We study the emergence of dissipative quantum chaos in a two-level system that is non-chaotic in isolation but coupled to a set of structured internal modes. These internal degrees of freedom exhibit chaotic characteristics, which are imprinted onto the reduced dynamics of the system. From a time-local master equation, we derive an effective time-dependent non-Hermitian Liouvillian and analyze its complex eigenvalues at each time step. Spectral statistics [1] reveal that the two-level system can retain clear signatures of quantum chaos present in its internal degree of freedom, under certain conditions. We further show that internal degree of freedominduced chaos correlates with the loss of coherence in the system, quantified by the degradation of purity [2, 3]. By extending the model to two qubits, we examine how chaotic internal modes degrade Hong-Ou-Mandel interference and thus generate particle distinguishability [4]. Our results demonstrate that spectral chaos in unobserved internal degrees of freedom can leave measurable traces in open quantum dynamics and quantum interference experiments.

[1] P. Kos, M. Ljubotina, and T. Prosen, “Many-body quantum chaos: Analytic connection to random matrix theory,” Physical Review X, vol. 8, no. 2, p. 021062, 2018.

[2] C. Dittel, G. Dufour, M.Walschaers, G.Weihs, A. Buchleitner, and R. Keil, “Totally destructive many-particle interference,” Phys. Rev. Lett., vol. 120, p. 240404, Jun 2018.

[3] C. Dittel, G. Dufour, G. Weihs, and A. Buchleitner, “Wave-particle duality of many-body quantum states,” Physical Review X, vol. 11, no. 3, p. 031041, 2021.

[4] M. Berkane, G. Dufour, and A. Buchleitner, “In prepration,”.