Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping

Abstract

This paper theoretically studies the coherent control of photon transmission along the coupled resonator optical waveguide (CROW) by doping artificial atoms in hybrid structures. We provide the several approaches correspondingly based on the mean field method and spin wave theory et al . In the present paper we adopt the two-time Green function approach to study the coherent transmission photon in a CROW with homogeneous couplings, each cavity of which is doped by a two-level artificial atom. We calculate the two-time correlation function for photon in the weakcoupling case. Its poles predict the exact dispersion relation, which results in the group velocity coherently controlled by the collective excitation of the doping atoms. We emphasize the role of the population inversion of doping atoms induced by some polarization mechanism.

Quantum many‐body phenomena in coupled cavity arrays

“…In the next subsections we first discuss how effective σ x σ x , σ y σ y and σ z σ z interactions together with an effective magnetic field Bσ z can be engineered and then explain how these can be combined to generate the full anisotropic Heisenberg model (36). …”

“…Both, XX and YY interactions and ZZ interactions can be combined to engineer the full Hamiltonian (36). This can be done via the Suzuki-Trotter formula.…”

“…For realising effective Hamiltonians such as (7), (30) or (36), some aspects still remain challenging for micro disc and micro toroidal cavities. One aspect is that atoms need to be trapped for a sufficiently long time close enough to the cavity surface to maintain a sufficient strong coupling regime.…”

“…These include the generation of entangled states such as cluster states [27,52,54,55] (see section 7.4), the controlled propagation of polaritonic excitations in cavity arrays [53,35,36,37,50], quantum gates [51] and the generation of single photons in parallel [56].…”

“…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].…”