Strongly interacting photons in hollow-core waveguides

Hollow-core photonic-crystal waveguides filled with cold atoms can support giant optical nonlinearities through nondispersive propagation of light tightly confined in the transverse direction. Here we explore electromagnetically induced transparency is such structures, considering a pair of counterpropagating weak quantum fields in the medium of coherently driven atoms in the ladder configuration. Strong dipole-dipole interactions between optically excited, polarized Rydberg states of the atoms translate into a large dispersive interaction between the two fields. This can be used to attain a spatially homogeneous conditional phase shift of $\pi$ for two single-photon pulses, realizing a deterministic photonic phase gate, or to implement a quantum nondemolition measurement of the photon number in the signal pulse by a coherent probe, thereby achieving a heralded source of single- or few-photon pulses.

Figure 1

(a) Level scheme of atoms resonantly interacting with quantum fields ${\mathrm{Ê}}_{1,2}$ and classical driving fields $\Omega {}_{1,2}$ on the corresponding transitions. $V_{\mathrm{dd}}$ denotes the DDI between atoms in Rydberg states $|d\rangle$. (b) The quantum fields transversely confined in a hollow-core waveguide of length $L$ filled with the atoms, counterpropagate as dark-state polaritons ${\mathrm{\Psi ̂}}_{1,2}$ having slow group velocities $v_{1,2}$ and interacting via long-range potential $\Delta {}_{12}(z_1-z_2)$ mediated by $V_{\mathrm{dd}}$. (c) The potential $\Delta {}_{{\mathit{ll}}^{\prime }}(\zeta )$ of Eq. (5), as a function of dimensionless distance $\zeta$, in units of $2C_{{\mathit{ll}}^{\prime }}/\hslash (\sqrt{2}w){}^3$ Hz.