Some remarks on 'superradiant' phase transitions in light-matter systems

In this paper we analyze properties of the phase transition that appears in a set of quantum optical models; Dicke, Tavis-Cummings, quantum Rabi, and finally the Jaynes-Cummings model. As the light-matter coupling is increased into the deep strong coupling regime, the ground state turns from vacuum to become a superradiant state characterized by both atomic and photonic excitations. It is pointed out that all four transitions are of the mean-field type, that quantum fluctuations are negligible, and hence these fluctuations cannot be responsible for the corresponding vacuum instability. In this respect, these are not quantum phase transitions. In the case of the Tavis-Cummings and Jaynes-Cummings models, the continuous symmetry of these models implies that quantum fluctuations are not only negligible, but strictly zero. However, all models possess a non-analyticity in the ground state in agreement with a continuous quantum phase transition. As such, it is a matter of taste whether the transitions should be termed quantum or not. In addition, we also consider the modifications of the transitions when photon losses are present. For the Dicke and Rabi models these non-equilibrium steady states remain critical, while the criticality for the open Tavis-Cummings and Jaynes-Cummings models is completely lost, i.e. in realistic settings one cannot expect a true critical behaviour for the two last models.Comment: 25 pages (single column), 6 figure

Exploring the quantum critical behaviour in a driven Tavis-Cummings circuit

Quantum phase transitions play an important role in many-body systems and have been a research focus in conventional condensed matter physics over the past few decades. Artificial atoms, such as superconducting qubits that can be individually manipulated, provide a new paradigm of realising and exploring quantum phase transitions by engineering an on-chip quantum simulator. Here we demonstrate experimentally the quantum critical behaviour in a highly-controllable superconducting circuit, consisting of four qubits coupled to a common resonator mode. By off-resonantly driving the system to renormalise the critical spin-field coupling strength, we have observed a four-qubit non-equilibrium quantum phase transition in a dynamical manner, i.e., we sweep the critical coupling strength over time and monitor the four-qubit scaled moments for a signature of a structural change of the system's eigenstates. Our observation of the non-equilibrium quantum phase transition, which is in good agreement with the driven Tavis-Cummings theory under decoherence, offers new experimental approaches towards exploring quantum phase transition related science, such as scaling behaviours, parity breaking and long-range quantum correlations.Comment: Main text with 3 figure

The Dicke model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity

We show that the motion of a laser-driven Bose-Einstein condensate in a high-finesse optical cavity realizes the spin-boson Dicke-model. The quantum phase transition of the Dicke-model from the normal to the superradiant phase corresponds to the self-organization of atoms from the homogeneous into a periodically patterned distribution above a critical driving strength. The fragility of the ground state due to photon measurement induced back action is calculated.Comment: 5 pages, 2 figure

Stochastic resonance driven by quantum shot noise in superradiant Raman scattering

We discuss the effects of noise on the timing and strength of superradiant Raman scattering from a small dense sample of atoms. We demonstrate a genuine quantum stochastic resonance effect, where the atomic response is largest for an appropriate quantum noise level. The peak scattering intensity per atom assumes its maximum for a specific non-zero value of quantum noise given by the square root of the number of atoms.Comment: 10 pages, 4 figure

Dicke-like quantum phase transition and vacuum entanglement with two coupled atomic ensembles

We study the coherent cooperative phenomena of the system composed of two interacting atomic ensembles in the thermodynamic limit. Remarkably, the system exhibits the Dicke-like quantum phase transition and entanglement behavior although the governing Hamiltonian is fundamentally different from the spin-boson Dicke Hamiltonian, offering the opportunity for investigating collective matter-light dynamics with pure matter waves. The model can be realized with two Bose-Einstein condensates or atomic ensembles trapped in two optical cavities coupled to each other. The interaction between the two separate samples is induced by virtual photon exchange