Orbital-resolved three-body recombination across a p-wave Feshbach resonance in ultracold $^6$Li

Abstract

We report precision, orbital-resolved measurements of three-body recombination near the 159~G $p$-wave Feshbach resonance in an ultracold gas of $^{6}$Li atoms prepared in their lowest hyperfine state. Using a radio-frequency gated protocol that suppresses magnetic-field transients below the milligauss level, we resolve loss features associated with the $|m_\ell|=1$ and $m_\ell=0$ orbital projections. The measured three-body loss coefficient $L_3$ is well captured by a thermally averaged cascade-recombination model, enabling extraction of the resonance splitting $δB$ and effective-range parameter $k_e$. At the lowest temperature, we obtain $δB = 7.6(3)$~mG and $k_e = 0.151(6)\,a_0^{-1}$, both in quantitative agreement with coupled-channel theory. These results establish orbital-resolved three-body spectroscopy as a precision probe of $p$-wave scattering and provide a benchmark for microscopic models of resonant few-body loss.

Figures (5)

• Figure 1: Comparison of atom-loss spectra near the 159 G $p$-wave Feshbach resonance obtained with and without the RF-gated protocol. Red points: spectra measured using the conventional method with a 50 ms holding time after the field step, showing a pronounced asymmetric low-detuning wing caused by eddy-current transients. Blue points: spectra taken using the RF-gated protocol with a 10 ms holding time, which suppresses field-transient asymmetries and restores the intrinsic symmetric line shape. Solid lines are fits to a model that accounts for three-body loss broadened by magnetic field noise, as detailed in Ref. Peng2025PRL.135.133401.
• Figure 1: Experimental time sequence of the magnetic field using the RF-gated protocol.
• Figure 2: Three-body loss coefficient $L_{3}$ as a function of magnetic-field detuning $\Delta B$ at various temperatures $T$. Solid lines represent fits to Eq. (\ref{['eq:fittingwithml']}). The $|m_{\ell}| = 1$ component and its corresponding zero-temperature resonance position are shown as dashed curves and vertical dashed lines, respectively, while the $m_{\ell} = 0$ component is shown as dash-dotted curves and lines. Vertical error bars indicate the $1\sigma$ statistical uncertainties obtained from fitting $N(t)$ with Eq. (\ref{['eq:3body_solution']}). The raw data and model-fitted values are given in Appendix \ref{['app:A']}, Tables A1 -A4.
• Figure 2: Time evolution of the atom number $N(t)$ (upper panels) and temperature $T(t)$ (lower panels) at selected magnetic field detunings $\Delta B$ corresponding to the features in Fig. \ref{['fig:L3data']}(b). Red solid curves represent fits using Eq. (\ref{['eq:3body_loss']}), while blue dashed curves show two-body fits for comparison. In the fitting procedure, $V_{\mathrm{eff}}(t)$ is constructed from $T(t)$ and linearly interpolated in time to evaluate the integral $\int_0^{t} 1/V_{\mathrm{eff}}(t')^{2}dt'$. The data points represent averages over 3 repeated measurements, with error bars indicating one standard deviation of the mean.
• Figure 3: Extracted microscopic parameters $\delta B$ (red), $k_e$ (green), and $K_{AD}$ (blue) as a function of $T$. The parameters remain almost constant below $T \lesssim 0.4\,\mu$K, indicating faithful probing of zero-energy $p$-wave scattering. Deviations at higher $T$ reflect the onset of near-unitary broadening. Error bars indicate the $1\sigma$ fitting uncertainties.