Two-Body Contact Dynamics in a Bose Gas near a Fano-Feshbach Resonance

Abstract

We investigate the real-time buildup of short-range correlations in a nondegenerate ultracold Bose gas near a narrow Fano-Feshbach resonance. Using rapid optical control, we quench the closed-channel molecular energy to resonance on submicrosecond timescales and track the evolution of the two-body contact through photodissociation losses. Repeated pulse sequences enhance sensitivity to early-time two-body losses and reveal long-lived coherence between atom pairs and molecular states. The observed dynamics are accurately reproduced by our dynamical two-channel zero-range theory, which explicitly accounts for the resonance's narrow width and finite closed-channel decay, establishing a predictive framework for correlation dynamics in quantum gases near Fano-Feshbach resonances.

Figures (11)

• Figure 1: Fano-Feshbach resonance (FFR) displacement induced by a spin-dependent light shift. Top: illustration of the coupling between the ground-state manifold with total angular momentum $J=8$ and the excited-state manifold associated with the transition at wavelength $\lambda = 530.306nm$, with $J' = 7$. This coupling induces a light shift that displaces the energy of the closed-channel molecular state $\left\vert\mathcal{C}\right\rangle$, while the open-channel collisional state $\left\vert\mathcal{O}\right\rangle$ remains unaffected. Bottom: loss features in the presence (disks) and absence (squares) of the spin-dependent light shift (SLS) laser, showing the optical displacement of the magnetic Fano-Feshbach resonance from $B_0$ to $B_1$ for a thermal sample of $^{162}$Dy with $N=3\times 10^4$ atoms and temperature $T= 1.24µK$. In the "SLS on" (resp. "SLS off") case we hold the sample for 15ms (resp. 150ms).
• Figure 2: Probing two-body loss dynamics. Atom number as a function of exposure time, $t_\mathrm{exp} = t_\mathrm{on} N_\mathrm{cycles}$, for three different values of $t_\mathrm{on}$ (see legend), at a temperature $T = 0.34µK$, and initial atom number $N_0 \approx 2 \times 10^4$. Here, $t_\mathrm{off} = 26µs$. Solid lines are fits using Eq. \ref{['eqtwobodyloss']}. Inset: schematic of the pulsing protocol.
• Figure 3: Two-body contact dynamics. (a) Measured two-body loss coefficient $L_2$ for different temperatures (see legends). Solid lines are fits using Eq. \ref{['eqForphi3']}. The shaded region indicates the value of $\bar{L}_2$ plus or minus one standard deviation. (b) Evolution of $\mathcal{C}_2 (t)$, scaled by its stationary value, for $R^\star \to 0$ and $\Gamma_\mathrm{b} =0$ (black dashed line), $R^\star \to \infty$ and $\Gamma_\mathrm{b} / 2\pi = 300kHz$ (red line), for a thermal sample at 1.4µK. (c) Same comparison for a thermal sample at 0.4µK. (d) Temperature dependence of $\mathcal{C}_2^{{\rm stat}} / n^2$, deduced from $\bar{L}_2$, and compared with the theoretical prediction from Eq. \ref{['eqC2narrowFFR']}. The blue dashed line shows the prediction from Eq. (\ref{['eqC2narrowFFR']}), with the values of $R^\star$ and $\Gamma_\mathrm{b}^\mathrm{on}$ given by Eq. (\ref{['values_Gb_Rs']}) and the corresponding error bars reflected by the shaded area.
• Figure 4: Coherent oscillations of the two-body loss rate. Normalized loss rate $L_2/L_2^{{\rm stat}}$ as a function of $t_\mathrm{off}$ for a fixed $t_\mathrm{on} = 3µs$. The solid line corresponds to numerical solutions of Eq. \ref{['eqForphi3']} using the parameters from Eq. \ref{['values_Gb_Rs']}. The values of $(T, \operatorname{Re}(E_0^{\rm off})/h)$ are $(0.41µK , -436kHz)$ for (a), $(0.41µK , -560kHz)$ for (b), and $(1.24µK , -560kHz)$ for (c).
• Figure 5: Determination of the narrow Fano-Feshbach resonance properties. Top: Resonance spectra of atom losses as a function of the modulation frequency $\Omega$ for various magnetic fields (see legend). For visual clarity, the different curves are vertically offset by consecutive integer values. The solid lines are fits to the data using Eq. \ref{['eqForphi3']}. Bottom: Resonance frequency as a function of magnetic field, for $I_0=0$ (SLS off) and $I_0 = 15 \mu\rm{W/\mu m^2}$ (SLS on). The solid line shows the expected dressed Feshbach dimer energy dependence on magnetic field with the parameters listed in Table \ref{['tab:FFR']}.