Exploring a strongly non-Markovian behavior

Hu-Ping Peng, Meng Xu

Non-Markovian environments with finite memory pose significant challenges for simulating open quantum many-body dynamics. Here, we employ the Lindblad-pseudomode approach to investigate a transverse-field Ising chain collectively coupled to a structured bosonic environment with a Lorentzian noise spectrum. The pseudomode representation enables an efficient treatment of strong system-bath coupling and non-Markovian memory effects. We show that the common environment induces effective long-range spin interactions, leading to bath-induced localization and enhanced ferromagnetic ordering beyond the behavior of the isolated chain. Our findings elucidate how structured environments can fundamentally alter many-body dynamics and demonstrate the utility of pseudomode methods for exploring strongly coupled open quantum systems beyond the Markovian regime.

Dariusz Chruściński, Andrzej Kossakowski

́Angel Rivas, Susana F. Huelga

Michael W. Jack, Matthew J. Collett, Daniel F. Walls

We present a formulation of non-Markovian quantum trajectories for open systems from a measurement theory perspective. In our treatment there are three distinct ways in which non-Markovian behavior can arise: a mode-dependent coupling between the bath (reservoir) and system, a dispersive bath, and spectral detection of the output into the bath. In the first two cases the non-Markovian behavior is intrinsic to the interaction; in the third case the non-Markovian behavior arises from the method of detection. We focus in detail on the trajectories that simulate real-time spectral detection of the light emitted from a localized system. In this case the non-Markovian behavior arises from the uncertainty in the time of emission of particles that are later detected. The results of computer simulations of the spectral detection of the spontaneous emission from a strongly driven two-level atom are presented.

Stefano Longhi

Spontaneous emission of a quantum emitter, such as an excited atom, is a fundamental process in quantum electrodynamics (QED), typically associated with exponential decay to the ground state accompanied by irreversible photon emission. This simple Markovian picture, however, is profoundly modified in the presence of time-delayed feedback, structured continua, or cooperative emission, as occurs when an emitter radiates in front of a mirror, when several emitters radiate collectively, or in the case of a giant atom. In such regimes, strong non-Markovian dynamics arise from photon reabsorption and interference effects, leading to pronounced deviations from exponential decay. Here we demonstrate the emergence of exceptional points (EPs) in these highly non-Markovian waveguide-QED environments, i.e., non-Markovian EPs. These EPs appear directly in the relaxation dynamics as sharp transitions to oscillatory behavior, manifested by the appearance of real zeros in the excited-state amplitude. We analyze in detail the spontaneous emission of giant atoms with two or more coupling points, highlighting the mechanisms leading to non-Markovian EPs, and show that similar phenomena arise in other waveguide-QED settings, such as the collective spontaneous emission of spatially separated point-like emitters. Our results reveal waveguide-QED systems as experimentally accessible platforms for realizing and exploring non-Markovian EP physics.

Ali Abu-Nada, Subhashish Banerjee, Vivek Balasaheb Sabale

The non-Markovian depolarizing channel is explored from the perspective of understanding its non-Markovian behavior as well as the occurrence of singularities. The study brings together the various ways to identify and quantify non-Markovianity. This includes dynamical techniques such as quantum information backflow witness, Breuer-Laine-Piilo, Rivas-Huelga-Plenio, and Hall-Cresser-Li-Andersson measures. In addition, geometrical visualization of non-Markovian effects is presented using the variation in the volume of accessible states during dynamical evolution. Further, a trajectory-based visualization of the dynamical map within the parameter space is presented. The trajectories traced during evolution demonstrate the loss of CP divisibility and the emergence of non-Markovianity under systematic variations of the system parameters. The effects of increasing system dimensions and qubit numbers on singularity and non-Markovianity are presented, with an extension of characterization techniques to higher-dimensional systems.