Many-Body Stückelberg Interference in Quantum Arrays

• Many-body Stückelberg interference is the temporal interference that arises when interacting quantum systems are periodically driven through avoided crossings, extending classic two-level LZSM interferometry.
• It is shaped by interparticle interactions, geometry, and coherence, with interference fringes manipulated via single- and dual-frequency driving protocols.
• Experimental studies in programmable Rydberg atom arrays reveal high-contrast oscillations and resonance effects that inform scalable quantum control, precision metrology, and Floquet engineering.

Many-body Stückelberg interference describes the phenomenon where non-monotonic, periodic driving of a quantum many-body system through avoided level crossings leads to temporal interference effects—generalizing the classic two-level Landau–Zener–Stückelberg–Majorana (LZSM) interferometry to ensembles with nontrivial interparticle interactions and collective phase dynamics. In many-body settings, both the occurrence and visibility of Stückelberg interference fringes are shaped by the system's microscopic interactions, geometry, and coherence properties. Experimental realization of this effect in large-scale programmable Rydberg atom arrays demonstrates the potential of temporal interference as a scalable control paradigm for nonequilibrium quantum state engineering (Sarkar et al., 12 Nov 2025).

1. Conceptual Foundations and Generalization to Many-Body Systems

Stückelberg interference in two-level quantum systems refers to temporal analogues of spatial interference: when a system's control parameter is swept through an avoided crossing twice per drive cycle, superposition and phase accumulation between the two eigenstate branches yields constructive or destructive interference in observables such as final state populations. The excited-state probability after a full cycle takes the form

$$P_e(T) = 4P_{\rm LZ}(1-P_{\rm LZ})\sin^2 \left(\frac{\Phi}{2} + \phi_0 \right)$$

where $P_{\rm LZ}$ is the Landau–Zener transition probability, $\Phi$ is the accumulated dynamical phase between crossings, and $\phi_0$ is the Stokes phase offset.

Transitioning to many-body systems, interactions introduce additional phase shifts and path amplitudes and generally cause scrambling of individual phase relations, potentially reducing or reshaping interference visibility. The core challenge is that, unlike in the single-particle situation, each constituent's Stückelberg path is influenced by its coupling to all others, leading to new interference channels, dispersive phase evolution, and geometry- or connectivity-dependent responses (Sarkar et al., 12 Nov 2025).

2. Theoretical Models: Driven Many-Body Hamiltonians and Floquet Structure

A canonical framework for many-body Stückelberg interference is the periodically modulated Rydberg Hamiltonian: $$H(t) = \sum_{i<j} V_{ij} n_i n_j + \sum_{i} \left[ \frac{\Omega(t)}{2} \sigma^x_i - \Delta(t) n_i \right]$$ where $n_i = \frac{1+\sigma^z_i}{2}$ counts Rydberg excitations, $V_{ij}$ are long-range van der Waals couplings, $\Delta(t)$ is a time-dependent detuning, and $\Omega(t)$ the Rabi frequency.

Standard driving protocols realize

$$\Delta(t) = \Delta_0 \cos(\omega t), \quad \Omega(t) = \Omega_0 \;\mathrm{(single-frequency)}$$

or

$$\Delta(t) = \Delta_0 \cos(\omega t), \quad \Omega(t) = \frac{\Omega_0}{2}[1+\cos(r\omega t)], \; r=2 \;\mathrm{(bi-frequency)}$$

Periodic passage through $\Delta(t)=0$ generates successive Stückelberg interferometers embedded in a many-body landscape.

Interactions $V_{ij}$ modify two-level splittings and the dynamical phases, producing correlation-dependent modulations. Floquet perturbation theory captures the generation of new excitation channels, with amplitudes scaling as $V_{ij}{n\omega}\mathcal{J}_n(\Delta_0/\omega)$, where $\mathcal{J}_n$ is the $n$th Bessel function. These interaction-induced channels shift interference minima, influence the contrast of fringes, and can induce resonance effects not captured by blockade-only (PXP) approximations (Sarkar et al., 12 Nov 2025).

3. Experimental Observation in Rydberg Atom Arrays

Programmable neutral-atom arrays (e.g., QuEra’s Aquila platform) provide a platform to probe many-body Stückelberg interference with up to 100 atoms. Experimental protocols involve:

• Initializing all atoms in the ground state $|g\rangle$.
• Applying a periodic driving cycle, modulating both detuning and coupling.
• Measuring Rydberg excitation density $n(T)$ after the cycle (including SPAM corrections).

Key regimes and parameter sets include:

• $\omega$ in $1.5$–$4.5$ rad/$\mu$s, $\Delta_0\approx20$ rad/$\mu$s, $\Omega_0$ in $2$–$5$ rad/$\mu$s, blockade radius $R_b\approx8.4\,\mu$m.
• Implementing single- and dual-frequency drives to probe different interference conditions.

One-dimensional “snake” chains and two-dimensional square/honeycomb arrays reveal distinct interference patterns resulting from their connectivity and interaction structure.

4. Phenomenology: Interference Patterns, Geometry, and Interaction Effects

Empirical measurements in one-dimensional chains show pronounced oscillations in the final Rydberg excitation density as a function of $\omega$, with vacuum-state (excitation) suppression below $1\%$ and visibility exceeding $70\%$. Bi-frequency drives deepen the suppression and maintain visibility even in parameter regimes where single-frequency driving leads to heating.

Increasing interatomic spacing shifts minima in the interference pattern, demonstrating direct sensitivity of the Stückelberg phase to finite-range interaction tails $V_{i,i+2}$. Two-dimensional arrays exhibit reduced visibility due to increased next-nearest-neighbor connectivity, but dual-frequency driving restores high-contrast fringes (e.g., $V\approx0.9$ in square arrays).

Time-resolved tracking of excitation density within the drive cycle confirms the two-step origin of the interference, with growth at the first crossing and recombination at the second; freezing the detuning after half a cycle eliminates fringes, verifying the Stückelberg origin.

Finite-range interactions (beyond nearest-neighbor blockade) induce phase channels in Fock space, creating additional resonance conditions that reshape the interference landscape in a geometry- and spacing-dependent way. These are not captured by constrained PXP or PPXPP models, which fail to reproduce observed quantitative features such as detuning-sign asymmetry and distance-dependent minima (Sarkar et al., 12 Nov 2025).

5. Extensions to Alternative Many-Body Platforms

Many-body Stückelberg interference extends beyond Rydberg ensembles:

• In spinor Bose–Einstein condensates under spatially inhomogeneous transverse and periodic longitudinal magnetic fields, Stückelberg interference manifests in spatial rather than temporal fringes. The position-dependent Landau–Zener probability and accumulated phases produce density patterns with sub-micron periodicity that reflect both external gradients and emergent dipole–dipole fields (Zhang et al., 2010).
• In multimode electromechanical hybrid systems (e.g., a superconducting qubit coupled to multiple acoustic modes), consecutive traversals through mode-specific avoided crossings yield multimode Stückelberg interference. The resultant fringe structures and spectral features depend on both the number of modes and the details of the parametric modulation, with applications in multi-channel coherent control and scalable hybrid quantum networks (Kervinen et al., 2019).
• In nonlinear, non-Hermitian bosonic systems (e.g., Bose–Hubbard dimers with interactions and nonreciprocal tunneling), many-body Stückelberg interference is modified by both nonlinearity and non-Hermicity. The accumulated phase is shifted by the interaction strength $\chi$, moving fringe positions, while nonreciprocity scales the visibility but does not affect the phase-matching condition in the weak-coupling limit. Enhanced complexity arises near exceptional points and phase transitions between Josephson and self-trapping regimes (Wang et al., 2023).

6. Applications and Implications

Demonstrated and suggested applications of many-body Stückelberg interference include:

• Microscopic Floquet control: Temporal interference provides a scalable mechanism for Floquet engineering, enabling selective stabilization or suppression of excitations in strongly driven quantum matter. By tuning drive harmonics (bi- or multi-frequency), states such as low-entropy vacua or scarred manifolds can be engineered (Sarkar et al., 12 Nov 2025).
• Precision metrology: The sensitivity of interference patterns to geometry and microscopic spacing enables high-resolution measurements of interparticle forces and field gradients.
• Quantum optimization and annealing: Temporal control of nonadiabatic passages via phase-matched driving enables balancing of speed and fidelity in quantum annealing protocols.
• Hybrid quantum system control: In superconducting–mechanical platforms, many-body Stückelberg interference is a tool for reconfigurable entanglement routing among oscillator modes.
• Spatial manipulation in ultracold gases: Spatial Stückelberg interference in spinor condensates enables engineered matter-wave beam splitters and detection of weak interactions.

A plausible implication is that many-body Stückelberg interference provides a unified experimental and theoretical lens for designing and diagnosing far-from-equilibrium quantum dynamics across various platforms.

7. Limitations and Future Directions

Current blockade-based or nearest-neighbor-constrained models are insufficient to quantitatively predict many-body Stückelberg interference; accurate modeling requires inclusion of finite-range interaction tails and multi-path phase channels. The breakdown of fringe contrast, emergence of new resonances, and geometry dependence observed in large Rydberg arrays necessitate fully microscopic treatments (Sarkar et al., 12 Nov 2025).

Open directions include extending these protocols to longer evolution (multiple drive cycles), exploiting higher-order harmonics for richer Floquet engineering, and probing interference dynamics in frustrated or disordered geometries. Exploring many-body Stückelberg effects in other correlated systems—such as dipolar gases, quantum dot arrays, or topological materials—may reveal new classes of nonequilibrium phases and inform the design of robust quantum simulators and quantum information architectures.

Platform or Model	Role of Many-Body Effects	Key Observables
Rydberg atom arrays (Sarkar et al., 12 Nov 2025)	Finite-range $V_{ij}$, geometry	$n(T)$, visibility
Spinor BEC (Zhang et al., 2010)	Dipolar fields, spatial gradients	Spatial fringe period, $n_\pm(x)$
Hybrid superconducting–mechanical (Kervinen et al., 2019)	Multimode avoided crossings	$P_e(A, \omega)$, Rabi splitting
Nonlinear non-Hermitian dimer (Wang et al., 2023)	Nonlinearity $\chi$, nonreciprocity	Fringe positions, visibility

Many-body Stückelberg interference thus emerges as a general principle underpinning temporal control, state stabilization, and phase-sensitive signal amplification in driven quantum matter, with broad applications in quantum simulation, computation, and metrology.