Observation of a Topological Berry Phase with a Single Phonon in an Ion Microtrap Array

Controlled quantum mechanical motion of trapped atomic ions can be used to simulate and explore collective quantum phenomena and to process quantum information. Groups of cold atomic ions in an externally applied trapping potential self-organize into “Coulomb crystals” due to their mutual electrostatic repulsion. The motion of the ions in these crystals is strongly coupled, and the eigenmodes of motion all involve multiple ions. While this enables studies of many-body physics, it limits the flexibility and tunability of the system as a quantum platform. Here, we demonstrate an array of trapped ions in individual trapping sites whose motional modes can be controllably coupled and decoupled by tuning the local applied confining potential for each ion. We show that a single motional quantum, or phonon, can be coherently shared among two or three ions confined at the vertices of an equilateral triangle 30 $μ$m on a side. We can adiabatically tune the ion participation in the motional modes around a closed contour in configuration space, observing that the single-phonon wavefunction acquires a topological Berry phase if the contour encircles a conical intersection of motional eigenvalue surfaces. We observe this phase by single-phonon interference and study its breakdown as the motional mode tuning becomes non-adiabiatic. Our results show that precise, individual quantum control of ion motion in a two-dimensional array can provide unique access to quantum multi-body effects.

💡 Research Summary

This paper reports the first experimental observation of a topological Berry phase acquired by a single phonon in a fully tunable two‑dimensional ion microtrap array. The authors fabricate a microfabricated surface‑electrode trap that creates three individual potential wells at the corners of an equilateral triangle with 30 µm side length, each holding a single ^9Be⁺ ion. By applying voltages to 30 control electrodes, they can independently adjust the curvature (second derivative) of the local trapping potential for each ion along its radial principal axis, while keeping the Coulomb coupling between the ions strong (Δk ≈ few kHz) compared with motional heating rates (≈ 10–30 phonons s⁻¹).

The collective radial motion of the three ions is described by a 3 × 3 Hessian matrix H that contains three contributions: a uniform curvature term k_offs I, a symmetric Coulomb interaction term Δk J (J being the all‑ones matrix), and two tunable parameters s_A and s_B that modify the curvature of sites A and B respectively. Diagonalising H yields three normal‑mode eigenvalues δk₁, δk₂, δk₃. For s_A = s_B = 0 the lower two eigenvalues intersect conically, forming a protected degeneracy (a conical intersection) dictated by the three‑fold rotational symmetry of the trap. The third eigenvalue stays separated by ≳ 3Δk.

After ground‑state cooling of all nine motional modes (average occupation ⟨n⟩ < 0.05), the experiment injects a single phonon into one site (C) using a weak resonant electric‑field pulse. Raman sideband pulses are then used to monitor the phonon’s coherent exchange among the three ions. By sweeping the voltage on the electrode near site A (δV_A) while keeping δV_B ≈ 0, the authors map out the eigenfrequency surfaces and confirm the conical intersection through fluorescence spectroscopy, matching the theoretical predictions of Eq. (1).

The key demonstration involves adiabatically varying (s_A(t), s_B(t)) along a closed loop that either encloses or avoids the conical intersection. When the loop encloses the degeneracy, the phonon’s wavefunction acquires a Berry phase of π, which is revealed as a sign reversal in the interference pattern obtained by a second π‑pulse that removes the phonon. The phase is independent of the exact shape or duration of the loop, provided the evolution remains adiabatic. Conversely, when the loop does not encircle the intersection, no phase shift is observed.

To probe the breakdown of adiabaticity, the authors accelerate the parameter sweep, inducing Landau‑Zener transitions between the two lower modes. The resulting loss of coherence and reduction of the observed π shift quantitatively matches a simple non‑adiabatic model, demonstrating control over both the geometric phase and its dynamical suppression.

The work establishes a versatile platform for engineering synthetic gauge fields, topological band structures, and many‑body Hamiltonians in a planar ion lattice where each site can be individually addressed and its motional frequency tuned. The ability to create, manipulate, and read out a single phonon’s topological phase opens avenues for Berry‑phase‑based quantum gates, simulation of conical‑intersection physics, and exploration of non‑Abelian geometric phases in larger ion arrays.