ical modeling of signals recorded by the detection sys- tem in the presence of imperfections. In Section V a de- tailed description of the experimental apparatus is given, along with a discussion of the origins of the imperfections, which is followed by an account of the measurements of the imperfections in Section VI. In Sections VII and VIII we discuss measurements and analysis of the PV ampli- tude and systematic effects, and ways of improving the accuracy of the PV measurements to better than 1% in order to measure the difference in the APV effects be- tween different isotopes and hyperfine components. Stark interference. In addition, this effect is minimized by the use of a power-build-up cavity to generate a stand- ing light wave. Since a standing wave has no net direction of propagation any transition rate which is linear in the M1 amplitude, will cancel out (see below). The advantages of the present experimental configura- tion can be demonstrated by considering Yb atoms in the presence of static electric, E , and magnetic, B , fields in- teracting with a standing monochromatic wave produced by two counter-propagating coherent waves in an optical cavity. The electric field in the standing wave, E , is a sum of the fields of the two waves. For resonant atoms, the transition rate from the ground state $^{1}$S$_{0}$ to the excited state $^{3}$D$_{1}$ is (see e.g. [13], Eq. (3.127)) As discussed in Ref. [1], the idea of the experiment is to excite the forbidden 408-nm transition (Fig. 1) with resonant laser light in the presence of a quasi-static elec- tric field. The PV amplitude of this transition arises due to PV mixing of the 5d6s $^{3}$D$_{1}$ and 6s6p $^{1}$P$_{1}$ states. The purpose of the electric field is to provide a refer- ence transition amplitude, which is due to Stark mixing of the same states interfering with the PV amplitude. In such an interference method [11, 12], one is measur- ing the part of the transition probability that is linear in both the reference Stark-induced amplitude and the PV amplitude. In addition to enhancing the PV dependent signal, the Stark-PV interference technique provides for all-important reversals that separate the PV effects from the systematics. where Γ is the natural linewidth of the transition, A$_{M}$ is the transition amplitude, and M = 0 , ± 1 is the mag- netic quantum number of the excited state. Here and in the rest of this section it is assumed that the individ- ual magnetic sublevels of the $^{3}$D$_{1}$ state are resolved. For convenience, we set ℏ = 1 henceforth and measure the transition rate in units of Γ. The transition amplitude A$_{M}$ is the sum of the electric- (E1) and magnetic- (M1) dipole transition amplitudes: The E1 amplitude has two contributions corresponding to the Stark- and PV- mixing of the $^{3}$D$_{1}$ and $^{1}$P$_{1}$ states. That is, Even though the APV effect in Yb is relatively large, and the M1 transition is strongly suppressed, the M1 transition amplitude is still three orders of magnitude larger than the PV amplitude. As a result, the geometry of the experiment was designed to suppress spurious M1- where β is the vector transition polarizability, ζ is re- lated to the reduced matrix element of the Hamilto- nian describing the weak interaction, and E 0 , ± 1 are the spherical components of the vector E . Although Stark- induced transitions are generally characterized by scalar, vector, and tensor polarizabilities [4, 11], for the case of a J = 0 → 1 transition, only the vector polarizability contributes. Equation (3) is derived in Appendix A. Similarly, the M1 transition amplitude has two com- ponents: one for each of the two counter-propagating laser beams. Let E + = E + ˆ E and E$_{−}$ = E − ˆ E denote the electric fields of the beams traveling in the k and − k di- rections, respectively. Then E = E + + E$_{−}$ and the M1 amplitude is given by where M is the reduced matrix element of the M1 tran- sition and k is a unit vector in the direction of the wavevector. Here we have introduced δ k = δk k with δk = ( E + − E $_{−}$) / E . For a perfect standing wave, E + = E − FIG. 1: (color online) Low-lying energy eigenstates of Yb and transitions relevant to the APV experiment. A$_{M}$ = A (E1) M + A (M1) M . (2) A (E1) M = A (Stark) M + A (APV) M = iβ ( − 1) $^{M}$( E × E )$_{−}$$_{M}$ + iζ ( − 1) $^{M}$E − $_{M}$, (3) A (M1) M = M ( − 1) $^{M}$( k × E $_{+}$)$_{−}$$_{M}$ + M ( − 1) $^{M}$( − k × E$_{−}$ )$_{−}$$_{M}$ = ( 1) $^{M}$( δ k E )$_{−}$$_{M}$ , (4) R$_{M}$ = 4 ℏ $^{2}$Γ | A$_{M}$ | $^{2}$, (1) 2 II. EXPERIMENTAL TECHNIQUE FOR THE APV MEASUREMENT