Measuring spectral functions of doped magnets with Rydberg tweezer arrays

Spectroscopic measurements of single-particle spectral functions provide crucial insight into strongly correlated quantum matter by resolving the energy and spatial structure of elementary excitations. Here we introduce a spectroscopic protocol for single-charge injection with simultaneous spatial and energy resolution in a Rydberg tweezer array, effectively emulating scanning tunneling microscopy. By combining this protocol with single-atom-resolved imaging, we go beyond conventional spectroscopy by not only measuring the single-particle spectral function but also directly imaging the microscopic structure of the excitations underlying spectral resonances in frustrated $tJ$ Hamiltonians. We reveal resonances associated with the formation of bound magnetic polarons – composite quasiparticles consisting of a mobile hole bound to a magnon – and directly extract their binding energy, spatial extent, and spin character. Finally, by exploiting the spatial tunability of our platform, we measure the local density of states across different lattice geometries. Our work establishes Rydberg tweezer arrays as a powerful platform for spectroscopic studies of strongly correlated models, offering microscopic control and direct real-space access to emergent quasiparticles in engineered quantum matter.

💡 Research Summary

In this work the authors introduce a versatile spectroscopic protocol that enables the injection of single charges (holes) with simultaneous spatial and energy resolution in a programmable array of Rydberg‑trapped neutral atoms. By combining a global microwave drive with a site‑dependent, time‑modulated light‑shift generated via a spatial light modulator, they engineer an effective Hamiltonian Ĥ(τ)=ℏΩ̃∑jαj e^{-iωτ} ĥ†j,↓ + h.c., where the complex amplitudes αj can be chosen to address a single lattice site (αj=δj,j0) or to create a standing‑wave pattern (αj=cos k·rj). The former realizes an atomic analogue of scanning tunneling microscopy (STM), providing a local density of states (LDOS), while the latter mimics angle‑resolved photo‑emission spectroscopy (ARPES) by selecting a well‑defined momentum k.

The experimental platform encodes three internal states of ^87Rb atoms into Rydberg levels: |↓⟩ = |60 P_{3/2}, m_J=½⟩, |h⟩ = |60 S_{1/2}, m_J=½⟩, and |↑⟩ = |59 P_{3/2}, m_J=½⟩. Dipole‑exchange interactions between atoms generate a hard‑core bosonic t‑J Hamiltonian in the limit J→0, with hopping amplitude t for ↓‑holes and negligible hopping for ↑‑holes. The hole injection rate in the linear‑response regime is Γ = 2πΩ̃² A(ω), where A(ω)=−(1/π)Im G_R^h(ω) is the single‑hole spectral function. The light‑shift modulation depth κ=Δ_LS/ω_LS determines the effective Rabi frequency Ω̃=J₁(κ)Ω and renormalizes the bare hopping to t̃=J₀(κ) t. Although the authors operate at κ≈0.7 to enhance signal‑to‑noise, they retain quantitative control by accounting for these Bessel‑function renormalizations and for small light‑shift induced energy offsets.

The protocol is first benchmarked on a two‑atom system. With only the global microwave, only the symmetric |+⟩ = (|h ↓⟩ + |↓ h⟩)/√2 state (k=0) is accessed, producing a single resonance at +t. Adding a light‑shift on one atom creates a sideband that couples to the antisymmetric |−⟩ state (k=π), revealing a second resonance at –t. The observed peak positions match theoretical predictions after including probe‑induced shifts and residual van‑der‑Waals spin‑spin interactions.

The authors then explore a frustrated triangular plaquette of three atoms. For a fully polarized background |↓↓↓⟩, kinetic frustration arises because a hole with positive hopping t cannot simultaneously adopt an antisymmetric wavefunction on all three bonds. The spectrum contains a q=0 symmetric band (energy +2t) and two degenerate q=±2π/3 antisymmetric bands (energy –2t). The global microwave alone probes only the q=0 mode; the local light‑shift enables access to the finite‑momentum modes, and both resonances are observed.

Introducing a magnon by preparing the initial state |↓↓↑⟩ dramatically changes the physics. The magnon forms a singlet with a neighboring ↓ spin, effectively flipping the sign of the hole hopping (t_eff≈−t) on the adjacent bond. This sign reversal lifts the frustration, allowing the hole to occupy the symmetric q=0 state as the lowest‑energy configuration (energy –2t). Consequently, a new low‑energy resonance appears, directly revealing the binding energy of a magnetic polaron—a composite quasiparticle consisting of a mobile hole bound to a magnon. By measuring the shift between the frustrated and unfrustrated spectra, the authors extract the polaron binding energy, its spatial extent (via the real‑space imaging of the hole‑magnon pair), and its spin character.

Finally, the technique is applied to larger geometries. By scanning the local injection site across 1‑D chains and 2‑D square and triangular lattices, the authors map the LDOS with site‑resolved precision, demonstrating how the local spectral weight depends on coordination number and lattice topology. The ability to combine spatially resolved snapshots with spectroscopic information opens avenues for probing non‑local correlators, string order, and topological edge states that are inaccessible to conventional solid‑state STM or ARPES.

Overall, this paper establishes Rydberg tweezer arrays as a powerful quantum‑simulation platform that can emulate both STM and ARPES, while offering unprecedented real‑space access to emergent quasiparticles such as magnetic polarons. The method provides a blueprint for future studies of strongly correlated models, including doped antiferromagnets, frustrated magnets, and moiré‑engineered lattices, where direct measurement of spectral functions and quasiparticle properties is essential for unraveling their complex many‑body physics.