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The dynamical signatures of quantum chaos in an isolated system are capturedby the spectral form factor, which exhibits as a function of time a dip, aramp, and a plateau, with the ramp being governed by the correlations in thelevel spacing distribution. While decoherence generally suppresses thesedynamical signatures, the nonlinear non-Hermitian evolution with balanced gainand loss (BGL) in an energy-dephasing scenario can enhance manifestations ofquantum chaos. In the Sachdev-Ye-Kitaev model and random matrix Hamiltonians,BGL increases the span of the ramp, lowering the dip as well as the value ofthe plateau, providing an experimentally realizable physical mechanism forspectral filtering. The chaos enhancement due to BGL is optimal over a familyof filter functions that can be engineered with fluctuating Hamiltonians.

Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos