We present an experimental system to generate large cross-phase modulation ͑XPM͒ in cold rubidium atoms. By using an efficient state-preparation technique in the 87 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 present our experimental and theoretical studies of multi-dark-state resonances (MDSRs) generated in a unique cold rubidium atomic system with only perturbing one of the lower states in the three-level EIT systems (through using one additional optical or microwave field connecting to the fourth auxiliary energy level). [9][10][11][12] In those dual EIT systems, two transparency windows are created, which can be used to allow transmissions of two probe beams simultaneous at two different wavelengths. The typical conditions for observing such dual dark-state resonances are four energy levels and three optical (or two optical and one microwave) fields.

We demonstrate a simple technique to prepare and determine the desired internal quantum states in multi-Zeeman-sublevel atoms. By choosing appropriate coupling and pumping laser beams, atoms can be easily prepared in a desired Zeeman sublevel with high purity or in any chosen ground-state population distributions. The population distributions or state purities of such prepared atomic states can be determined by using a weak, circularlypolarized probe beam due to differences in transition strengths among different Zeeman sublevels. Preparing well-defined internal quantum states in multi-Zeeman-sublevel atoms (or spin-polarized quantum-state engineering) will be very important in demonstrating many interesting effects in quantum information processing with multi-level atomic systems.PACS numbers: 42.50.Gy, 32.80.Pj, 03.65.Wj 1 Preparing atoms into one specified internal quantum state and determining the population distribution in multi-Zeeman-sublevel atomic systems are very important in studying atom-field interactions, especially interesting schemes for quantum information processing such as light storage [1], quantum phase gate [2][3][4][5], and entanglement between atomic assemble and photons [6] or between a single trapped ion and a single photon [7].Demonstrations of these novel effects require more than two atomic energy levels and welldefined initial internal quantum state for the atoms, which can not be accomplished by simple optical pumping as in the case for a two-level atomic system. Although in most cases interesting effects can be experimentally demonstrated by simply considering degenerate Zeeman levels, so no specific ground-state population preparations are needed (as in the cases of electromagnetically induced transparency (EIT) [8-10] and photon storage [11]), there are many effects that demand better quantum-state preparation and determination in the multi-Zeeman-sublevel atomic systems. For example, in order to demonstrate quantum phase gate in multi-level atomic systems, such as the five-level M-type [3] and five-level combined M and tripod-type [5] systems, initial ground-state populations have to be prepared in specific Zeeman sublevels. Other examples include synthesis of arbitrary quantum states [12] and many other multi-level atomic systems for quantum information processing. Although specific atomic ground states were prepared in some of the previous experiments and the population distributions were estimated [6], no simple optical techniques have been developed, to the best of our knowledge, to determine the ground-state populations of the prepared internal quantum states of the atoms. Such measurements are very important in determining the coherent time of the photon storage [13], achieving large entanglement between photons and the atomic assemble [6], and realizing quantum phase gates due to cross-phase