Analytic approximations to the phase diagram of the Jaynes-Cummings-Hubbard model

Abstract

We discuss analytic approximations to the ground state phase diagram of the homogeneous Jaynes-Cummings-Hubbard (JCH) Hamiltonian with general short-range hopping. The JCH model describes e.g. radial phonon excitations of a linear chain of ions coupled to an external laser field tuned to the red motional sideband with Coulomb mediated hopping or an array of high-Q coupled cavities containing a two-level atom and photons. Specifically we consider the cases of a linear array of coupled cavities and a linear ion chain. We derive approximate analytic expressions for the boundaries between Mott-insulating and superfluid phases and give explicit expressions for the critical value of the hopping amplitude within the different approximation schemes. In the case of an array of cavities, which is represented by the standard JCH model we compare both approximations to numerical data from density-matrix renormalization group (DMRG) calculations.

Repulsively induced photon superbunching in driven resonator arrays

“…The JCH is known to possess a localized-delocalized transition as either the hopping J is increased, or the Jaynes-Cummings parameter is made more negative. This transition is similar in some respects to the phase transition of the BH model, although it also differs in fundamental ways on account of the different nature of the systems' intrinsic excitations (bosons and polaritons, respectively) [14][15][16][17][18]22]. Figure 6 presents evidence that the mechanism underlying the bunched emission discussed above in the context of a the driven Bose-Hubbard model persists in this qualitatively different setting for realistic atom-resonator couplings and loss rates and is therefore observable in near-future state-of-the art experiments involving just two coupled resonators.…”

“…To this end, there have been recent efforts to identify signatures of the equilibrium quantum phase transition as originally proposed in Refs. [10][11][12][13][14][15][16][17][18] which survive under lossy dynamics.…”

Non-equilibrium many-body effects in driven nonlinear resonator arrays

“…However, the BH Hamiltonian involves only a single species of bosons (photons in this case), while the excitations of the JCH model have both photonic and atomic components. Consequently, the equilibrium physics of the JCH model is expected to be richer as shown in [25][26][27][28][29]. Studying the JCH out of equilibrium, as naturally implemented in open driven CRAs, is likely to highlight even more interesting differences with novel features beyond the realm of the driven BH model.…”

Effective spin physics in two-dimensional cavity QED arrays

“…The advantage of the model (11) is that it is exactly solvable providing us with useful analytical insights. Using the usual angular momentum algebra 4 One should verify the self-consistency of the condition (9) when performing the simulation of the parent TC model, i.e. to check, whether the resulting cavity occupation is such that…”

“…In this context, the use of cavities plays a prominent role as the strong confinement of the electromagnetic field implies strong interaction with matter coupled to the cavity modes. In particular, it offers possibilities to realize and study a plethora of quantum light-matter many-body Hamiltonians such as the so-called Jaynes-Cummings-Hubbard or Rabi-Hubbard models [1][2][3][4][5][6][7][8][9][10][11], or quantum fluids of light, where the effective interaction between light fields is mediated by a nonlinear medium [12][13][14]. This offers ways to study various physical phenomena such as excitation propagation in chiral networks [15][16][17], the physics of spin glasses [18][19][20] and quantum Hopfield networks [21,22], self-organization of the atomic motion in optical cavities [23][24][25][26][27] or quantum phase transitions in arrays of nanocavity quantum dots [28] and in Coulomb crystals [29].…”