We report experimental observations on the simultaneous electromagnetically induced transparency (EIT) effects for probe and trigger fields (double EIT) as well as the enhanced cross-phase modulation (XPM) between the two fields in a four-level tripod EIT system of the $D1$ line of ${}^{87}\mathrm{Rb}$ atoms. The XPM coefficients (larger than $2\times {10}^{-5}{\mathrm{cm}}^2/\mathrm{W}$) and the accompanying transmissions (higher than 60%) are measured at a slight detuning of the probe field from the exact EIT-resonance condition. The system and enhanced cross-Kerr nonlinearities presented here can be applied to quantum information processes.

The dependence of the shift of an optical bistability hysteresis curve on the nonlinear phase shift induced by a controlling light is observed in a four-level atomic system of ${}^{87}\mathrm{R}\mathrm{b}$ inside an optical ring cavity. In the process the intensity of the coupling beam keeps constant and the atomic system is operated at near conditions of coherent population trapping due to atomic coherence. The refractive and absorptive ${\chi }^{(3)}$ nonlinearities enhanced by atomic coherence provide the physical mechanism of the phenomena. Based on the effects, all-optical flip-flop and storage of optical pulse signals with a low peak power of several tens of microwatts are implemented.

We present an experimental system to generate large cross-phase modulation (XPM) in cold rubidium atoms. By using an efficient state-preparation technique in the ${}^{87}\mathrm{Rb}$ $D1$ line, an ideal four-level tripod-type atomic system is formed, which generates large cross-Kerr nonlinearity via interacting dark states in this system. The induced phase shift due to XPM for the probe beam is measured for different trigger beam intensities, which is the key to achieving conditional quantum phase gates and many other applications in quantum information processing.

We investigate, both theoretically and experimentally, the phenomenon of polarization rotation of a weak, linearly polarized optical (probe) field in an atomic system with multiple three-level electromagnetically induced transparency (EIT) subsystems. The polarization rotation angle can be controlled by a circularly polarized coupling beam, which breaks the symmetry in number of EIT subsystems seen by the left and right circularly polarized components of the weak probe beam. A large polarization rotation angle (up to 45°) has been achieved with a coupling beam power of only $15\mathrm{mW}$. Detailed theoretical analyses including different transition probabilities in different transitions and Doppler-broadening are presented and the results are in good agreements with the experimentally measured results.

We propose and experimentally demonstrate a mechanism to achieve coherent control of the polarization rotation of an optical field in a multilevel electromagnetically induced transparency (EIT) system in rubidium atoms. By choosing a properly polarized coupling field and transition energy levels, the symmetry of the atomic medium to the propagation of two orthogonal polarization components of a weak linearly polarized probe field can be broken, which leads to a coherently controlled rotation of the probe field polarization. This mechanism of coherently controlled optical polarization rotation makes use of asymmetry in EIT subsystems for the two circular polarization components of the probe beam with a contribution from different transition strengths (due to different Clebsh-Gordan coefficients) in this multilevel atomic system.

We investigate, both theoretically and experimentally, the cross-Kerr nonlinearity generated in a four-level tripod system in the ${}^{87}\mathrm{Rb}$ D1 line. The system exhibits simultaneous electromagnetically induced transparency (EIT) windows for two weak (probe and trigger) fields and the enhanced cross-Kerr nonlinearity by EIT. The cross-Kerr nonlinear phase shifts for probe (trigger) field are measured at several different intensities of trigger (probe) field. The results show that large cross-phase modulation (XPM) coefficients can be achieved at low light intensities.