Chaotic Bloch oscillations in dissipative optical systems driven by a periodic train of coherent pulses

We study the response of an optical system with the Kerr nonlinearity demonstrating Bloch oscillations to a periodic train of coherent pulses. It has been found out that the intensity of the field excited in the system by pulses resonantly depends on the train period. It is demonstrated numerically and analytically that the response of the system is stronger when the period of the driving pulses is commensurate with the period of the Bloch oscillations. Moreover, large enough pulses are capable to induce the instabilities which eventually lead to onset of chaotic Bloch oscillations of the wave-function envelope bouncing both in time and space. The analysis reveals that these instabilities are associated with period-doubling bifurcations. A cascade of such bifurcations with increase of the pulse amplitude triggers the chaotic behavior.

Automated summary

We investigated the response of an optical system with Kerr nonlinearity to a periodic train of coherent pulses. The intensity of the excited field in the system was found to depend resonantly on the pulses' period. Numerical and analytical results demonstrated that the system's response is stronger when the pulse period is commensurate with the period of Bloch oscillations. Moreover, sufficiently large pulses can induce instabilities leading to chaotic Bloch oscillations of the wave-function envelope in both time and space. These instabilities are associated with period-doubling bifurcations, with a cascade of such bifurcations triggering the chaotic behavior.