Quantum theory of heating of a single trapped ion

The heating of trapped ions due to the interaction with a {\it quantized environment} is studied {\it without performing the Born-Markov approximation}. A generalized master equation local in time is derived and a novel theoretical approach to solve it analytically is proposed. Our master equation is in the Lindblad form with time dependent coefficients, thus allowing the simulation of the dynamics by means of the Monte Carlo Wave Function (MCWF) method.Comment: 4 pages, 3 figure

Misbelief and misunderstandings on the non--Markovian dynamics of a damped harmonic oscillator

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.Comment: 6 pages, 2 figures, added info: submitted to J. Opt. B: Quantum and Semiclass. Opt., Special Issue of the 10th Central European Workshop on Quantum Optics, reference added, discussion clarifie

Non-Markovian quantum jumps

Open quantum systems that interact with structured reservoirs exhibit non-Markovian dynamics. We present a quantum jump method for treating the dynamics of such systems. This approach is a generalization of the standard Monte Carlo Wave Function (MCWF) method for Markovian dynamics. The MCWF method identifies decay rates with jump probabilities and fails for non-Markovian systems where the time-dependent rates become temporarily negative. Our non-Markovian quantum jump (NMQJ) approach circumvents this problem and provides an efficient unravelling of the ensemble dynamics.Comment: 4 pages, 2 figures.V2: rewritten abstract and introduction, title modified. V3: published version, new example case with photonic band ga

Sudden transition between classical and quantum decoherence

We study the dynamics of quantum and classical correlations in the presence of nondissipative decoherence. We discover a class of initial states for which the quantum correlations, quantified by the quantum discord, are not destroyed by decoherence for times t < \bar{t}. In this initial time interval classical correlations decay. For t > \bar{t}, on the other hand, classical correlations do not change in time and only quantum correlations are lost due to the interaction with the environment. Therefore, at the transition time \bar{t} the open system dynamics exhibits a sudden transition from classical to quantum decoherence regime.Comment: version accepted for publication by Physical Review Letter

Non-Markovian reservoir-dependent squeezing

The squeezing dynamics of a damped harmonic oscillator are studied for different types of environment without making the Markovian approximation. The squeezing dynamics of a coherent state depend on the reservoir spectrum in a unique way that can, in the weak coupling approximation, be analyzed analytically. Comparison of squeezing dynamics for Ohmic, sub-Ohmic and super-Ohmic environments is done showing a clear connection between the squeezing--non-squeezing oscillations and reservoir structure. Understanding the effects occurring due to structured reservoirs is important both from a purely theoretical point of view and in connection with evolving experimental techniques and future quantum computing applications.Comment: 8 pages, 2 figures, submitted to Proceedings of CEWQO200

Thermodynamic fingerprints of non-Markovianity in a system of coupled superconducting qubits

The exploitation and characterization of memory effects arising from the interaction between system and environment is a key prerequisite for quantum reservoir engineering beyond the standard Markovian limit. In this paper we investigate a prototype of non-Markovian dynamics experimentally implementable with superconducting qubits. We rigorously quantify non-Markovianity highlighting the effects of the environmental temperature on the Markovian to non-Markovian crossover. We investigate how memory effects influence, and specifically suppress, the ability to perform work on the driven qubit. We show that the average work performed on the qubit can be used as a diagnostic tool to detect the presence or absence of memory effects.Comment: 9 page

Lindblad and non--Lindblad type dynamics of a quantum Brownian particle

The dynamics of a typical open quantum system, namely a quantum Brownian particle in a harmonic potential, is studied focussing on its non-Markovian regime. Both an analytic approach and a stochastic wave function approach are used to describe the exact time evolution of the system. The border between two very different dynamical regimes, the Lindblad and non-Lindblad regimes, is identified and the relevant physical variables governing the passage from one regime to the other are singled out. The non-Markovian short time dynamics is studied in detail by looking at the mean energy, the squeezing, the Mandel parameter and the Wigner function of the system.Comment: 13 pages, 4 figures, v2:added discussion on Wigner function, squeezing, and Mandel paramete

Entanglement trapping in a non-stationary structured reservoir

We study a single two-level atom interacting with a reservoir of modes defined by a reservoir structure function with a frequency gap. Using the pseudomodes technique, we derive the main features of a trapping state formed in the weak coupling regime. Utilising different entanglement measures we show that strong correlations and entanglement between the atom and the modes are in existence when this state is formed. Furthermore, an unexpected feature for the reservoir is revealed. In the long time limit and for weak coupling the reservoir spectrum is not constant in time.Comment: 10 pages, 16 figure