Optical Control of the Resonant Dipole-Dipole Interaction between Rydberg Atoms

We report on the local control of the transition frequency of a spin $1/2$ encoded in two Rydberg levels of an individual atom by applying a state-selective light shift using an addressing beam. With this tool, we first study the spectrum of an elementary system of two spins, tuning it from a nonresonant to a resonant regime, where “bright” (super-radiant) and “dark” (subradiant) states emerge. We observe the collective enhancement of the microwave coupling to the bright state. We then show that after preparing an initial single spin excitation and letting it hop due to the spin-exchange interaction, we can freeze the dynamics at will with the addressing laser, while preserving the coherence of the system. In the context of quantum simulation, this scheme opens exciting prospects for engineering inhomogeneous $XY$ spin Hamiltonians or preparing spin-imbalanced initial states.

Figure 1

(a) Scheme of the levels relevant for the experiment. The spin-$1/2$ states are encoded in two Rydberg levels. Microwaves couple $|\uparrow ⟩$ to $|\downarrow ⟩$ with Rabi frequency ${\mathrm{\Omega }}_{\mathrm{mw}}$. The addressing beam couples $|\uparrow ⟩$ with $|6P_{1/2}⟩$ off-resonantly to induce a local light shift $\mathrm{\Delta }{\omega }_0$. (b) Experimental setup. Two atoms separated by a distance $R$ and aligned along the quantization axis, defined by a $B=7\mathrm{G}$ magnetic field. The 1005 nm addressing beam is focused on a single atom. (c) Light shift $\mathrm{\Delta }{\omega }_0$ of state $|\uparrow ⟩$ measured by microwave spectroscopy, as a function of the detuning ${\mathrm{\Delta }}_{\text{addr}}$ of the addressing laser. The full line represents the parameter-free expected light shift $\mathrm{\Delta }{\omega }_0={\mathrm{\Omega }}_{\text{addr}}^2/4{\mathrm{\Delta }}_{\text{addr}}$ with the calculated Rabi frequency ${\mathrm{\Omega }}_{\text{addr}}/(2\pi )=158\mathrm{MHz}$. Error bars are smaller than the symbol size.

Figure 2

(a) Two-atom energy structure in the resonant (left) and off-resonant (right) limit. (b) Microwave spectroscopy for $U/h=0.40\mathrm{MHz}$ ($R=25\mu \mathrm{m}$) and ${\mathrm{\Omega }}_{\mathrm{mw}}/(2\pi )=0.1\mathrm{MHz}$ starting from $|\uparrow \uparrow ⟩$. At resonance, the dark state is not coupled anymore by the microwave field. (c) Rabi oscillation for $U/h=4.09\mathrm{MHz}$ ($R=12\mu \mathrm{m}$) driven by microwaves with a Rabi frequency ${\mathrm{\Omega }}_{\mathrm{mw}}/(2\pi )=1.6\mathrm{MHz}$. Upper panel: driving the single atom transition $|\uparrow ⟩\leftrightarrow |\downarrow ⟩$ at ${\mathrm{\Delta }}_{\mathrm{mw}}=0$. Lower panel: observing the enhanced microwave coupling on the transition $|\uparrow \uparrow ⟩\leftrightarrow |+⟩$ at ${\mathrm{\Delta }}_{\mathrm{mw}}=-U$. Error bars are smaller than the symbol size.

Figure 3

(a) Experimental sequence to observe the freezing of the spin-exchange dynamics by the addressing beam with $\mathrm{\Delta }{\omega }_0/(2\pi )=4.8\mathrm{MHz}$ and $U/h=0.40\mathrm{MHz}$ ($R=25\mu \mathrm{m}$). (b) Spin-exchange dynamics $|\uparrow \downarrow ⟩\leftrightarrow |\downarrow \uparrow ⟩$ driven by the dipole-dipole interaction at a measured frequency $2U/h=0.80\mathrm{MHz}$. (c) The addressing beam stops the exchange during a time $\tau =600\mathrm{ns}$ (gray area). [(d)–(f)] The spin exchange is frozen when $|\psi ⟩=-(1/\sqrt{2})(|\uparrow \downarrow ⟩+i|\downarrow \uparrow ⟩)$ and the addressing energy shift imprints a relative dynamical phase $\mathrm{\Delta }{\omega }_0\tau =2\pi$, $2.5\pi$, $3\pi$ [(d)–(f)] between $|\uparrow \downarrow ⟩$ and $|\downarrow \uparrow ⟩$. Error bars are smaller than the symbol size. Solid lines are sinusoidal fits with fixed frequency $2U/h$.