We show that the strong coupling of a quantum light field and correlated quantum matter induces exotic quantum fluctuations in the matter sector. We determine their spectral characteristics and reveal the impact of the atomic $s$-wave scattering. In particular, we derive the dissipative Landau and Beliaev processes from the microscopic Hamiltonian using imaginary-time path integrals. By this, their strongly sub-Ohmic nature is revealed analytically. A competition between damping and antidamping channels is uncovered. Their intricate influence on physical observables is quantified analytically and the Stokes shift of the critical point is determined. This illustrates the tunability of the quantum matter fluctuations by exploiting strong light-matter coupling.

• Received 2 June 2023
• Revised 28 August 2023
• Accepted 27 November 2023

DOI:https://doi.org/10.1103/PhysRevResearch.6.L012024

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Published by the American Physical Society