The surprisingly rich physics of the modulated quantum pendulum


Université de Toulouse

In classical mechanics, a pendulum whose parameters are modulated in time provides a standard example for introducing classical chaos, with the emergence of mixed or fully chaotic stroboscopic phase spaces. In quantum physics, although the Schrödinger equation is fully linear, the same Hamiltonian offers the possibility of studying weak and strong localization and chaos-assisted tunneling [1]. We will detail our recent results in this direction. Using quantum control techniques to drive the pendulum appropriately [2], we have recently extended the accessible physics in this system by demonstrating the production of squeezed states and matter wave transport with a quantum ratchet [3], performing qubit-based quantum computations and carrying out various quantum simulations based on Floquet Hamiltonian engineering including the generation of a synthetic and tunable cristal [4].

[1] Chaos-assisted tunneling resonances in a synthetic Floquet superlattice, M. Arnal, G. Chatelain, M. Martinez, N. Dupont, O. Giraud, D. Ullmo, B. Georgeot, G. Lemarié, J. Billy and D. Guéry-Odelin, Science Advances 6, eabc4886 (2020).

[2] Quantum state control of a Bose-Einstein condensate in an optical lattice, N. Dupont, G. Chatelain, L. Gabardos, M. Arnal, J. Billy, B. Peaudecerf, D. Sugny, D. Guéry-Odelin PRX Quantum 2, 040303 (2021).

[3] A regular Hamiltonian halting ratchet for matter wave transport, N. Dupont, L. Gabardos, F. Arrouas, N. Ombredane, J. Billy, B. Peaudecerf, D. Guéry-Odelin Phys. Rev. Lett. 131, 133401 (2023).

[4] Emergence of a tunable crystalline order in a Floquet-Bloch system from a parametric instability, N. Dupont, L. Gabardos, F. Arrouas, G. Chatelain, M. Arnal, J. Billy, P. Schlagheck, B. Peaudecerf and D. Guéry-Odelin, Proc. Natl. Acad. Sci. (USA) 120, no. 32, e2300980120 (2023).



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