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Protocols for a Many-Body Phase Microscope: From Coherences and d-Wave Superconductivity to Green’s Functions

Christof Weitenberg1,*, Luca Asteria2, Ola Carlsson3,4, Annabelle Bohrdt3,4, and Fabian Grusdt3,4

  • *Contact author: christof.weitenberg@tu-dortmund.de
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PRX Quantum 7, 033068 – Published 28 September, 2026

DOI: https://doi.org/10.1103/99mf-c8tv

Abstract

Quantum gas microscopes probe quantum many-body lattice states via projective measurements in the occupation basis, enabling access to various density and spin correlations. Phase information, however, cannot be directly obtained in these setups. Recent experiments went beyond this by measuring local current operators and local phase fluctuations. Here we propose how Fourier-space manipulation in a matter-wave microscope allows access to various long-range off-diagonal correlators in experimentally realistic settings, realizing a many-body phase microscope. We demonstrate in particular how the fermionic d-wave superconducting order parameter in arbitrary Hubbard-type models, the non-equal time Green’s function yielding the spectral function, or the hidden order of composite bosons in a fractional Chern insulator can be directly measured. Our results show the great potential of matter-wave microscopy for accessing exotic correlators including phases and coherences and characterizing intriguing quantum many-body states.

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Popular Summary

Quantum systems can have very intricate order parameters that are hard to access experimentally, but crucial for understanding the systems. One actively pursued route towards a better understanding is quantum simulation with well-controlled experimental platforms such as ultracold atoms in optical lattices, but the challenge of detecting order remains. In this work, we propose realistic protocols for accessing the predicted order parameters in important states of matter. The protocols are based on many-body interferometer schemes, which give access to phase coherence over varying distances within the system. The techniques will allow to solve major challenges in quantum simulation, such as the detection of fractional Chern insulators and d-wave superconductors, which is important for settling the phase diagram of the doped Fermi Hubbard model and ultimately for understanding high-temperature superconductors.

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PRX Quantum 7, 033068– Published 28 September, 2026
  • Received 18 February 2026
  • Accepted 24 August 2026
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