Precision Test of Mass-Ratio Variations with Lattice-Confined Ultracold Molecules

We propose a precision measurement of time variations of the proton-electron mass ratio using ultracold molecules in an optical lattice. Vibrational energy intervals are sensitive to changes of the mass ratio. In contrast to measurements that use hyperfine-interval-based atomic clocks, the scheme discussed here is model independent and does not require separation of time variations of different physical constants. The possibility of applying the zero-differential–Stark-shift optical lattice technique is explored to measure vibrational transitions at high accuracy.

Figure 1

A proposed scheme for precision Raman spectroscopy of ${\mathrm{Sr}}_2$ ground state vibrational level spacings. A two-color photoassociation pulse prepares molecules in the $v=-3$ vibrational level. Subsequently, a Raman pulse couples $v=-3$ and $v=27$, via $v^{\prime }\sim 40$ of $0_u^{+}$. Negative vibrational numbers imply counting from the top of the potential with the least-bound level being $-1$.

Figure 2

(a) The model potential curve for the ${\mathrm{Sr}}_2$ ground state (solid line), and the Morse potential fitted to three parameters (dashed line). (b) Vibrational energy sensitivities to $\Delta \mu /\mu$, as a function of the vibrational number $v$.

Figure 3

Calculated dipole moments squared between vibrational levels of the $X$ and $0_u^{+}$ electronic states as a function of the binding energy for vibrational levels of $0_u^{+}$ ($J=0$ and $J^{\prime }=1$). The results for $v=0$, 27, and $-3$ of $X$ are shown.

Figure 4

Magic frequencies for the optical lattice near 910 nm ($10990{\mathrm{cm}}^{-1}$). The calculated detunings from resonance are $\sim 1.5$ and $-3\mathrm{GHz}$ for Schemes I and II, respectively.