Lattice-enabled detection of spin-dependent three-body interactions

Abstract

We present the experimental detection of coherent three-body interactions, often masked by stronger two-body effects, through nonequilibrium spin dynamics induced by controllably quenching lattice-confined spinor gases. Three-body interactions are characterized through both real-time and frequency domain analyses of the observed dynamics. Our results, well-described by an extended Bose-Hubbard model, further demonstrate the importance of three-body interactions for correctly determining atom distributions in lattice systems, which has applications in quantum sensing via spin singlets. The techniques demonstrated in this work can be directly applied to other atomic species, offering a promising avenue for future studies of higher-body interactions with broad relevance to strongly-interacting quantum systems.

Figures (4)

• Figure 1: (a) Illustration of $F=1$ atoms in lattice sites with a filling factor $n=2$ (left) or $n=3$ (right) based on the three-body model, Eq. \ref{['ThreeBody']}. Black filled circles (open circles) represent $m_F=0$ atoms in the excited (ground) states. Red (blue) spheres represent $m_F=1$ ($m_F=-1$) atoms in excited states. The characteristic frequency of sites with $n$ particles is $f_n = \Delta E_n/h$ where $\Delta E_n$ is the energy gap between the first excited state and the ground state and $h$ is the Planck constant. $V_2$ ($U_2$) is the spin-dependent three-body (two-body) interaction. Axes are not to scale. (b) Dashed and solid lines respectively display the predicted $f_n$ versus $q$ at $V_2/U_2= -0.074$ based on the two-body and three-body models (see Eqs. \ref{['TwoBody']} and \ref{['ThreeBody']}).
• Figure 2: Real-time Analysis. Triangles display the observed time evolution of $\rho_0$ at $q=75~\mathrm{Hz}$ and $U_2\approx73~\mathrm{Hz}$. The solid (dashed) line is a multi-sinusoidal fit with frequencies $f_n$ predicted by the three-body (two-body) model (see Eqs. \ref{['TwoBody']}-\ref{['ThreeBody']}). Inset: Circles represent the ratio of $V_2$ to $U_2$ extracted from fitting the observed spin dynamics (see the solid line in main panel and Eq. \ref{['ThreeBody']}). The line is the Eq. \ref{['V2U2']} prediction.
• Figure 3: Frequency-Domain Analysis. Black triangles (black thin solid lines) display the (a) real and (b) imaginary components of the non-padded (zero-padded) Fourier spectrum $A(f)$ for the observed spin dynamics at $q/U_2\approx 0.85$. Red dotted (blue thick solid) lines show theoretical simulations of the Fourier spectrum based on the three-body (two-body) model at the optimal $V_2=-4.8(6)~\mathrm{Hz}$ and $U_2=76(1)~\mathrm{Hz}$ (see Eq. \ref{['TwoBody']} and Eq. \ref{['ThreeBody']}). Red arrows highlight significantly improved agreements in the theory-experiment comparison using the three-body model.
• Figure 4: Number distribution $\chi_n$ for results extracted using the two-body (blue) and three-body models (red) for the (a) $q/U_2 \approx 0.85$ dataset shown in Fig. \ref{['fig:3']} and (b) a dataset taken at $q/U_2 \approx 0.60$. Hatched regions indicate the uncertainties (see SM SM).