Weak interactions in an atomic system by external electromagnetic fields or nucleon-nucleon interaction cause perturbations in the wave-function and energy levels of electrons, which allow for transitions that are otherwise forbidden. Of particular interest are magnetic dipole (M1) transitions, Stark-induced transitions, and parity non-conserving (PNC) transitions. The PNC interaction in the hyperfine ground states is dominantly due to the anapole moment of the nucleus and there has been up-to-date only one such measurement carried out in any system; the Boulder group's ground-breaking measurement of the anapole moment in atomic cesium in 1997. Their result derived from two different hyperfine transitions, however, did not agree with the meson-coupling model from high energy physics experiments. Therefore, it is important to revisit the anapole moment through another method to cross-check the Boulder group's measurement. Our goal is to excite the nuclear-spin-dependent (NSD) PNC ground hyperfine transitions in cesium via radio-frequency (rf) and Raman excitation to directly determine the anapole moment. I present our progress toward measurement of the NSD transition in an atomic Cs beam geometry. We have developed a broadband rf cavity resonator to strongly suppress the magnetic dipole (M1) transition while enhancing the forbidden PNC electric dipole (E1) transition. We employed an injection locking scheme to generate a pair of phase-coherent Raman lasers far detuned from the cesium D2 line (852 nm) with a 9.2 GHz frequency difference. I report various measurement data from atomic signal via rf and Raman excitation. In the next generation of measurements, we will carry out interference experiments between rf and Raman transitions by varying the phase relations of the rf and Raman lasers fields. Finally, based on the measurements, I discuss a novel robust measurement technique involving interference of the Raman, M1 and E_PNC contributions.<br>

Atomic parity violation measurements provide a way to probe physics beyond the Standard Model. They can provide constraints on conjectures of a massive Z′ bosonor a light boson, or searches of dark energy. Using the two-pathway coherent control technique, our group plans to make a new measurement of the weak interaction induced parity non-conservation (PNC) transition moment (<i>E_PNC</i>) on the cesium 6S→7S transition. We will coherently interfere a 2-photon transition with the Stark and PNC transitions to amplify and extract the PNC amplitude. Previously, our lab has measured the magnetic dipole transition moment on the same 6S→7S transition to about 0.4% uncertainty using this technique. In this dissertation, I discuss improvements made to the system, and review what future upgrades are needed for a new<i> E</i>_{<i>PNC </i>}measurement. Key systematics are also described. For an accurate determination of <i>E_PNC</i>, properties of cesium such as the scalar (<i>α</i>) and vector (<i>β</i>) transition polarizabilities are needed. I present improved determinations of keyelectric dipole matrix elements, and calculate new high precision determinations of <i>α</i> and <i>β</i>. Finally, using <i>β</i> and the previously measured value of <i>E_PNC/β</i>, I calculate new values for the weak charge of the cesium nucleus Q_w.<br>