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Momentum-Resolved Two-Dimensional Spectroscopy as a Probe of Nonlinear Quantum Field Dynamics

Duilio De Santis1,2,*,†, Alex Gómez-Salvador2,*, Nataliia Bazhan3, Sebastian Erne3, Maximilian Prüfer3, Claudio Guarcello4, Davide Valenti1, Jörg Schmiedmayer3, and Eugene Demler2

  • 1Dipartimento di Fisica e Chimica “E. Segrè”, Group of Interdisciplinary Theoretical Physics, Università degli Studi di Palermo, I-90128 Palermo, Italy
  • 2Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
  • 3Vienna Center for Quantum Science and Technology (VCQ), Atominstitut, TU Wien, Vienna, Austria
  • 4Dipartimento di Fisica “E. R. Caianiello”, Università degli Studi di Salerno, I-84084 Fisciano, Salerno, Italy

  • *These authors contributed equally to this work.
  • †Contact author: ddesantis@phys.ethz.ch
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Phys. Rev. Lett. 136, 233401 – Published 9 June, 2026

DOI: https://doi.org/10.1103/tfdm-qshs

Abstract

Emergent collective excitations constitute a hallmark of interacting quantum many-body systems, yet in solid-state platforms their study has been largely limited by the constraints of linear-response probes and by finite momentum resolution. We propose to overcome these limitations by combining the spatial resolution of ultracold atomic systems with the nonlinear probing capabilities of two-dimensional spectroscopy (2DS). As a concrete illustration, we analyze momentum-resolved 2DS of the quantum sine-Gordon model describing the low-energy dynamics of two weakly coupled one-dimensional Bose-Einstein condensates. This approach reveals distinctive many-body signatures, most notably asymmetric cross-peaks reflecting the interplay between isolated (B2 breather) and continuum (B1 pair) modes. The protocol further enables direct characterization of anharmonicity and disorder, establishing momentum-resolved 2DS as both a powerful diagnostic for quantum simulators and a versatile probe of correlated quantum matter.

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  91. We note that Figs. 3 and 3 presents the system’s response summed over all k, where the bound state is expected to dominate (as indicated by the linear response). This accounts for the appearance of only a sub-2B1 peak in this case. Rephasing phenomena are observed, in a similar fashion, in the k-resolved case as well.

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  93. Note that in Fig. 3 we plot the absolute-value peak, but both real and imaginary parts are in principle experimentally accessible, enabling their full characterization.

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Phys. Rev. Lett. 136, 233401– Published 9 June, 2026
  • Received 4 December 2025
  • Revised 31 March 2026
  • Accepted 30 April 2026
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