Transport of Photonic Bloch Wave in Arrayed Two-Level Atoms

Abstract

In a quantum system of arrayed two-level atoms interacting with light, the interacted (dressed) photon is propagating in a periodic medium and its eigenstate ought to be of Bloch type with lattice symmetry. As the energy of photon is around the spacing between the two atomic energy levels, the photon will be absorbed and is not in the propagating mode but the attenuated mode. Therefore an energy gap exists in the dispersion relation of the photonic Bloch wave of dressed photon in addition to the nonlinear behaviors due to atom-light interactions. There follows several interesting results which are distinct from those obtained through a linear dispersion relation of free photon. For example, slow light can exist, the density of state of dressed photon is non-Lorentzian and is very large around the energy gap; the Rabi oscillations become monotonically decreasing in some cases; and besides the superradiance occurs at long wavelengths, the spontaneous emission is also very strong near the energy gap because of the high density of state.

Photon-Assisted Perfect Conductivity Between Arrays of Two-Level Atoms

“…(Please notice that our self-mass (Eq. (18)) is not exactly the same as that in refs 70 & 71 ). It is nonlinear with an energy gap near the energy spacing , around there the momenta are complex corresponding to attenuated light waves.…”

“…70 , the photonic propagator satisfies the following Dyson’s equationwhere is the propagator of free photon with being an infinitesimal positive number, is the reciprocal lattice vector (for all integer values of n ), and iswhich is the renormalization correction of self-mass to the photonic propagator from the light-matter interaction. We can then obtain the photonic dispersion relation through a calculation similar to that done in refs 70 & 71 as,as is shown in Fig. 4.…”

“…71 , the dressed photon propagator iswhere denotes crystal momentum conservation, i . e ., , if ; , otherwise; and the function is defined as 71 and ([] is the Gauss notation), .

Figure 4Dispersion. Dispersion relations of versus [blue line], and versus [red line] of photonic field propagating in an array of 2LA.

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“…2 in ref. 71 . The inset shows the DOS (in arbitrary unit) of the (dressed) photon around the resonant energy .…”

Simulation of the Effect of the Detuning in the Performance of the Two-level System

“…The pumping of the laser can be later described by phenomenological relaxation processes between two levels. The description of statistical dynamics of a statistical ensemble of TLS atoms interacting with a classical electric field has described by the Bloch equations [4][5]. More realistic description of media, especially of typical laser media a coherent additional field in addition to the coupling to the environment, the Hamiltonian has to be extended by the dipole interaction, we use the interaction Hamiltonian in rotative wave approximation (RWA) [6].…”