Realizing Distance-Selective Interactions in a Rydberg-Dressed Atom Array

Measurement-based quantum computing relies on the rapid creation of large-scale entanglement in a register of stable qubits. Atomic arrays are well suited to store quantum information, and entanglement can be created using highly-excited Rydberg states. Typically, isolating pairs during gate operation is difficult because Rydberg interactions feature long tails at large distances. Here, we engineer distance-selective interactions that are strongly peaked in distance through off-resonant laser coupling of molecular potentials between Rydberg atom pairs. Employing quantum gas microscopy, we verify the dressed interactions by observing correlated phase evolution using many-body Ramsey interferometry. We identify atom loss and coupling to continuum modes as a limitation of our present scheme and outline paths to mitigate these effects, paving the way towards the creation of large-scale entanglement.

Figure 1

Two-color Rydberg macrodimer dressing. (a) Utilizing macrodimer potentials for Rydberg dressing provides strongly localized interactions (blue), which are in stark contrast to typical soft-core interactions $J_{\mathrm{sc}}$ obtained by coupling to asymptotic interaction curves (gray). Crosses denote the distances present in the array. The spins are arranged in a two-dimensional square array with a spacing $a_{\mathrm{lat}}$ and are illuminated by the UV laser with wave vector ${\mathbf{k}}_{\mathrm{uv}}$ oriented along the diagonal direction of the array and parallel to the magnetic field $\mathbf{B}$. At an interatomic distance $R=\sqrt{2}{a}_{\mathrm{lat}}$ and an orientation $\mathbf{R}\parallel \mathbf{B}$, where the molecular Rabi couplings feature a narrow maximum, we expect to achieve a spin coupling $J_{\mathrm{th}}=2\pi \times 370(40)\mathrm{Hz}$. (b) At large distances, Rydberg interaction potentials are described by van der Waals interactions (gray marker). At smaller distances, one finds macrodimer binding potentials energetically shifted by $U^{\nu }$ from the asymptotic state $|ee⟩$ (blue marker). (c) We perform a two-photon excitation scheme from the ground state $|\uparrow \uparrow ⟩$ via intermediate states $|\uparrow e⟩$, $|e\uparrow ⟩$ detuned by $\mathrm{\Delta }$ to molecular states $|{\mathrm{\Psi }}^{\nu }⟩$ using Rabi couplings ${\mathrm{\Omega }}_{\mathrm{sb}}$ and ${\mathrm{\Omega }}_C^{\nu }$. In our dressing sequence, we work at finite two-photon detunings ${\delta }_{\nu }$ to the molecular states. The two excitation fields are generated by modulating sidebands at frequencies ${\omega }_{\mathrm{C}}\pm {\omega }_{\mathrm{sb}}$ on our UV frequency ${\omega }_C$. (d) Performing atom-loss spectroscopy, we find the vibrational spectrum slightly blue-detuned from the single-photon Rydberg transition coupled by the red sideband (here for ${\omega }_{\mathrm{sb}}=2\pi \times 723\mathrm{MHz}$).

Figure 2

Two-spin correlations. (a) We encode our spin states in two hyperfine ground states coupled by a microwave field. Spin interactions are probed using many-body Ramsey interferometry. (b) We evaluate spin-spin correlations $C_{\mathbf{R}}^{(2)}$ for increasing interaction time and find a strong signal at a distance $\mathbf{R}=(1,-1)a_{\mathrm{lat}}$ matching the strongly coupled lattice diagonal. The value at the origin was excluded. (c) The observed spin dynamics $C_{1,-1}^{(2)}(t)$ originates from correlated spin flips during the Ramsey sequence, as shown in exemplary images from our quantum gas microscope. Error bars in the correlation signal were calculated using a bootstrap algorithm (delete-1 jackknife). We fit the observed spin dynamics to a master equation and obtain $J=2\pi \times 318(20)\mathrm{Hz}$ and ${\mathrm{\Gamma }}_{|\to ⟩}^{\mathrm{fit}}=0.46(5){\mathrm{ms}}^{-1}$ (solid line). The red shaded area corresponds to the calculated dynamics using the same model with the calculated spin coupling $J_{\mathrm{th}}$ and the experimentally calibrated atom loss ${\mathrm{\Gamma }}_{|\to ⟩}^{\mathrm{ex}}=0.6(1){\mathrm{ms}}^{-1}$. Here, uncertainties originate from $J_{\mathrm{th}}$ and ${\mathrm{\Gamma }}_{|\to ⟩}^{\mathrm{ex}}$. The gray shaded region represents measured two-spin correlations $C_{\mathbf{R}}^{(2)}$ at other distances.

Figure 3

Higher-order correlations. (a) In addition to $C_{1,-1}^{(2)}(t)$ (red), we expect to also observe connected three-spin correlations $C_{{\mathbf{R}}_{\mathbf{1}}{\mathbf{R}}_{\mathbf{2}}}^{(3)}$ (blue) for distance vectors ${\mathbf{R}}_1={\mathbf{R}}_2=(1,-1)a_{\mathrm{lat}}$ in our spin system. (b) A calculation for both correlators without dissipation reveals that $C_{1,-1}^{(3)}(t)$ is expected to appear with a delay relative to $C_{1,-1}^{(2)}(t)$. At a later time $t_C$, all coupled spins evolve into a cluster state. (c) Observed correlation dynamics of $C_{1,-1}^{(3)}(t)$. The solid line represents a calculation using the model parameters obtained by fitting $C_{1,-1}^{(2)}(t)$. The dynamics is in qualitative agreement with the calculation without dissipation but the amplitude of the signal is damped. The blue-shaded region represents the theoretical expectation. The gray shaded region represents the background at other distances ${\mathbf{R}}_{\mathbf{2}}$ while ${\mathbf{R}}_{\mathbf{1}}=(1,-1)a_{\mathrm{lat}}$. Error bars in the correlation signal are calculated using a bootstrap algorithm (delete-1 jackknife).

Figure 4

Photodissociation into continuum modes. (a) Performing spectroscopy of the lowest vibrational line reveals a shift $V_{\mathrm{pd}}$ from the expected line position (orange), which increases with laser power (gray to red), here for ${\omega }_{\mathrm{sb}}=2\pi \times 728\mathrm{MHz}$. (b) This linear light shift $V_{\mathrm{pd}}/(2\pi )=a({\mathrm{\Delta }}_C){[{\mathrm{\Omega }}_C/(2\pi )]}^2$ agrees very well with the theoretical model (solid line). (c) The calculation assumes a coupling ${\mathrm{\Omega }}_{\mathrm{C}}$ into singly excited pair states occupying motional continuum states by the carrier field. (d) By varying ${\omega }_{\mathrm{sb}}$, we measure the dependency of $a({\mathrm{\Delta }}_C)$ on the carrier detuning ${\mathrm{\Delta }}_{\mathrm{C}}$ between the molecular state and the intermediate state and find agreement with the calculation (dashed blue line). The blue shaded region indicates the varying contributions from different partial waves, which contribute to a broadening of the resonance, as shown in the inset for ${\mathrm{\Delta }}_{\mathrm{C}}/2\pi =-3.6$, $-6.35$, and $-10.1\mathrm{MHz}$ (red to gray). Here, solid lines represent the theoretical expectation and error bars on the data points indicate the $1\sigma -67\%$ confidence interval of fitted resonance profiles.