Search results for "markovian dynamics"
showing 10 items of 13 documents
Effective hamiltonian approach to the non-Markovian dynamics in a spin-bath
2010
We investigate the dynamics of a central spin that is coupled to a bath of spins through a non-uniform distribution of coupling constants. Simple analytical arguments based on master equation techniques as well as numerical simulations of the full von Neumann equation of the total system show that the short-time damping and decoherence behaviour of the central spin can be modelled accurately through an effective Hamiltonian involving a single effective coupling constant. The reduced short-time dynamics of the central spin is thus reproduced by an analytically solvable effective Hamiltonian model.
Non-Markovian master equation for the XX central spin model
2008
The non-Markovian correlated projection operator technique is applied to the model of a central spin coupled to a spin bath through non uniform XX Heisenberg coupling. The second order results of the Nakajima-Zwanzig and of the time-convolutionless methods are compared with the exact solution considering a fully polarized initial bath state.
Entanglement control via reservoir engineering in ultracold atomic gases
2013
We study the entanglement of two impurity qubits immersed in a Bose-Einstein condensate (BEC) reservoir. This open quantum system is particularly interesting because the reservoir and system parameters are easily controllable and the reduced dynamics is highly non-Markovian. We show how the model allows for interpolation between a common dephasing scenario and an independent dephasing scenario by simply modifying the wavelength of the superlattice superposed to the BEC, and how this influences the dynamical properties of the impurities. We demonstrate the existence of very rich entanglement dynamics correspondent to different values of reservoir parameters, including phenomena such as entan…
Misbeliefs and misunderstandings about the non-Markovian dynamics of a damped harmonic oscillator
2003
We use the exact solution for the damped harmonic oscillator to discuss some relevant aspects of its open dynamics often mislead or misunderstood. We compare two different approximations both referred to as Rotating Wave Approximation. Using a specific example, we clarify some issues related to non--Markovian dynamics, non--Lindblad type dynamics, and positivity of the density matrix.
Simulating open quantum systems with trapped ions
2005
This paper focuses on the possibility of simulating the open system dynamics of a paradigmatic model, namely the damped harmonic oscillator, with single trapped ions. The key idea consists in using a controllable physical system, i.e. a single trapped ion interacting with an engineered reservoir, to simulate the dynamics of other open systems usually difficult to study. The exact dynamics of the damped harmonic oscillator under very general conditions is firstly derived. Some peculiar characteristic of the system’s dynamics are then presented. Finally a way to implement with trapped ion the specific quantum simulator of interest is discussed.
Class of exact memory-kernel master equations
2016
A well-known situation in which a non-Markovian dynamics of an open quantum system $S$ arises is when this is coherently coupled to an auxiliary system $M$ in contact with a Markovian bath. In such cases, while the joint dynamics of $S$-$M$ is Markovian and obeys a standard (bipartite) Lindblad-type master equation (ME), this is in general not true for the reduced dynamics of $S$. Furthermore, there are several instances (\eg the dissipative Jaynes-Cummings model) in which a {\it closed} ME for the $S$'s state {\it cannot} even be worked out. Here, we find a class of bipartite Lindblad-type MEs such that the reduced ME of $S$ can be derived exactly and in a closed form for any initial produ…
Non-Markovian dynamics of a single electron spin coupled to a nuclear spin bath
2008
We apply the time-convolutionless (TCL) projection operator technique to the model of a central spin which is coupled to a spin bath via nonuniform Heisenberg interaction. The second-order results of the TCL method for the coherences and populations of the central spin are determined analytically and compared with numerical simulations of the full von Neumann equation of the total system. The TCL approach is found to yield an excellent approximation in the strong field regime for the description of both the short-time dynamics and the long time behavior.
Competition between memory-keeping and memory-erasing decoherence channels
2014
We study the competing effects of simultaneous Markovian and non-Markovian decoherence mechanisms acting on a single spin. We show the existence of a threshold in the relative strength of such mechanisms above which the spin dynamics becomes fully Markovian, as revealed by the use of several non-Markovianity measures. We identify a measure-dependent nested structure of such thresholds, hinting at a causality relationship among the various non-Markovianity witnesses used in our analysis. Our considerations are then used to argue the unavoidably non-Markovian evolution of a single-electron quantum dot exposed to both intrinsic and Markovian technical noise, the latter of arbitrary strength.
Quantum collision models: Open system dynamics from repeated interactions
2022
We present an extensive introduction to quantum collision models (CMs), also known as repeated interactions schemes: a class of microscopic system-bath models for investigating open quantum systems dynamics whose use is currently spreading in a number of research areas. Through dedicated sections and a pedagogical approach, we discuss the CMs definition and general properties, their use for the derivation of master equations, their connection with quantum trajectories, their application in non-equilibrium quantum thermodynamics, their non-Markovian generalizations, their emergence from conventional system-bath microscopic models and link to the input-output formalism. The state of the art o…
Exciting a Bound State in the Continuum through Multi-Photon Scattering plus Delayed Quantum Feedback
2019
Excitation of a bound state in the continuum (BIC) through scattering is problematic since it is by definition uncoupled. Here, we consider a type of dressed BIC and show that it can be excited in a nonlinear system through multi-photon scattering and delayed quantum feedback. The system is a semi-infinite waveguide with linear dispersion coupled to a qubit, in which a single-photon, dressed BIC is known to exist. We show that this BIC can be populated via multi-photon scattering in the non-Markovian regime, where the photon delay time (due to the qubit-mirror distance) is comparable with the qubit's decay. A similar process excites the BIC existing in an infinite waveguide coupled to two d…