Dynamics, thermalization and propagation of quantum systems in complex environments

• Applicant: Ines de Vega, Ph.D.
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Theoretical Condensed Matter Physics
• Term: from 2017 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 329368667

• Final Report Year: 2021

Final Report Abstract

In our quest to accurately describe open quantum systems, one approach has been to develop more powerful mathematical and numerical tools to reach the so-called strong coupling or non-Markovian regime, where the open system and its environment evolve on similar time-scales. In this case, the environment is strongly affected by the open system, and this affects in turn the way it interacts with it at future times. Thus, the environment has a memory that produces a very rich phenomenology on the open system dynamics, even if this is a simple two-level impurity or a non-interacting system. As analyzed in this project, this includes for instance the absence of thermalization, or the formation of system-environment single-photon or multiple-photon bound or entangled states. Additionally, open quantum systems may be complex by themselves, such as interacting many body systems. In this case, as we have analyzed, the interplay between the eigenstate structure of the open system and the dissipation process produced by the environment provides for a very rich dissipative dynamics, reflected in the emergence of multiple of decay channels for each system energy transition. Our analysis has included exploring the conditions for this dissipative process to drive the open system towards a thermal state, the effects of the system criticality on such process, as well as the validity of certain approximations often considered in its description, such as the secular approximation. Finally, as we increase our precision to describe the dynamics of open quantum systems, and experimental scenarios diversify, it is of primary importance to revisit the models and the mathematical formalism that we have used so far. A particularly interesting situation emerges for systems coupled to non-harmonic environments. In this regard, we showed that for some parameter regimes it is not possible to properly define a weak coupling limit, often used to approximate such non-Harmonic environments in terms of virtual harmonic oscillators. In detail, we considered non-harmonic molecular environments of two types: dye molecules, and diatomic molecules described via Morse oscillators. We found that their second order moments, required to obtain the system’s weak coupling equations, do not decay (or decay at extremely low rates), giving rise not only to ill-defined weak coupling equations but also to the impossibility of defining a Markov limit. A similar situation occur for environments formed by two-level fluctuators, like the ones affecting superconducting qubits. We also showed how these regimes are linked to strong non-Markovian effects in the open system dynamics, and in some cases to the presence of non-invertible dynamical maps, a feature that formally implies the absence of a master equation to describe its dynamics.

Publications

• Stable-unstable transition for a bose-hubbard chain coupled to an environment. Phys. Rev. A, 97:053610, May 2018
  Chu Guo, Ines de Vega, Ulrich Schollwöck, and Dario Poletti
  
• Dynamics of multiple atoms in one-dimensional fields. Phys. Rev. A, 99:013845, Jan 2019
  Carlo Cascio, Jad C. Halimeh, Ian P. McCulloch, Alessio Recati, and Inés de Vega
  
• Nonreciprocal quantum transport at junctions of structured leads. Phys. Rev. B, 99:245134, Jun 2019
  Eduardo Mascarenhas, François Damanet, Stuart Flannigan, Luca Tagliacozzo, Andrew J. Daley, e John Goold, and Inés de Vega
  
• Thermalization in the quantum ising model-approximations, limits, and beyond. Quantum Science and Technology, 4(3):034002, jun 2019
  Daniel Jaschke, Lincoln D Carr, and Inés de Vega
  
• Dephasing dynamics of an impurity coupled to an anharmonic environment. Phys. Rev. A, 101:012101, Jan 2020
  Max Bramberger and Inés De Vega
  
• Prethermalization of quantum systems interacting with non-equilibrium environments. 22(8):083067, aug 2020
  Andreu Anglés-Castillo, Mari Carmen Bañuls, Armando Pérez, and Inés De Vega
  
• The quantum dynamical map of the spin boson model
  Inés de Vega
  
• Impurity dephasing in a bose–hubbard model. 23(3):033018, mar 2021
  Fabio Caleffi, Massimo Capone, Inés de Vega, and Alessio Recati
  
• Neural network based qubit environment characterization. 2021
  Miha Papič and Inés de Vega
  
• Open quantum systems in thermal nonergodic environments. Phys. Rev. A, 103:032204, Mar 2021
  Carlos A. Parra-Murillo, Max Bramberger, Claudius Hubig, and Inés De Vega