Inducing, and enhancing, many-body quantum chaos by continuous monitoring

It is intuitively expected, and supported by earlier studies, that many-body quantum chaos is suppressed, or even destroyed, by dissipative effects induced by continuous monitoring. We show here that this is not always the case. For this purpose, we study the quenched dynamics of a continuously monitored Sachdev-Ye-Kitaev (SYK) model, described by the Lindblad formalism, coupled to a thermal environment modeled by another SYK maintained at constant temperature. We find that the combined effect of monitoring and the thermal bath drives the system toward a non-thermal steady state independently of the initial conditions. The corresponding retarded Green's function exhibits two stages of exponential decay, with rates that depend non-monotonously on the thermal bath coupling and the monitoring strength. In the limit of weak coupling, the late time decay of the Green's function, computed analytically, is closely related to that of the thermal bath. Strikingly, we identify a range of parameters in which continuous monitoring, despite being a source of decoherence, induces or enhances quantum chaotic dynamics suppressed by the thermal bath. For instance, in the limit of weak coupling to the thermal bath, the Lyapunov exponent increases sharply when monitoring is turned on. For intermediate values of the thermal bath coupling, the Lyapunov exponent exhibits re-entrant behavior: it vanishes at zero or sufficiently weak monitoring strength, and becomes positive again as the monitoring strength is increased. Our results offer intriguing insights on the mechanisms leading to quantum scrambling which paves the way to its experimental control and consequently to a performance enhancement of quantum information devices.