Periodically Driven Quantum Matter : The case of resonant modulations – Archive ouverte HAL

N. Goldman 1 J. Dalibard 2 M. Aidelsburger 3 N. R. Cooper 4, 5

N. Goldman, J. Dalibard, M. Aidelsburger, N. R. Cooper. Periodically Driven Quantum Matter : The case of resonant modulations. Physical Review A, 2015, 91 (3), pp.033632. ⟨10.1103/PhysRevA.91.033632⟩. ⟨hal-03740659⟩

Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a time-independent effective Hamiltonian, which is generally identified through a perturbative treatment. Here, we present a general formalism that describes time-modulated physical systems, in which the driving frequency is large, but resonant with respect to energy spacings inherent to the system at rest. Such a situation is currently exploited in optical-lattice setups, where superlattice (or Wannier-Stark-ladder) potentials are resonantly modulated so as to control the tunneling matrix elements between lattice sites, offering a powerful method to generate artificial fluxes for cold-atom systems. The formalism developed in this work identifies the basic ingredients needed to generate interesting flux patterns and band structures using resonant modulations. Additionally, our approach allows for a simple description of the micromotion underlying the dynamics; we illustrate its characteristics based on diverse dynamic-lattice configurations. It is shown that the impact of the micromotion on physical observables strongly depends on the implemented scheme, suggesting that a theoretical description in terms of the effective Hamiltonian alone is generally not sufficient to capture the full time evolution of the system.

  • 1. Center for Nonlinear Phenomena and Complex Systems
  • 2. LKB (Jussieu) – Laboratoire Kastler Brossel
  • 3. LKB [Collège de France] – Laboratoire Kastler Brossel
  • 4. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
  • 5. TCM – Theory of Condensed Matter Group

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