Nonlocal Random Walk over Quasienergy Levels of a Driven Quantum Oscillator

The thermal distribution over the energy levels of a quantum system weakly coupled to a bath is formed as a result of the coupling-induced interlevel transitions. The transitions are thermally activated and, in a multilevel system, can be thought of as a random walk over the levels. Usually only transitions between a few neighboring levels matter. We show that a different situation occurs for periodically driven quantum oscillators. Such systems are described by Floquet (quasienergy) states. Here, the quantum noise that invariably accompanies relaxation, leads to transitions between the quasienergy levels even for T=0. We find that the stationary distribution is formed due to transitions not only between neighboring, but also between remote levels, even though the transition rates exponentially fall off with the number of intermediate levels. We study an oscillator driven close to its tripled eigenfrequency. In many respects, this is a generic example of a classically multistable driven system. It has three period-3 states, and the nonlocality of the interlevel transitions determines the rate of switching between these states. Surprisingly, this switching occurs via transitions over the quasienergy barrier rather than tunneling.