Nonreciprocal Landau-Zener Tunneling in the Presence of Heat-Bath-Induced Colored Noise

Abstract: In this work, we investigate the effects of heat-bath-induced colored noise on nonreciprocal Landau-Zener tunneling. We perform numerical calculations of the instantaneous energy levels and find that noise induces stochastic fluctuations in these levels. Beyond such fluctuations, sufficiently large nonreciprocity parameters enable noise to further trigger the emergence of multiple exceptional points. The corresponding tunneling probability is significantly modified by colored noise. On the one hand, colored noise generally enhances the tunneling probability under nonadiabatic sweeping. On the other hand, it can break the reciprocity of Landau-Zener tunneling in the adiabatic limit. In particular, for large nonreciprocity parameters, the adiabatic tunneling probability is insensitive to noise and determined by exceptional points. We plot the phase diagram of tunneling probability as a function of the sweep rate and nonreciprocity parameter, for different amplitudes and correlation times of colored noise. Analytically, we derive the exact expression for the tunneling probability in the absence of noise and an approximate solution in the white-noise limit, employing Weber functions and the Wiener-Hermite expansion method. Some implications of our theory are discussed.