Can quantum entanglement occur between two unlike particles, like one photon and one electron? Or one proton and one electron?
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1In this paper a mechanical oscillator was entangled with a superconducting electrical circuit. – DanielSank Nov 18 '18 at 03:57
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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.
Chiral Anomaly
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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 07:25
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@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. – Chiral Anomaly Nov 18 '18 at 12:56
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Thanks for this, do you have a paper to reference where more can be read about entanglement between a proton and an electron? – Shedbot Sep 25 '23 at 17:03
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@Shedbot The book cited in the answer is one good source. If you search online for the keywords "singlet hydrogen", you'll find sources acknowledging that the spins of the electron and proton in the ground state of hydrogen are in a singlet state, which implies that they're entangled. The fact that being in a singlet state implies entanglement is reviewed in
https://www.physics.rutgers.edu/~steves/Mark_and_Janos/Lectures/Lecture_22_Entanglement.pdf,and you can find more sources by searching for "singlet engangled". – Chiral Anomaly Sep 28 '23 at 13:41