Observation of a $p$-wave optical Feshbach resonance

We demonstrate a $p$-wave optical Feshbach resonance (OFR) using purely long-range molecular states of a fermionic isotope of ytterbium ${}^{171}$Yb, following the proposition made by K. Goyal et al. [Phys. Rev. A 82, 062704 (2010)]. The $p$-wave OFR is clearly observed as a modification of a photoassociation rate for atomic ensembles at about 5 $\mu$K. A scattering phase shift variation of $\delta \eta =0.022$ rad is observed with an atom loss rate coefficient $K=28.0\times {10}^{-12}$ cm${}^3$/s.

Figure 1

Relevant molecular states and adiabatic potentials for the $p$-wave OFR experiment. Tuning and monitoring lasers ($\lambda =555.8$ nm) are tuned near PA resonances at $-355.4$ and $-212.4$ MHz from the ${}^1{S}_0+{}^3{P}_1$ asymptote. The excited states are previously observed PLR molecular states arising from the hyperfine interaction. A part of the wave function of the $p$-wave scattering state $F_{\text{scat}}$ as well as the wave function of the state for the monitoring ${\varphi }_{\text{mon}}$ are shown. Note that the energy scale of the ground-state potential is enlarged by a factor of 100 compared with the excited-state potential to show the centrifugal barrier of approximately 44 $\mu$K in height.

Figure 2

(a), (b) $p$-wave OFR spectra with only the tuning laser (solid circles) and with both the tuning and monitoring lasers (open circles). The number of atoms remaining after the OFR pulse ($N$) is plotted with respect to the tuning laser detuning from the ${}^1{S}_0+{}^3{P}_1$ asymptote (${\Delta }_{\text{atom}}$). The error bars in the figure shows the statistical uncertainty of number of atoms. The data obtained with different temperatures, (a) $T=7.2$ $\mu$K and (b) 4.5 $\mu$K, are shown. The dotted lines show the atom loss spectra calculated with the laser-induced linewidth ${\Gamma }_{\text{tun}}/2\pi =16.5$ and 16.2 kHz, for (a) and (b), respectively. The asymmetric atom loss spectra, indication of the OFR effect, is clearly observed with the monitoring laser. The spectra are well reproduced in solid lines with minimal fitting parameters, as discussed in the main text. (c) Calculated variation of $\eta$ using the value of ${\Gamma }_{\text{tun}}$ obtained from the fit for $T=7.2$ $\mu$K.

Figure 3

Calculated wave-function overlap integral $\langle {\varphi }_{\text{mon}}|F_{\text{scat}}\rangle$ for the monitoring state ($-212.4$ MHz) and the scattering state as a function of the phase shift $\eta$, for (a) a wide range and (b) near the background phase shift ${\eta }_0=0.127$ at $T=5.6$ $\mu$K. The overlap integral is normalized with respect to the overlap integral at ${\eta }_0$, denoted as ${\langle {\varphi }_{\text{mon}}|F_{\text{scat}}\rangle }_0$. Dots are the numerical results with lines showing the guide to the eye. A large overlap integral can be seen near $\eta =1.7$ and $-1.4$, representing the location of the shape resonances. Near ${\eta }_0$ the variation of the overlap integral is quite linear with respect to $\eta$, with zero at ${\eta }^{\prime }=0.116$. The shaded region shows the range where the variation of $\eta$ is observed at a current study.

Figure 4

Calculated variation of the scattering wave function $F_{\text{scat}}$ for various $\eta$. A large modification of the wave function inside the centrifugal barrier ($r<7.0$ nm) can be seen within a small variation of $\eta$.