Stark shift and parity nonconservation for near-degenerate states of xenon

We identify a pair of near-degenerate states of opposite parity in atomic Xe, the $5p^{5}10s{}^2{[3/2]}_2^o$ at $E=94759.927$ cm${}^{-1}$ and $5p^{5}6f{}^2{[5/2]}_2$ at $E=94759.935$ cm${}^{-1}$, for which parity- and time-odd effects are expected to be enhanced by the small energy separation. We present theoretical calculations which indicate narrow widths for both states and we report a calculated value for the weak matrix element, arising from configuration mixing, of $\left|W\right|=2.1$ Hz for ${}^{132}\mathrm{Xe}$. In addition, we measured the Stark effect of the $5p^{5}6f$ ${}^2{[5/2]}_2$ and $5p^{5}6f{}^2{[3/2]}_2$ ($E=94737.121{\mathrm{cm}}^{-1}$) states. The Stark shift of the $6f$ states is observed to be negative, revealing the presence of nearby $6g$ states at higher energies, which have not been observed before. The Stark-shift measurements imply an upper limit on the weak matrix element of $\left|W\right|<5$ Hz for the near-degenerate states ($10s{}^2{[3/2]}_2^o$ and $6f{}^2{[5/2]}_2$), which is in agreement with the presented calculations.

Figure 1

(a) Partial energy-level diagram of Xe (not to scale) showing the pair of near-degenerate states (1) and (2). The solid lines represent the $\sim$211 nm radiation used for the measurements of the Stark effect of the $6f$ states using a (2+1) REMPI scheme, see Sec. 4. The analysis of the measurements of the Stark effect of the two 6$f$ states reveals the presence of the $6g$ and $6h$ states, which have not been observed before. (b) Schematic drawing of the experimental setup used for the Stark-shift measurements. (i) A collimated Xe beam is intersected at right angles by a linearly polarized light beam from a $\sim$211 nm pulsed laser. The laser pulse excites the atoms from the ground state to the excited state of interest, and subsequently ionizes the atoms. The electric field along the $z$ axis is used to accelerate the ions down the time-of-flight (TOF) tube towards a microchannel-plate (MCP) detector; this is also the electric field in the Stark effect measurements. The polarization of the laser beam is controlled with a $\lambda /2$ plate. For excitation to the $\left|M\right|=2$ sublevels (with quantization axis along $\widehat{z}$) of the $6f$ excited states, the polarization of the laser beam is set perpendicular to the $z$ axis. (ii) Additional optics used only for the calibration of the electric field, which is realized through the Stark-shift measurements of the $n=2$ states in H using a Doppler-free REMPI scheme (see discussion in Sec. 3b).

Figure 2

The dominant diagram for the weak matrix element between the near-degenerate states (1) and (2). Dashed line is the Coulomb interaction, and the cross stands for the weak interaction. Other diagrams can be obtained by adding an exchange diagram (swapping states $6f$ and $5p$) and by moving the operator of the weak interaction in turn to every other electron line. Similar diagrams describe the electric dipole transition amplitude. In the latter case, the cross would stand for the electric dipole operator.

Figure 3

Theory and experimental data for the Stark effect of the two-photon $1s\text{−}2s$ transition of hydrogen. The calculated shifts for the mixed $2s_{1/2}$ (orange, dashed), $2p_{1/2}$ (gray, solid), and $2p_{3/2}$ (blue, solid) states are presented as a function of the electric field strength. The zero value in the energy axis which corresponds to the unperturbed energy of the $2p_{1/2}$ state, and consequently the energy splittings between the $2p_{1/2}$ state and the $2s_{1/2}$ and $2p_{3/2}$ states, represent the Lamb shift and the fine-structure splitting, respectively [7] (see inset). The unperturbed $2p_{3/2},m_j=\pm 3/2$ (blue, dashed) state is also presented. The hyperfine structure is neglected under our experimental conditions; see text for discussion.

Figure 4

Experimental data of the Stark shift of states (a) $6f$ ${}^2[3/2]$ $J=2$ $(94737.121$ cm${}^{-1})$; $M=0$ (solid line), $\left|M\right|=1$ (dotted line), $\left|M\right|=2$ (dashed line) Zeeman sublevels and (b) $6f$ ${}^2[5/2]$ $J=2$ $(94759.935$ cm${}^{-1})$, $M=0$ (solid line), $\left|M\right|=2$ (dashed line) Zeeman sublevels, along with the theoretical prediction for the Stark shift of the $\left|M\right|=1$ Zeeman sublevels (dotted line) using the polarizability and hyperpolarizability obtained from fitting Eq. (17) to the observed energy shifts of the $M=0$ and $\left|M\right|=2$ Zeeman sublevels. In both cases, the different Zeeman sublevels were identified by exploiting the degenerate two-photon selection rules (Table 5), made possible via the control of the polarization state of the laser beam.