AC-driven Quantum Phase Transitions

• Applicant: Privatdozent Dr. Gernot Schaller, since 4/2017
• Subject Area: Theoretical Condensed Matter Physics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2013 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 235452962

• Final Report Year: 2019

Final Report Abstract

The first part of the project dealt with periodic-driving extensions of models that exhibit ground state, excited state, or topological quantum phase transitions. Under the assumption of fast driving, the dynamics is stroboscopically governed by an effective Floquet Hamiltonian. This new effective Floquet Hamiltonian can exhibit a plethora of additional interesting properties, for example new critical points/lines separating new phases or excited state quantum phase transitions. In particular, topological transitions were found to be related to dynamical instabilities. In effect, this first part of the project has established for a large number of examples that periodic driving is a useful tool to explore and engineer nonequilibrium states of matter. From the perspective of quantum simulation, effective Floquet Hamiltonians can be stroboscopically simulated by simpler but driven models. Aiming more at applications, the second part of the project extended the discussion to periodically driven dissipative systems. As a benchmark model, new analytic expansions of the driven spin-boson model have been derived. Furthermore, by employing an extended space representation, tools from Full Counting Statistics and reaction-coordinate mappings have been used to derive generalized master equations for driven open systems beyond the standard weak coupling limit that also allow to infer the heat exchange statistics with the reservoirs. Applying this to concrete questions, it has been possible to analyze periodically driven open systems as the working fluid of a quantum heat engine or an electron pump. The methods derived within the project are universally applicable also to other setups and may have impact on Floquet engineering, stroboscopic simulation of Hamiltonians, heat engines, and electron pumps.

Publications

• ac-driven quantum phase transition in the Lipkin-Meshkov-Glick model, Physical Review E 87, 052110 (2013)
  G. Engelhardt, V. M. Bastidas, C. Emary, and T. Brandes
  
• Quantum Criticality and Dynamical Instability in the Kicked-Top Model, Phyical Review Letters 112, 140408 (2014)
  V. M Bastidas, P. Perez-Fernandez, M. Vogl, and T. Brandes
  
• Excited-state quantum phase transitions and periodic dynamics, Physical Review A 91, 013631 (2015)
  G. Engelhardt, V. M. Bastidas, W. Kopylov, and T. Brandes
  
• Driven Open Quantum Systems and Floquet Stroboscopic Dynamics, Physical Review Letters 117, 250401 (2016)
  S. Restrepo, J. Cerrillo, V. M. Bastidas, D. G. Angelakis, and T. Brandes
  
• Random-walk topological transition revealed via electron counting, Physical Review B 96, 241404(R) (2017)
  G. Engelhardt, M. Benito, G. Platero, G. Schaller, and T. Brandes
  
• From quantum heat engines to laser cooling: Floquet theory beyond the Born–Markov approximation. New Journal of Physics 20, 053063 (2018)
  S. Restrepo, J. Cerrillo, P. Strasberg, and G. Schaller