TABLE I: Lowest-order terms contributing to the normalized transition-rate modulation amplitudes r M . The Stark-contribution, r (Stark) M , has several terms that are produced due to different imperfections and impacts all three Zeeman components, M = 0 , ± 1. In order to determine which terms could potentially mimic the PV asymmetry in K , we discriminate the PV contribution to K with respect to the B-field reversal and flip of the polarization angle, θ . Switching to a different Zeeman component of the transition is also a reversal, which is in- corporated in the expression for the asymmetry, K . Anal- ysis of the noise affecting the accuracy of PV-asymmetry measurements demonstrate that the highest signal-to- noise ratio is achieved when θ = ± π/ 4, and therefore, the polarization flip is a change of the polarization an- gle by π/ 2. Thus, the normalized-amplitude combina- tion (14) must be determined for four different combina- tions of the B-field directions and light-polarization an- gles: K (+ B, + π/ 4), K ( − B, + π/ 4), K (+ B, − π/ 4), and K ( − B, − π/ 4), so that terms having different symmetries with respect to the reversals can be isolated: The result of this procedure is summarized in Table II. TABLE II: List of the lowest-order terms contributing to the asymmetry K for | θ | = π/ 4 sorted with respect to their re- sponse to the reversals. K$_{4}$ corresponding to a rather long list of terms that are invariant with respect to all reversals, is not shown in the table. The PV asymmetry contributing to K 1 is B-field even, θ -flip odd. It competes with the second-order terms that are a combination of the E-field and B-field alignment im- perfections and stray fields. Using the theoretical value of ζ ≃ 10 − 9 ea$_{0}$ [14, 15] combined with the measured | β | = 2 . 24 +0 . 07 − 0 12 × 10 − 8 ea$_{0}$/(V/cm) [4, 7], the expected Downstream from the collimator, the atoms enter the main interaction region where the Stark- and PV-induced transitions take place. Up to 80 mW of light at the tran- sition wavelength of 408 . 345 nm in vacuum is produced by frequency doubling the output of a Ti:Sapphire laser (Coherent 899) using the Wavetrain cw ring-resonator doubler. After shaping and linearly polarizing the laser beam, ≈ 10 mW of the 408-nm radiation is coupled into a power buildup cavity (PBC) inside the vacuum chamber. FIG. 4: (color online) Schematic of the power buildup cavity. A schematic of the Yb-APV apparatus is shown in Fig. 2. A beam of Yb atoms is produced (inside of a vacuum chamber with a residual pressure of ≈ 3 × 10 − 6 Torr) with an effusive source: a stainless-steel oven loaded with Yb metal, operating at 500 − 600 $^{◦}$C. The oven is outfitted with a multi-slit nozzle, and there is an external vane collimator reducing the spread of the atomic beam in the horizontal direction. The resulting Doppler width of the 408-nm transition is ≈ 12 MHz [7]. The forbidden 408-nm transition is excited by resonant laser light coupled into the power-buildup cavity in the presence of the magnetic and electric fields. The transi- tion rates are detected by measuring the population of the $^{3}$P$_{0}$ state, where 65% of the atoms excited to the $^{3}$D$_{1}$ state decay spontaneously (Fig. 1). This is done by resonantly exciting the atoms with 649-nm light to the 6s7s $^{3}$S$_{1}$ state downstream from the main interac- tion region, and by collecting the fluorescence resulting from the decay of this state to the $^{3}$P$_{1}$ and $^{3}$P$_{2}$ states and subsequently, from the decay of the $^{3}$P$_{1}$ state to the ground state $^{1}$S$_{0}$ (556 nm transition). As long as the 408- nm transition is not saturated, the fluorescence intensity measured in the probe region is proportional to the rate of that transition. V. EXPERIMENTAL APPARATUS PV asymmetry, 16 ζ/β ˜ E , is ∼ 4 · 10 − $^{4}$, for θ = π/ 4 and ˜ E$_{0}$ = 2 kV/cm. For a typical value of misalignments and “parasitic” fields, e$_{y,z}$/ ˜ E$_{0}$ and ˜ b$_{x}$/B (on the order of 10 − 3 in the present apparatus), the contribution of the “parasitic” terms may be up to a few percent of the total value of K $_{1}$. Ways of measuring the contribution of these imperfections are discussed in the following sections. 5 r (APV) M r (M1) M r ( φ ) M M = 0 + 4 ζ cot θ β ˜ E$_{0}$ 0 0 M = − 1 − 4 ζ tan θ β ˜ E$_{0}$ + 4 δk M (˜ e y − ˜ e z tan θ ) β ˜ E 2 0 + 4 e z φ tan θ ˜ E$_{0}$ M = +1 − 4 ζ tan θ β ˜ E$_{0}$ − 4 δk M (˜ e y − ˜ e z tan θ ) β ˜ E 2 0 − 4 e z φ tan θ ˜ E$_{0}$    K 1 2 K 3 4    = 1 4    − 1 − 1 +1 +1 1 +1 +1 − 1 +1 − 1 +1 1 +1 +1 +1 +1    ·    K (+ B, + θ ) ( − B, + θ ) K (+ B, − θ ) ( − B, θ )   $^{.}$ (20) K$_{1}$ K$_{2}$ K$_{3}$ 8(˜ e y e z + ˜ e z e y ) ˜ E 2 0 + 16 ˜ b x e y B ˜ E$_{0}$ + 16 ζ β ˜ E$_{0}$ 16 b ′ $_{x}$e y B ˜ E$_{0}$ 16 b ′ $_{x}$e z B ˜ E$_{0}$