On this page, you can find supplementary videos to the paper Reinforcement Learning to Autonomously Prepare Floquet-Engineered States: Inverting the Quantum Kapitza Oscillator [1].

The movies below show three stages of time evolution:

• (i) the oscillator is subject to the control field in the presence of the Floquet drive. The arrow direction indicates the direction of the horizontal control kick.
• (ii) Once the control stage is over, the Floquet-drive is kept on but the control field is turned off.
• (iii) Both the Floquet drive and the control are turned off, and the system evolves under the free oscillator Hamiltonian $H_0$, see paper.

Movie 1 shows the real-space probability distribution of being in the target state for the quantum Kapitza oscillator, following the best-encountered RL protocol. The control process takes $N_T=15$ drive cycles, and the drive protocol contains $8$ steps per cycle. The oscillator parameters are $N_T=15$ periods with $8$ steps each, $\Omega/\omega_0=10$, $A=2$ and $m\omega_0=1$.

Movie 2 shows the real-space probability distribution of being in the target state for the quantum Kapitza oscillator, following the best Stochastic Descent protocol. The control process takes $N_T=15$ drive cycles, and the drive protocol contains $8$ steps per cycle. The oscillator parameters are $N_T=15$ periods with $8$ steps each, $\Omega/\omega_0=10$, $A=2$ and $m\omega_0=1$.

Movie 3 shows the classical Kapitza pendulum dynamics, following the best-encountered RL protocol. The control process takes $N_T=4$ drive cycles, and the drive protocol contains $8$ steps per cycle. The pendulum parameters are $N_T=4$ periods with $8$ steps each, $\Omega/\omega_0=10$, $A=2$ and $m\omega_0=1$.

References:
[1] M.B., arXiv: 1808.08910 (2018).