ to $\vert \ell, m\pm 1\rangle$.


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