Quantum phase transitions of light in the Dicke-Bose-Hubbard model

Abstract

We extend the idea of quantum phase transitions of light in atom-photon system with Dicke-Bose-Hubbard model for arbitrary number of two-level atoms. The formulations of eigenenergies, effective Rabi frequencies, and critical chemical potentials for two atoms are derived. With a selfconsistent method, we obtain a complete phase diagram for two two-level atoms on resonance, which indicates the transition from Mott insulator to superfluidity and with a mean excitations diagram for confirmation. We illustrate the generality of the method by constructing the dressed-state basis for arbitrary number of two-level atoms. In addition, we show that the Mott insulator lobes in the phase diagrams will smash out with the increase of atom numbers. The results of this work provide a step for studying the effects with combinations of Dicke-like and Hubbard-like models to simulate strongly correlated electron systems using photons.

Quantum many‐body phenomena in coupled cavity arrays

“…This approach to implementing effective many-body models, which can have suitable parameters, has been proposed in [44]. The phase transitions of a model with several two level systems in each cavity have also been studied in [39,47].…”

“…Since then a substantial number of publications have extended these ideas in a variety of directions. These include photonic Mott insulators [25,26], spin models [27,28,29,30,31,32], dynamical effects [33,34,35,36,37], multi component models [38], phase diagrams [39,40,41,42,43], alternative physical realisations [44,45,46,47,48], experimental signatures [49,50] and quantum information applications [51,52,53,54,55,56]. In fact, historically, some quantum information proposals [51] were presented before the theory for effective many-body models [21,22,23].…”

Circuit QED: superconducting qubits coupled to microwave photons

“…An array of resonators each containing a qubit that induces a Kerr nonlinearity will be a realization of the boson Hubbard model (Fisher et al, 1989) which exhibits both superfluid and Mott insulator phases. There is now a burgeoning interest in seeing 'quantum phase transitions of light' (Greentree et al, 2006;Illuminati, 2006;Hart-mann and Plenio, 2007;Jarrett et al, 2007;Rossini and Fazio, 2007;Angelakis et al, 2007;Hartmann et al, 2008;Makin et al, 2008;Aichhorn et al, 2008;Cho et al, 2008c;Cho et al, 2008a;Zhao et al, 2008;Na et al, 2008;Lei and Lee, 2008;Cho et al, 2008b;Ji et al, 2009;Hartmann et al, 2009;Grochol, 2009;Dalidovich and Kennett, 2009;Carusotto et al, 2009;Schmidt and Blatter, 2009;Koch and Le Hur, 2009;Lieb and Hartmann, 2010;Hartmann, 2010;Schmidt et al, 2010;Houck et al, 2012;Hayward et al, 2012;Nissen et al, 2012;Petrescu et al, 2012;Hwang and Choi, 2013;Schmidt and Koch, 2013). Since the transmon qubit is itself an anharmonic oscillator, one might imagine it would be easier to simply use a lattice of coupled transmons to realize the boson Hubbard model (with negative Kerr coefficient).…”

Quantum phase transition of nonlinear light in the finite size Dicke Hamiltonian

“…Schemes to realize composite Dicke models have been proposed, e.g., by combining photon hopping between identical cavities in the photon-blockade regime. Mott-insulator to superfluid QPT has been demonstrated in the Dicke-BoseHubbard model for an arbitrary number of two-level atoms [27]. More exotic QPTs of light have been predicted in a Heisenberg spin 1 / 2 Hamiltonian [28], two species of Bose-Hubbard model [29], arrays of coupled cavities [30,31], and dual-species optical-lattice cavities [32].…”