Strongly interacting photons and many-body cavity QED

4 problems

• Replica symmetry breaking in multimode-cavity spin glasses

  Partially resolved

  Atoms in a cavity with many light modes interact with random signs, like the frustrated magnets called spin glasses and like associative-memory networks. The question is whether they show the hallmark of a true spin glass.

• Does an equilibrium superradiant phase transition exist in cavity QED?

  Contested

  Simple models predict that enough atoms in a cavity will spontaneously fill it with light in their lowest energy state. General theorems forbid this, yet loopholes have been proposed.

• Crystallization of photons in Rydberg media

  Open

  Theory predicts that photons slowed in a Rydberg atom cloud can repel so strongly that they line up like a crystal. This has not been seen for more than a few photons.

• Fractional quantum Hall states of light with many photons

  Open

  Light trapped in a twisted cavity and made to interact through Rydberg atoms has formed a two-photon version of a fractional quantum Hall state. The goal is to build one with many photons and check its unusual properties.