Many-body quantum chaos in stroboscopically-driven cold atoms

In quantum chaotic systems, the spectral form factor (SFF), defined as the Fourier transform of two-level spectral correlation function, is known to follow random matrix theory (RMT), namely a 'ramp' followed by a 'plateau' in late times. Recently, a generic early-time deviation from RMT, so-called the 'bump', was shown to exist in random quantum circuits as toy models for many-body quantum systems. We demonstrate the existence of 'bump-ramp-plateau' behavior in the SFF for a number of paradigmatic and stroboscopically-driven 1D cold-atom models: spinless and spin-1/2 Bose-Hubbard models, and nonintegrable spin-1 condensate with contact or dipolar interactions. We find that the scaling of the many-body Thouless time t(Th) -the onset of RMT-, and the bump amplitude are more sensitive to variations in atom number than the lattice size regardless of the hyperfine structure, the symmetry classes, or the choice of driving protocol. Moreover, t(Th) scaling and the increase of the bump amplitude in atom number are significantly slower in spinor gases than interacting bosons in 1D optical lattices, demonstrating the role of locality. We obtain universal scaling functions of SFF which suggest power-law behavior for the bump regime in quantum chaotic cold-atom systems, and propose an interference measurement protocol. Characterization of quantum chaotic systems involves a detailed understanding of their spectral properties. This work analyses such features in ultracold driven one-dimensional atomic gases, with emphasis on emerging universal scaling in early time deviations of the spectral form factor from random matrix theory predictions, outlining a potential experimental observational protocol.

Automated summary

In quantum chaotic systems, the spectral form factor (SFF) follows random matrix theory (RMT) predictions, with a 'ramp' followed by a 'plateau' in late times. However, recent studies have shown a deviation from RMT known as the 'bump' in random quantum circuits. This study demonstrates the 'bump-ramp-plateau' behavior in several one-dimensional cold-atom models and investigates the sensitivity of the scaling and bump amplitude to atom number.