Pierre Nataf, Mehmet Dogan, Karyn Le Hur
We show that the Heisenberg Uncertainty Principle represents a sensitive probe of superradiant quantum phase transitions in standard models of photons such as the Dicke Hamiltonian. The latter embodies an ensemble of two-level systems interacting with one quadrature of a single and uniform bosonic field. We derive exact results in the thermodynamical limit and for a finite number N of two-level systems: as a reminiscence of the entanglement properties between light and the two-level systems, the product $\Delta x\Delta p$ diverges at the quantum critical point as $N^{1/6}$. We generalize our results to the double quadrature Dicke model where the two quadratures of the bosonic field are now coupled to two independent sets of two-level systems. Our findings can be tested using Bose-Einstein condensates in optical cavities and circuit Quantum Electrodynamics.
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http://arxiv.org/abs/1204.3065
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