I'm a beginner and amateur interested in quantum physics.
I would like to know if entangled systems of natural states exist or whether such systems require human intervention?
Is it possible? Either no or yes, Why?
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The answer is definitely yes. The ground states (and low-lying eigenstates) of many-body systems are generically entangled. Examples include the ground states of local quantum field theories (which describe the fundamental particles and forces of nature) and ground states of fermionic lattice models (which describe much of the solid matter we see around us). The reason for this is simple: these systems are composed of many interacting constituents. Take for example the magnetic dipoles associated with the spins of atoms in a lattice. These spins are quantum mechanical, which means the orientations of their dipole moments fluctuate even at low temperatures, due to the uncertainty principle. In addition, the dipoles interact with each other because of the magnetic fields that they produce. Therefore these intrinsic quantum fluctuations become correlated with each other, via the mutual magnetic interaction of the spins. The appearance of local quantum fluctuations that are globally correlated is one of the essential features of entangled states.
The entanglement of many-body ground states is highly relevant, since many systems are nearly in their quantum ground states even at everyday temperatures. Examples include the electrons in a typical metal, or the electromagnetic radiation field at optical frequencies. This is true whenever the typical energy scales of the system are large compared to room temperature (i.e. the Fermi energy for a metal, or the frequency of optical radiation).
Interestingly, the principle of locality places quite severe restrictions on the kinds of entangled ground states that actually appear in nature. Typically, these states obey area laws. That is, the amount of entanglement between a sub-region of the system and the rest scales with the area of the boundary of the sub-region, rather than its volume. For more information on area laws, see J. Eisert et al., Rev. Mod. Phys. 82, 277 (2010).
In short, entanglement is perfectly normal. I am sure that entanglement is ubiquitous in, say, atoms with more than one incomplete subshell, as well as in some kind of organic molecules, but I am not a quantum chemistry expert and can’t provide an easy-to-realize example.
Generally, any decay process produce particle states that are entangled in some way but, to be specific and illustrative, many particle decay processes produce spin-entangled particles, namely those where a particle of lesser spin decays to particles of (summarily) greater spin. Consider a spin-0 particle, such as π0, that decays to several (two or three) particles with spin, as the most obvious example.
The problems with understanding “entanglement” (which states are “entangled” and which are not) are based on the problems with understanding “quantum state”, that is a tricky (and not very reliable) concept despite its apparent mathematical simplicity. It is not easy to define what does a “quantum state” mean objectively, to exclude assumptions of an observer completely.