Dynamics of one-dimensional quantum many-body systems in time-periodic linear potentials
arXiv:2006.11299 · doi:10.1103/PhysRevA.102.033310
Abstract
We study a system of one-dimensional interacting quantum particles subjected to a time-periodic potential linear in space. After discussing the cases of driven one- and two-particles systems, we derive the analogous results for the many-particles case in presence of a general interaction two-body potential and the corresponding Floquet Hamiltonian. When the undriven model is integrable, the Floquet Hamitlonian is shown to be integrable too. We determine the micro-motion operator and the expression for a generic time evolved state of the system. We discuss various aspects of the dynamics of the system both at stroboscopic and intermediate times, in particular the motion of the center of mass of a generic wavepacket and its spreading over time. We also discuss the case of accelerated motion of the center of mass, obtained when the integral of the coeffcient strenght of the linear potential on a time period is non-vanishing, and we show that the Floquet Hamiltonian gets in this case an additional static linear potential. We also discuss the application of the obtained results to the Lieb-Liniger model.
22 pages, 4 figures
References in corpus (11)
- Topological characterization of periodically-driven quantum systems
- Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
- Dynamical control of matter-wave tunneling in periodic potentials
- Absence of Quantum Time Crystals
- Single Particle Tunneling in Strongly Driven Double Well Potentials
- Exploring dynamic localization with a Bose-Einstein condensate
- Hypersonic Bose-Einstein Condensates in Accelerator Rings
- Composite fermionization of 1-D Bose-Bose mixtures
- BCS theory of driven superconductivity
- Finding zeros of the Riemann zeta function by periodic driving of cold atoms
- Lieb-Liniger gas in a constant force potential