Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration

We study the interaction of a weak probe field, having two orthogonally polarized components, with an optically dense medium of four-level atoms in a tripod configuration. In the presence of a coherent driving laser, electromagnetically induced transparency is attained in the medium, dramatically enhancing its linear as well as nonlinear dispersion while simultaneously suppressing the probe field absorption. We present the semiclassical and fully quantum analysis of the system. We propose an experimentally feasible setup that can induce large Faraday rotation of the probe field polarization and therefore be used for ultrasensitive optical magnetometry. We then study the Kerr nonlinear coupling between the two components of the probe, demonstrating a novel regime of symmetric, extremely efficient cross-phase modulation, capable of fully entangling two single-photon pulses. This scheme may thus pave the way to photon-based quantum information applications, such as deterministic all-optical quantum computation, dense coding, and teleportation.

Figure 1

(Color online) Level scheme of tripod atoms interacting with weak probe $\mathcal{E}$ and strong driving $E_d$ fields. Upper inset: copropagating probe with circularly left- and right-polarized components ${\mathcal{E}}_{1,2}$, and driving $E_d$ fields pass through the atomic medium that is subject to the longitudinal magnetic field $B$. Lower inset: Perpendicular arrangement of the probe and driving fields that is suitable for cold atomic gas.

Figure 2

(Color online) Absorption and dispersion spectra $(\delta ={\omega }_p-{\omega }_{31}^0)$ for the ${\mathcal{E}}_1$ and ${\mathcal{E}}_2$ components of the probe in the presence of a strong driving $({\Omega }_d=0.6\Gamma )$ and a weak magnetic $(\Delta =0.1\Gamma )$ field, in units of the linear resonant absorption coefficient $a_0$.