Coherent control of time-periodically forced matter waves

• Applicant: Professor Dr. Martin Holthaus
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2009 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 144180541

• Final Report Year: 2015

Final Report Abstract

During the first funding period of this project, parallels between ultracold atoms in modulated optical lattices and electrons in laser-driven crystalline solids have been worked out theoretically to the extent that ultracold atoms in driven optical lattices may now be employed as “strong-field simulators”. Particular emphasis has been placed on coherent control strategies opened up by the use of forcing pulses, instead of pure ac forcing with constant amplitude. In addition, an extension of Bloch’s “acceleration theorem” to spatio-temporal lattices has been given. These theoretical proposals have meanwhile been taken up experimentally; pioneering first measurements of multiphoton-like transitions in driven optical lattices have been published by K. Sengstocks Hamburg group [arXiv:1505.02657]. The attempt to characterize the quasi-equilibrium state of driven quantum gases, made during the second period, has led to the recognition that here the usual strategy of coupling to an external heat bath has to be abandoned: For driven systems, the presence of such a heat bath necessarily enforces a continuous energy flow into the environment, and influences the Floquet-state occupation numbers in the steady state. Future studies in this direction should consider weakly interacting driven quantum gases which serve as their own heat bath. The question under what conditions a forced Bose-Einstein condensate remains stable has been studied in considerable detail. The starting point of these studies was a construction of the time-dependent macroscopic wave function which does not rely on the explicit breaking of the U (1) symmetry associated with particle number conservation, but is based on a comparison of the dynamics of N and (N − 1) Bose particles, respectively. This has shown that macroscopic wave functions may persist even under strong forcing; provided the flow in Fock space possesses a certain property dubbed “stiffness”. On the other hand, it is predicted that macroscopic wave functions can be dynamically destroyed almost instantaneously upon entering a chaotic regime.

Publications

• 2011. Controlled wave packet manipulation with driven optical lattices. Phys. Rev. A 84, 063617
  Arlinghaus, S., Holthaus, M.
  
• 2011. Generalized acceleration theorem for spatiotemporal Bloch waves. Phys. Rev. B 84, 054301
  Arlinghaus, S., Holthaus, M.
  
• 2012. ac Stark shift and multiphoton-like resonances in low-frequency-driven optical lattices. Phys. Rev. A 85, 063601
  Arlinghaus, S., Holthaus, M.
  
• 2012. Kilohertz-driven Bose-Einstein condensates in optical lattices. Adv. At. Mol. Opt. Phys. 61, 515–547
  Arimondo, E., Ciampini, D., Eckardt, A., Holthaus, M., Morsch, O.
  
• 2014. Energy flow in periodic thermodynamics. Phys. Rev. E 89, 012101
  Langemeyer, M., Holthaus, M.
  
• 2014. Fluctuations of the order parameter of a mesoscopic Floquet condensate. Phys. Rev. A 90, 053614
  Gertjerenken, B., Holthaus, M.
  
• 2014. Quasiparticle tunneling in a periodically driven bosonic Josephson junction. Phys. Rev. A 90, 053622
  Gertjerenken, B., Holthaus, M.
  
• 2014. Trojan quasiparticles. New J. Phys. 16, 093009
  Gertjerenken, B., Holthaus, M.
  
• 2015. Emergence and destruction of macroscopic wave functions. EPL 111, 30006
  Gertjerenken, B., Holthaus, M.
  
• 2015. N -coherence vs. t-coherence: An alternative route to the Gross-Pitaevskii equation. Annals of Physics 362, 482–510
  Gertjerenken, B., Holthaus, M.