Directed transport within Hamiltonian dynamics: From theory to cold atoms experiments

• Applicant: Professor Dr. Peter Hänggi
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2006 to 2015
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 30082554

• Final Report Year: 2016

Final Report Abstract

With this second phase of our funded project we continued to study directed transport in Hamiltonian systems which arc subjected to external driving, thereby taking the systems far away from equilibrium. The main focus has been on the directed transport in quantum systems that are subjected to unbiased, periodic time-dependent driving. In doing so, one can study a fully coherent non-equilibrium quantum transport in absence of decoherent and dissipative influences. The main results obtained were the controlled transport in a setup of only one atom which can be set into motion with its interaction with a starter atom. A temporal periodic driving induces new band structures, technically known as so termed Floquet bands. These Floquet bands allow for novel transport schemes that can not be archived otherwise. Our theoretical results have been devised so as to become experimentally validated. The optimal validation scheme are ultra cold atoms that can be manipulated with external time-dependent forces by use of time-dependent modulated counter-propagating optical lattice beams. Our studies resulted in two specific Theory- Experiment collaborations with the findings jointly published. Naturally, there remain several open issues that remained untouched in our studies. Most importantly among these are the role of higher spatial dimensions and the intriguing role of strong interactions amongst the cold atoms. Although in part already addressed within our published works the interplay of time-dependent driving and (quantum) dissipation presents a formidable challenge which calls for improved treatments beyond the weak-to-moderate coupling regime in presence of (strong) external driving.

Publications

• Coherent Ratchets in Driven Bose-Einstein Condensates, Phys. Rev. Lett. 104, 228901 (2010)
  G. Benenti, G. Casati, S. Denisov, S. Flach, P. Hänggi, B. Li, D. Poletti
  
• Ein Förderband für kalte Atome, Physik Journal 9, no. 2, 18-20 (2010)
  P. Hänggi, S. Denisov
  
• Quantum machine using cold atoms, J. Comp. Theor. Nanosci. 7, 2441-2447 (2010)
  A. V. Ponomarev, S. Denisov, P. Hänggi
  
• Transporting Cold Atoms in Optical Lattices with Ratchets: Mechanisms and Symmetries. In: Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Y. Kivshar (eds.), Springer Series in Optical Sciences, 150, 181-194 (Springer Verlag, Berlin, Heidelberg, 2010)
  S. Denisov, S. Flach, P. Hänggi
  
• Quantum ratchet transport with minimal dispersion rate, Phys. Rev. A 84, 043617 (2011)
  F. Zhan, S. Denisov, A.V. Ponomarev, P. Hänggi
  
• Tuning the mobility of a driven Bose-Einstein condensate via diabatic Floquet bands, Phys. Rev. Lett. 110, 135302 (2013)
  T. Salgor, S. Kling, S. Denisov, A. Ponomarev, P. Hänggi, M. Weitz
  
• Tunable Transport with broken space-time symmetries, Phys. Rep. 538, 77-120 (2014)
  S. Denisov, S. Flach, P. Hänggi
  
• Cooperative surmounting of bottlenecks, Phys. Rep. 586, 1-51 (2015)
  D. Hennig, C. Mulhern, L. Schimansky-Geier, G.P. Tsironis, P. Hänggi
  
• Experimental control of transport resonances in a coherent quantum rocking ratchet. Nature Communications volume 7, Article number: 10440 (2016)
  C. Grossert, M. Leder, S. Denisov, P. Hänggi, M. Weitz