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The Dicke model describing an ensemble of two-state atoms interacting with a single quantized mode of the electromagnetic field ͑with omission of the  2 term͒ exhibits a zero-temperature phase transition at a critical value of the dipole coupling strength. We propose a scheme based on multilevel atoms and cavity-mediated Raman transitions to realize an effective Dicke model operating in the phase transition regime. Optical light from the cavity carries signatures of the critical behavior, which is analyzed for the thermodynamic limit where the number of atoms is very large.

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The spectral and temporal response of an optical cavity resonantly coupled to an ensemble of barium atoms has been investigated experimentally. The empty-cavity transmission resonances are found to split in the presence of the atoms and, under these conditions, the cavity's temporal response is found to be oscillatory. These eA'ects may be viewed as a manifestation of a vacuum-field Rabi splitting, or as a simple consequence of the linear absorption and dispersion of the intracavity atoms.

A quantum simulator is a well-controlled quantum system that can follow the evolution of a prescribed model whose behaviour may be difficult to determine. A good example is the simulation of a set of interacting spins, where phase transitions between various spin orders can underlie poorly understood concepts such as spin liquids. Here we simulate the emergence of magnetism by implementing a fully connected non-uniform ferromagnetic quantum Ising model using up to 9 trapped 171 Yb + ions. By increasing the Ising coupling strengths compared with the transverse field, the crossover from paramagnetism to ferromagnetic order sharpens as the system is scaled up, prefacing the expected quantum phase transition in the thermodynamic limit. We measure scalable order parameters appropriate for large systems, such as various moments of the magnetization. As the results are theoretically tractable, this work provides a critical benchmark for the simulation of intractable arbitrary fully connected Ising models in larger systems.