Photon-Mediated Spin-Exchange Dynamics of Spin-1 Atoms

We report direct observations of photon-mediated spin-exchange interactions in an atomic ensemble. Interactions extending over a distance of $500\mu \mathrm{m}$ are generated within a cloud of cold rubidium atoms coupled to a single mode of light in an optical resonator. We characterize the system via quench dynamics and imaging of the local magnetization, verifying the coherence of the interactions and demonstrating optical control of their strength and sign. Furthermore, by initializing the spin-1 system in the $m_f=0$ Zeeman state, we observe correlated pair creation in the $m_f=\pm 1$ states, a process analogous to spontaneous parametric down-conversion and to spin mixing in Bose-Einstein condensates. Our work opens new opportunities in quantum simulation with long-range interactions and in entanglement-enhanced metrology.

Figure 1

Experimental setup and scheme for generating spin-exchange interactions. (a) Driven cavity with atoms (red), transverse magnetic field, and imaging lens. The drive field is detuned by ${\delta }_{\pm }$ from Raman resonances. (b) Pairwise interactions are generated by one atom scattering a photon from the driven cavity mode (purple) into the orthogonally polarized cavity mode (blue), and a second atom rescattering the photon. This mechanism can produce spin-exchange interactions (i),(ii) or spin mixing (iii). Red circles indicate spin states $m=-1$ (empty), $m=0$ (half-filled), and $m=1$ (full).

Figure 2

Cavity-mediated spin-exchange interactions. (a) Driving the cavity induces spin excitations to hop from the right side of the atomic cloud ($A$) to the left (e.g., $B$) and back. The vector light shift $\mathrm{\Omega }(x)$ (b) (yellow) and atomic density profile $\rho (x)$ (b) (blue) serve as input to a mean-field model (c) of the spin dynamics. (d) Oscillations in excitation density ${\rho }_{\mathrm{exc}}$ vs time along cuts $A$ and $B$; lines are guides to the eye.

Figure 3

Optical control of spin-exchange interactions. (a) Spins in regions $A$ and $B$ are initially oriented along ${\widehat{f}}_x$ and ${\widehat{f}}_y$, respectively. Light-induced interactions convert this transverse polarization into a signal in $⟨f^z⟩$, shown for two different drive frequencies. Color scale indicates $⟨f^z⟩$ (hue) and density $\rho$ (saturation). (b) Varying the drive frequency changes the sign of interactions from antiferromagnetic (red) to ferromagnetic (blue). Solid curve is a fit with amplitude as the only free parameter. Right plot (ii) shows agreement of interaction strength $|⟨{\chi }_i⟩|$ with theory across 2 orders of magnitude. Inset shows spin relaxation rate $⟨{\gamma }_i⟩$.

Figure 4

Cavity-mediated spin mixing in a cloud of $N={10}^5$ atoms. (a) Average side mode population $N_s$ (blue circles) and population difference $F_z$ (red diamonds) vs $\sqrt{\overline{n}⟨{\mathrm{\Omega }}^2⟩}t$ [37], measured for interaction times $0\le t\le 1.2\mathrm{ms}$ with typical intracavity photon number $\overline{n}\approx 3\times {10}^3$. Inset: images from 40 iterations of the experiment with $t=400\mu \mathrm{s}$; colors indicate fractional population in each state. (b) Fluctuations in side mode population $\mathrm{\Delta }{N}_s$ (blue circles) and population difference $\mathrm{\Delta }{F}_z$ (red diamonds). Solid blue curves are obtained by fitting $N_s$ with the model in Eq. (4) and plotting the corresponding prediction for $\mathrm{\Delta }{N}_s$ with no free parameters. Dashed blue line in (a) indicates saturation level $N_s/N=2/3$ for the side mode population. Dashed green line in (b) indicates detection noise.