Superfluid–Mott-insulator transition of light in the Jaynes-Cummings lattice

Abstract

Regular arrays of electromagnetic resonators, in turn coupled coherently to individual quantum two-level systems, exhibit a quantum phase transition of polaritons from a superfluid phase to a Mott-insulating phase. The critical behavior of such a Jaynes-Cummings lattice thus resembles the physics of the Bose-Hubbard model. We explore this analogy by elaborating on the mean-field theory of the phase transition and by presenting several useful mappings which pinpoint both similarities and differences of the two models. We show that a field-theory approach can be applied to prove the existence of multicritical curves analogous to the multicritical points of the Bose-Hubbard model, and we provide analytical expressions for the position of these curves.

Universal postquench coarsening and aging at a quantum critical point

“…To leading order it would then suffice to insert the bare Keldysh function g K (q, t, t) in Eq. (94). Since g K decays exponentially to G K eq the integral is convergent in the limit Λ → ∞.…”

“…Dissipation in those system has been engineered, for example, by coupling to other species 92 . Dissipative nanowires near a transition to a superconducting state 93 and an ensemble of qubits in a photon cavity 94,95 provide further realizations for N = 2. A realization for N = 3 is the quantum dimer antiferromagnet TlCuCl 3 shown in Fig.…”

Polaritonic properties of the Jaynes–Cummings lattice model in two dimensions

“…The quantum phase transition from the Mott to the superfluid phase has been investigated by means of density matrix renormalization group [13,14], the variational cluster approach [15,16], quantum Monte Carlo (QMC) [17], and analytically by means of strong coupling perturbation theory [18,19]. Results are also available on mean field level [5,20]; some signatures of the quantum phase transition have also been determined from exact diagonalization of small systems consisting of a few cavities [6,21,22]. The spectral properties of the JCL model have been evaluated in Refs.…”

Scattering and Bound States of two Polaritons in an Array of Coupled Cavities

“…In the recent years, the investigation of the physics in one-dimensional (1D) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and two-dimensional (2D) [14][15][16][17][18][19][20][21][22][23] array of coupled cavities has attracted a lot of attention. It is predicted that, such systems can be used in quantum information processing [1][2][3][4][5] as well as the quantum simulation of many-body systems, e.g., the quantum phase simulation [10][11][12][13][14][15][16][17][18][19][20], quantum Hall effect [21] and Bose-Einstein condensate [22].…”

“…It is predicted that, such systems can be used in quantum information processing [1][2][3][4][5] as well as the quantum simulation of many-body systems, e.g., the quantum phase simulation [10][11][12][13][14][15][16][17][18][19][20], quantum Hall effect [21] and Bose-Einstein condensate [22]. For the few-body physics of coupled cavities, many authors have studied the single-photon transmission in a 1D cavity array coupled with a single atom [1], and the dynamics of a single polariton in a 1D cavity array with each cavity coupled to an atom [2,7].…”