Spin interferometry in a beam of ultracold molecules

Abstract

We describe a spin interferometer using ultracold YbF molecules and develop the complete set of techniques needed to measure the electron's electric dipole moment, $d_e$, with this apparatus. The molecules are cooled in an optical molasses and prepared in a single internal quantum state. A Raman transition prepares a spin superposition which evolves in parallel magnetic and electric fields before a second Raman transition maps the phase onto the populations of two hyperfine states. These populations are read out using detectors that have spatial and temporal resolution and approach unit efficiency. We characterize the efficiencies and fidelities of all these steps and evaluate the sensitivity of this approach to measuring $d_e$.

Figures (6)

• Figure 1: (a) Illustration of the experiment. (b) Relevant energy levels of $^{174}$YbF, together with lasers (green) and microwaves (orange) used in the experimental sequence. The lower levels are rotational ($N$) and hyperfine ($F$) states within $X^{2}\Sigma^{+} (v=0)$. The upper levels are the two parity (${\cal P}$) components of $A^{2}\Pi_{1/2}(v=0,J= 1/2)$. From left to right the steps are: laser cooling; optical pumping; Raman transfer; detector A; detector B; detail showing the $(F,m_F)$ levels coupled by Raman lasers. (c) Time-of flight profiles recorded by EMCCDs (points with solid lines) and PMTs (dashed lines) in the first (blue) and second (red) detectors. Vertical axis applies to EMCCD data. PMT data is scaled by the ratio of detection efficiencies to make it visible on the same scale. (d) Images from the end-on camera for laser cooling off (upper) and on (lower).
• Figure 2: Detector characterization, showing efficiency of measuring $P_{0,1}$ as a function of microwave powers, $\Pi^{\rm MW}_{A,B}$. Signals are normalized to those obtained without optical pumping [population remains in $N=1$]. (a) Signal ratios as a function of $\Pi^{\rm MW}_{B}$, with molecules prepared in $F=0$ and $\Pi^{\rm MW}_{A}=12$ dBm. (b) Signal ratios as a function of $\Pi^{\rm MW}_{A}$ with molecules prepared in $F=1$ and $\Pi^{\rm MW}_{B}=5$ dBm. Points: $r_A$ (red) and $r_B$ (blue). Lines: model described in Appendix B.
• Figure 3: (a) Raman transfer in the recombiner, for three different velocities, plotted as asymmetry versus two-photon detuning. Data is from EMCCDs. Parameters are $\Delta = -9.55\times 10^9$ rad/s and $\Omega_{0,1}=5.7 \times 10^7$ rad/s. Points: data. Lines: Gaussian fits. (b) Transfer efficiency in the splitter ($\chi_1$, orange circles) and recombiner ($\chi_2$, purple squares). (c) Doppler shifts in the two regions, with linear fits.
• Figure 4: (a) Interference fringes for the same three velocities as Fig. \ref{['fig:stirap']}. Points: data. Lines: Fit to Eq. (\ref{['eq:interference_model_averaged_evaluated']}). Inset: EMCCD images in ${\cal D}_A$ and ${\cal D}_B$ at the top and bottom of the fringe. (b, c) Fit parameters ${\cal B, C }$ for various speeds (red circles) compared to the values expected from the model in Appendix C (blue triangles).
• Figure 5: Rate model to describe detectors.