Superradiance and Dipole Ordering of an N Two-Level System Interacting with Optical Near Fields

A model is presented for a system of N two-level excitons interacting with each other via optical nearfields represented as localized photons. In a low exciton density limit, quantum dynamics of the dipolemoments or quantum coherence between any two energy levels is linear. As the exciton density becomeshigher, the dynamics becomes nonlinear, and the system has several kinds of quasi-steady states of thedipole distribution depending on the system parameters. These quasi-steady states are classified with thehelp of the effective Hamiltonian that is derived from the renormalization of degrees of freedom oflocalized photons with a unitary transformation. Among them there exist a ‘‘ferromagnetic’’ state(dipole-ordered state), in which all electric dipoles are aligned in the same direction, and an ‘‘anti-ferromagnetic’’ state, where all dipoles alternatingly change the direction. In addition, we show that anarbitrary state can be transformed into a dipole-ordered state by manipulating initial values of thepopulation differences appropriately. For example, if we initially prepare a dipole-forbidden state, whichis similar to the ‘‘anti-ferromagnetic’’ state and cannot be coupled with propagating far fields, and if wemanipulate the distribution of the population differences properly, the initial state evolves into a dipole-ordered state. The radiation property of such dipole-ordered states is examined in detail. Neglectingenergy dissipation by radiation, we find that some of the ordered states show strong radiation equivalentto Dicke’s superradiance. Then by introducing a radiation reservoir, the dissipative master equation isderived. Solving the equation with and without quantum correlations, we numerically show that multiplepeaks in the radiation profile can survive in both cases. The mechanism of this phenomenon is discussed,and a brief comment on an application to photonic devices on a nanometer scale is given.