Coherent Excitation Transfer in a Spin Chain of Three Rydberg Atoms

We study coherent excitation hopping in a spin chain realized using highly excited individually addressable Rydberg atoms. The dynamics are fully described in terms of an $XY$ spin Hamiltonian with a long range resonant dipole-dipole coupling that scales as the inverse third power of the lattice spacing, $C_3/R^3$. The experimental data demonstrate the importance of next neighbor interactions which are manifest as revivals in the excitation dynamics. The results suggest that arrays of Rydberg atoms are ideally suited to large scale, high-fidelity quantum simulation of spin dynamics.

Figure 1

(a) Individual ${}^{87}\mathrm{Rb}$ atoms in microtraps aligned along the quantization axis, defined by a $B=6\mathrm{G}$ magnetic field. (b) Excitation lasers couple the ground state $|g⟩=|5S_{1/2},F=2,m_F=2⟩$ and the Rydberg state $|\uparrow ⟩=|62D_{3/2},m_J=3/2⟩$ with an effective Rabi frequency ${\mathrm{\Omega }}_{\text{opt}}$. Microwaves couple $|\uparrow ⟩$ to $|\downarrow ⟩=|63P_{1/2},m_J=1/2⟩$, with Rabi frequency ${\mathrm{\Omega }}_{\text{MW}}$. (c) Microwave-driven Rabi oscillation of a single atom between $|\uparrow ⟩$ and $|\downarrow ⟩$, yielding ${\mathrm{\Omega }}_{\text{MW}}=2\pi \times 4.6\mathrm{MHz}$.

Figure 2

(a) Sequence to observe spin exchange between two atoms. (b) Excitation hopping between states $|\uparrow \downarrow ⟩$ (blue disks) and $|\downarrow \uparrow ⟩$ (red disks) of two atoms separated by $R=30\mu \mathrm{m}$. Solid lines are sinusoidal fits, with frequency $2E/h$. (c) Interaction energy $E$ (circles) versus $R$. Error bars are smaller than the symbols size. The line shows the theoretical prediction $C_3/R^3$ with $C_3^{\text{th}}=7965\mathrm{MHz}\mu {\mathrm{m}}^3$. The shaded area corresponds to our systematic 5% uncertainty in the calibration of $R$.

Figure 3

Spin excitation transfer along a chain of three Rydberg atoms with nearest-neighbor separation of $20\mu \mathrm{m}$. (a) Theoretical dynamics for a system initially prepared in $|\uparrow \downarrow \downarrow ⟩$, and evolving under a Hamiltonian similar to (1), but with only nearest-neighbor interactions. (b) The same as (a), but for the full Hamiltonian (1), including long-range interactions. (c) Experimental data (points) and prediction of the model taking into account experimental imperfections (see text), with no adjustable parameters. For perfect preparation and readout, the probabilities $P_{\uparrow \downarrow \downarrow }$ (respectively, $P_{\downarrow \uparrow \downarrow }$, $P_{\downarrow \downarrow \uparrow }$) and $P_{100}$ (respectively, $P_{010}$, $P_{001}$) would coincide.

Figure 4

Influence of the temperature on $P_{001}(\tau )$: simulated dynamics at zero temperature (black dashed line), and adding either only atom loss (green dotted line), or only atomic motion (blue solid line).