Quantum Entanglement between unlike particles

Question

Can quantum entanglement occur between two unlike particles, like one photon and one electron? Or one proton and one electron?

Answer 1

Yes, entanglement does occur between two unlike particles. For example, in the lowest-energy state of a hydrogen atom, the spins of the electron and proton are entangled with each other. To be specific, they are in the superposition $$ |\psi\rangle\sim \big|\uparrow\,\downarrow\big\rangle - \big|\downarrow\,\uparrow\big\rangle \tag{1} $$ where the first arrow indicates the spin-direction of the electron and the second arrow indicates the spin-direction of the proton. (Reference: Griffiths, Introduction to Quantum Mechanics, section 6.5, "Hyperfine splitting".) For simplicity, I'm only showing the spin degrees of freedom here.

Another example is positronium, a short-lived bound state of an electron and a positron (anti-electron). In positronium, the electron and positron form a two-particle "orbital" around their center of mass, so their locations are entangled with each other.

Related: Entanglement in atoms, nuclei and quantized fields