P12: Driven dissipative phase transitions in open quantum systems
An important parameter for the response of an open quantum system described by a master equation is the dissipative gap separating the lowest negative eigenvalue of the transition-rate matrix from the stationary-state zero eigenvalue. Driven dissipative phase transitions may occur in open systems when this dissipative gap becomes vanishingly small on the scale of the bandwidth of driving.
For bosonic quantum systems, a paradigmatic situation is that of a self-interacting photon mode, examples being a polariton with repulsive Kerr nonlinearity due to photon-atom interaction or a qubit coupled to microwave photons. In the presence of a driving which couples to the boson coordinate, a hysteresis occurs in the mode-occupation, when sweeping back and forth the boson “potential” (e.g., by laser detuning). A key issue is to understand how hysteresis, understood from the linear quantum dynamics of the open system (the photon mode), can be related to nonlinear, classical mean-field equations for its occupation . In this project, we will investigate the role of quantum fluctuations in the hysteresis, which is ignored in the nonlinear mean-field approach. To this end, we combine the master equation approach with the full counting statistics for driven systems in the Floquet description .
A less studied case of systems, in which hysteresis can occur, are hybrid fermion-boson systems, such as molecular transistors, considered as quantum dots coupled to a few discrete vibrational modes. In such systems, the Franck-Condon effect suppresses transition rates involving large changes of the bosonic coordinate relative to “pure electronic” transitions [3,4,5] (see also the project of A. Khedri from the first funding period). In the sec-ond part of this project, we will explore possibilities for driven dissipative phase transitions in such electronic systems with vibrational modes. We will make use of a close formal analogy that we noted  between the hysteretic response in bosonic systems to pumping through nanoelectronic circuits as studied in the RTG : In an appropriate limit, the hysteresis area can be related to the non-adiabatic Landsberg pumping connection.
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