Anisotropic Polarizability of Ultracold Polar ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ Molecules

We report the measurement of the anisotropic ac polarizability of ultracold polar ${}^{40}\mathrm{K}{}^{87}\mathrm{Rb}$ molecules in the ground and first rotationally excited states. Theoretical analysis of the polarizability agrees well with experimental findings. Although the polarizability can vary by more than 30%, a “magic” angle between the laser polarization and the quantization axis is found where the polarizability of the $|N=0,m_N=0⟩$ and the $|N=1,m_N=0⟩$ states match. At this angle, rotational decoherence due to the mismatch in trapping potentials is eliminated, and we observe a sharp increase in the coherence time. This paves the way for precise spectroscopic measurements and coherent manipulations of rotational states as a tool in the creation and probing of novel quantum many-body states of polar molecules.

Figure 1

(a) Experimental schematic. The lattice beam propagates along $\widehat{x}$, the magnetic field points in the $\widehat{z}$ direction, and the polarization of the lattice light makes an angle $\theta$ with the magnetic field in the $y\mathrm{\text{−}}z$ plane. (b) Schematic of rotational energy states. The degeneracy of the $N=1$ level is split in a magnetic field. (c) A sketch of the optical dipole potentials for the $|0,0⟩$ and $|1,0⟩$ states. A Gaussian is overlaid to show the density distribution of the molecular cloud in the trap. When the two states are connected by a 2.22 GHz microwave drive, there is effectively a spatially varying detuning across the cloud due to the difference in the trap potentials.

Figure 2

Parametric heating resonances in the far-off-resonance optical dipole trap for $\theta =57$ degrees. The $y$-axis shows the rms size in $\widehat{x}$ of an expanded gas of KRb (Rb) after 5 ms (21 ms) of time of flight. The curves have been offset vertically for clarity. Using Gaussian fits (lines), we determine the center of the parametric heating resonances for (from bottom to top) Rb, and KRb in the $|0,0⟩$, $|1,0⟩$, $|1,1⟩$, and $|1,-1⟩$ states. The resonant frequency allows us to extract the trap depth for each state.

Figure 3

The ac polarizability of KRb at 1064 nm for the $|0,0⟩$ (black squares), $|1,0⟩$ (blue circles), $|1,1⟩$ (red inverted triangles), and $|1,-1⟩$ (green triangles) states. Error bars are from the fit uncertainty in the center of the parametric heating resonances and correspond to $\pm 1$ standard deviation. Theory lines are a simultaneous fit to Eq. (1) and the polarizabilities from the solution of $H$ with three free parameters ${\theta }_m$, ${\alpha }_{\perp }$, and ${\alpha }_{\parallel }$. Open symbols represent a separate measurement where the polarizability is extracted from the shift in the microwave transition frequency.

Figure 4

The Ramsey coherence time measured in the one-dimensional optical lattice as a function of angle. A sharp increase in coherence time is observed at the magic angle where the polarizabilities of the $|0,0⟩$ and $|1,0⟩$ states are matched. Inset: A Ramsey oscillation fit to a damped sine wave to extract the coherence time for $\theta =51°$.