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That is, the quanta are in bound states where there are least upper bounds and greatest lower bounds to their energy states but there are at least a countably infinite many energy levels they can assume? I'm particularly interested in examples of entangled systems with this property. Any physical examples that can be created in the laboratory?

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I find it hard to understand what you're asking. What do you mean by least upper bounds? Are looking for a system whose energy is bounded above and below? If so, the hydrogen atom is an example. –  Bruce Connor Aug 12 '13 at 21:58
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As I understand your question, an electron (or a hole) in a doped semiconductor meets your requirements; there are an (effectively) infinite number of energy levels available to these particles between the Fermi sea and the binding energy (work function) of the semi-conductor.

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Dave, does Spice Ice also meet these requirements? Like the qasiparticles in Dysprosium Titanate for example.. –  Mr X Aug 13 '13 at 3:37
    
@MrX Don't know for sure. might be worth asking as its own question. –  Dave Aug 13 '13 at 14:05
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