# Quantum Entanglement between unlike particles

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

• In this paper a mechanical oscillator was entangled with a superconducting electrical circuit. – DanielSank Nov 18 '18 at 3:57

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.

• The entanglement of proton and electron was found by the spectroscopical research. Coming from classical electrodynamics it was claimed a spin. Nearly the same time was discovered the magnetic dipole moments of subatomic particles. In your examples, the entanglement of these magnetic moments are interchangeable with the entangled spins? – HolgerFiedler Nov 18 '18 at 7:25
• @HolgerFiedler The entanglement between the electron/proton spins can also be described as entanglement between the orientations of their magnetic dipole moments. I think both descriptions are equally valid. – Dan Yand Nov 18 '18 at 12:56