Tunneling-assisted optical information storage with lattice polariton solitons in cavity-QED arrays

Considering two-level media in the array of weakly coupled nanocavities, we reveal a variety of dynamical regimes, such as diffusion, self-trapping, soliton, and breathers for the wave packets in the presence of photon tunneling processes between the next-nearest cavities. We focus our attention on the low-branch bright polariton soliton formation, due to the two-body polariton-polariton scattering processes. When detuning frequency is manipulated adiabatically, the low-branch lattice polariton localized states, i.e., solitons and breathers evolving between photonlike and matterlike states, are shown to act as carriers for spatially distributed storage and retrieval of optical information.

Figure 1

Schematic for our proposed 1D cavity- QED array, in which each cavity contains the ensemble of two-level atoms as qubits. Cavities are formed by the defects in a photonic waveguide crystal, with period $d$ that, in fact, represents characteristic size of cavity; ${\xi }_x$ and ${\sigma }_x$ are characteristic spatial scales of the optical field and atomic wave-function localization, respectively. In this work, we assume that ${\sigma }_x<{\xi }_x\le d$.

Figure 2

Tunneling energies between the nearest ${\Omega }_1$ (solid curves) and the next-nearest neighbors ${\Omega }_2$ (dashed curves) are shown as a function of the size of cavity $d$. The widths of wave functions for cavity field and atoms are estimated as ${\xi }_x=1\mu \mathrm{m}$ and ${\sigma }_x=0.4\mu \mathrm{m}$, respectively. The dependence of $C^2$ on $d$ for the same values of detuning $\delta$ is plotted in the inset.

Figure 3

(a) Dynamical phase diagram, (b) effective polariton mass, shown in the inverse form $1/m_0^{*}$, and (c) the corresponding Hamiltonian energy contour are shown in terms of the momentum $cos\left(p_0\right)$ and detuning frequency $\delta$, respectively, for the parameters $d=2\mu \mathrm{m}$, ${\gamma }_0=5$, and ${\eta }_0=0$. The markers A and B (C) shown in (a) correspond to the polariton soliton (breather) states, which are used below for the storage and retrieval of optical information shown in Fig. 6.

Figure 4

The group velocity $v_g$ versus time $t$ for ${\gamma }_0=5$, $p_0=\pi /2$. Beginning from the top of the figure, $\delta \equiv {\delta }_{\mathrm{C}}\approx 137.86\mathrm{GHz}$ and $v_0\equiv v_g(t=0)=330214\mathrm{m}/\mathrm{s}$ (dashed curve); $210\mathrm{GHz}$ and $v_0=148415\mathrm{m}/\mathrm{s}$ (green curve); $\delta ={\delta }_{\mathrm{S}}\approx 265\mathrm{GHz}$ and $v_0=94379\mathrm{m}/\mathrm{s}$ (dotted line); $380\mathrm{GHz}$ and $v_0=46382\mathrm{m}/\mathrm{s}$ (brown curve); $\delta ={\delta }_{\mathrm{BR}}\approx 393.66\mathrm{GHz}$ and $v_0=43250\mathrm{m}/\mathrm{s}$ (dashed-dotted red curve); $500\mathrm{GH}z$ and $v_0=26907\mathrm{m}/\mathrm{s}$ (solid red curve). In the inset, dependence of $\delta$ versus ${\gamma }_0$ for $p_0=\pi /2$ is plotted.

Figure 5

Trajectories in the $\eta \text{−}\gamma$ plane for various atom-field detuning $\delta$ with initial conditions ${\gamma }_0=5$, ${\eta }_0=0$ for (a) $cos\left(p_0\right)=0.4$ and (b) $cos\left(p_0\right)=-0.94$. The magnitudes of $\delta$ in (a) are $80\mathrm{GHz}$ (for an unlabeled green curve), $115$ and $120\mathrm{GHz}$ (for inside and outside brown curves, respectively). Black dot in (a) corresponds to solitonic regime of the wave-packet parameters for $\delta ={\delta }_{\mathrm{S}}\approx 99.24\mathrm{GHz}$.

Figure 6

(a) Manipulation for the wave packet is demonstrated through a time-dependent frequency detuning $\delta \left(t\right)$, for the lattice polariton soliton solutions marked in Fig. 3. Parameter $\chi =2\pi \times 500\mathrm{MHz}$. Spatial-temporal evolution in a wave-packet storage and retrieval for the lattice polariton soliton, with the components shown schematically for the photonlike part ${\left|\psi \right|}^2$ in (b), and atomic excitation part ${\left|\varphi \right|}^2$ for soliton (c) and breather (d), respectively. Here, the cavities are shown as the purple points in the $X$ direction.

Figure 7

Fidelity $F$ versus relative wave-packet width ${\Gamma }_0={\Gamma }_{\mathrm{out}}/{\Gamma }_{\mathrm{in}}$ and parameter ${\theta }_0={\Gamma }_{\mathrm{in}}^2({\theta }_{\mathrm{out}}-{\theta }_{\mathrm{in}})$.