Perturbation theories for open System Detector dynamics
Final Report Abstract
The general goal of the research project was an improved understanding of system-detector correlations in presence of dissipation. In traditional approaches, the action of a detector was usually only described effectively, e.g. by using the projective measurements. In contrast, a realistic quantum detector will nearly always also perturb the measured system, leading for example to the exchange of energy. In this project, several realistic detector models have been examined for their back-action on the system. To do this, the dynamics of parts of the detectors has been taken into account explicitly. It has been possible to quantify the detector back-action on the probed system in terms of energy exchange and also modifications of the systems entropy production. Beyond the original intentions, this also enabled the inclusion of external feedback control models, of which a simple one allowed for an interpretation as a Maxwell demon. In this case, the second law had to be modified by an information current entering the system due to the feedback loop to remain consistent. In an attempt to construct an autonomous control loop, the system-detector setup turned out to be a thermo-electric generator converting a temperature gradient into electric power, with an efficiency bounded by Carnot efficiency. When reduced to the system, the interaction with the detector and controller unit effectively mimicked a Maxwell demon. In particular this all-inclusive description of a Maxwell demon allows much more quantitative statements than Landauers principle, and the corresponding publication has received some public attention too (discussion e.g. in phys.org, Scientific American, and Science News). Though these principles have been exemplified at hands of a specific model, intrinsic feedback loops can be also constructed for many other models, giving rise to interesting further research venues. The research project has also provided insight into transport through a wide range of models, including quantum-critical ones. Here, it was found that within the weak-coupling approximation transport signatures such as the net current faithfully reflect the original phase diagram even in far-fromequilibrium regimes (where local quantities do not) and also in presence of disorder. For stronger system-reservoir interactions it is however still an open question how the phase diagram of critical models is modified in presence of dissipation. Regarding the methods, the project led to a significant advance of counting statistics beyond mere particle counting. With including the statistics of energy exchanges, it has become possible to understand the dynamics of entropy production in open systems even in presence of detectors mediating feedback control and also in particular strong-coupling regimes. A general theory of counting statistics in the strong-coupling regime – e.g. in non-interacting models – is however still an interesting open question.
Publications
- Charge Qubit Purification by an Electronic Feedback Loop, Physical Review Letters 107, 050501 (2011)
G. Kiesslich, G. Schaller, C. Emary, and T. Brandes
- Criticality in transport through the quantum Ising chain, Physical Review Letters 109, 240402 (2012)
M. Vogl, G. Schaller, and T. Brandes
(See online at https://doi.org/10.1103/PhysRevLett.109.240402) - Stochastic Thermodynamics for ”Maxwell demon” feedbacks, Europhysics Letters 99, 30003 (2012)
M. Esposito and G. Schaller
(See online at https://doi.org/10.1209/0295-5075/99/30003) - Single electron transistor strongly coupled to vibrations: Counting Statistics and Fluctuation Theorem, New Journal of Physics 15, 033032 (2013)
G. Schaller, T. Krause, T. Brandes, and M. Esposito
(See online at https://doi.org/10.1088/1367-2630/15/3/033032) - Thermodynamics of a physical model implementing a Maxwell demon, Physical Review Letters 110, 040601 (2013)
P. Strasberg, G. Schaller, T. Brandes, and M. Esposito
(See online at https://doi.org/10.1103/PhysRevLett.110.040601) - Open Quantum Systems Far from Equilibrium, Springer Lecture Notes in Physics 881, Springer, (2014)
G. Schaller
