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Two-dimensional spectroscopy of bosonic collective excitations in disordered many-body systems

Alex Gómez-Salvador1,*,†, Ivan Morera1,*, Marios H. Michael2, Pavel E. Dolgirev3, Danica Pavicevic2, Albert Liu4, Andrea Cavalleri2,5, and Eugene Demler1

  • *These authors contributed equally to this work.
  • †Contact author: asalvador@ethz.ch
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Phys. Rev. Research 8, 043031 – Published 9 October, 2026

DOI: https://doi.org/10.1103/zsbw-2yzb

Abstract

We present a theoretical approach for computing and analyzing two-dimensional spectroscopy of bosonic collective excitations in disordered many-body systems. Specifically, we employ the Keldysh formalism to derive, within a nonperturbative treatment of disorder effects, the third-order nonlinear response and obtain two-dimensional spectroscopy maps. In the weak nonlinear regime of our formalism, we demonstrate the ability of the echo peak to distinguish between elastic and inelastic scattering processes, in perfect agreement with the intuition developed in isolated two-level systems. Furthermore, we discuss unique many-body effects on the echo peak signature arising from interaction-induced quantum fluctuations. In particular, we show that these quantum fluctuations induce a finite nonrephasable broadening and examine how the echo peak is influenced by the attractive or repulsive nature of the collective excitations.

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Phys. Rev. Research 8, 043031– Published 9 October, 2026
  • Received 1 October 2025
  • Accepted 19 September 2026
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