Stimulated Raman adiabatic passage preparation of a coherent superposition of ThO $H^3{\mathrm{\Delta }}_1$ states for an improved electron electric-dipole-moment measurement

Experimental searches for the electron electric-dipole moment (EDM) probe new physics beyond the standard model. The current best EDM limit was set by the ACME Collaboration [Science 343, 269 (2014)], constraining time-reversal symmetry $\left(T\right)$ violating physics at the TeV energy scale. ACME used optical pumping to prepare a coherent superposition of ThO $H^3{\mathrm{\Delta }}_1$ states that have aligned electron spins. Spin precession due to the molecule's internal electric field was measured to extract the EDM. We report here on an improved method for preparing this spin-aligned state of the electron by using stimulated Raman adiabatic passage (STIRAP). We demonstrate a transfer efficiency of $75\%\pm 5\%$, representing a significant gain in signal for a next-generation EDM experiment. We discuss the particularities of implementing STIRAP in systems such as ours, where molecular ensembles with large phase-space distributions are transferred via weak molecular transitions with limited laser power and limited optical access.

Figure 1

(a) Schematic of the measurement apparatus used in the present work. A collimated pulsed beam of ThO molecules enters the interaction region. The spin-aligned state is prepared, precesses in parallel electric and magnetic fields, and is read out in the detection region by linearly polarized light, with resulting fluorescence collected and detected by photomultiplier tubes (PMTs). The initial state can be populated using either (b) an optical pumping scheme similar to that used in ACME I, or (c) a STIRAP scheme. We alternate between the two methods for comparison purposes by blocking the corresponding laser beams.

Figure 2

(a) Power spectral densities of the 690 nm lasers are typical of stabilized ECDLs, with a very narrow central component on top of a much weaker broad pedestal. The antireflection (AR) -coated diodes provide a 10 dB reduction in the noise pedestal compared to the off-the-shelf diodes. (b) Typical laser beam intensity profiles (along the $\widehat{x}$ axis) at the center of the molecular beam (integrated over a 5 mm range along $\widehat{z}$, blue line) and Gaussian fits (dashed red line). The beam profiles are greatly separated for clarity.

Figure 3

(a) Efficiency of population transfer from ground state $|X,J=0\rangle$ to a spin-aligned state in the $|H,J=1\rangle$ state, as a function of the spatial overlap of the pump and Stokes beams (laser beam widths $\approx 150\mu \mathrm{m})$ for the experiment (blue) and simulation (red dashed line). Insets along the top show the relative positions of the optical field pulses, as they are encountered by the molecules, traveling from left to right. Power saturation behavior of the (b) pump 690 nm laser and (c) Stokes 1090 nm laser.

Figure 4

(a) Density plot showing variation of the measured transfer efficiency with the detunings of the two lasers. Green (red) dashed lines are a guide to the eye, and they indicate the extent of the pump (Stokes) one-photon resonance FWHM linewidth. Dotted black lines that indicate constant two-photon detunings are drawn at $\delta \in 2\pi \times \{-4,-2,0,+2,+4\}$ MHz. (b) Spin analysis fringes showing coherent preparation of the aligned-spin electron state, data (blue), and sinusoidal fit (red line).