Entanglement dynamics for two harmonic oscillators coupled to independent environments

We study the entanglement evolution between two harmonic oscillators having different free frequencies each leaking into an independent bath. We use an exact solution valid in the weak coupling limit and in the short time non-Markovian regime. The reservoirs are identical and characterized by an Ohmic spectral distribution with Lorents-Drude cut-off. This work is an extension of the case reported in [Phys. Rev. A 80, 062324 (2009)] where the oscillators have the same free frequency.Comment: 8 pages, 3 figures, submitted to Physica Script

Time resolved quantum dynamics of double ionization in strong laser fields

Quantum calculations of a 1+1-dimensional model for double ionization in strong laser fields are used to trace the time evolution from the ground state through ionization and rescattering to the two electron escape. The subspace of symmetric escape, a prime characteristic of nonsequential double ionization, remains accessible by a judicious choice of 1-d coordinates for the electrons. The time resolved ionization fluxes show the onset of single and double ionization, the sequence of events during the pulse, and the influences of pulse duration, and reveal the relative importance of sequential and non-sequential double ionization, even when ionization takes place during the same field cycle

Quantum model for double ionization of atoms in strong laser fields

We discuss double ionization of atoms in strong laser pulses using a reduced dimensionality model. Following the insights obtained from an analysis of the classical mechanics of the process, we confine each electron to move along the lines that point towards the two-particle Stark saddle in the presence of a field. The resulting effective two dimensional model is similar to the aligned electron model, but it enables correlated escape of electrons with equal momenta, as observed experimentally. The time-dependent solution of the Schr\"odinger equation allows us to discuss in detail the time dynamics of the ionization process, the formation of electronic wave packets and the development of the momentum distribution of the outgoing electrons. In particular, we are able to identify the rescattering process, simultaneous direct double ionization during the same field cycle, as well as other double ionization processes. We also use the model to study the phase dependence of the ionization process.Comment: 14 pages, 16 figures, version accepted for publication in Phys. Rev.

Dynamics of quantum entanglement in Gaussian open systems

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the dynamics of entanglement for a system consisting of two uncoupled harmonic oscillators interacting with a thermal environment. Using Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the evolution of entanglement in terms of the covariance matrix for a Gaussian input state. For some values of the temperature of environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a repeated collapse and revival of entanglement take place. We determine the asymptotic Gaussian maximally entangled mixed states (GMEMS) and their corresponding asymptotic maximal logarithmic negativity.Comment: 10 pages, 2 figures; talk at the International Workshop on Quantum Non-Stationary Systems, Brasilia, Brazil (2009

Entanglement dynamics of bipartite system in squeezed vacuum reservoirs

Entanglement plays a crucial role in quantum information protocols, thus the dynamical behavior of entangled states is of a great importance. In this paper we suggest a useful scheme that permits a direct measure of entanglement in a two-qubit cavity system. It is realized in the cavity-QED technology utilizing atoms as fying qubits. To quantify entanglement we use the concurrence. We derive the conditions, which assure that the state remains entangled in spite of the interaction with the reservoir. The phenomenon of sudden death entanglement (ESD) in a bipartite system subjected to squeezed vacuum reservoir is examined. We show that the sudden death time of the entangled states depends on the initial preparation of the entangled state and the parameters of the squeezed vacuum reservoir.Comment: 10 pages, 5 figures, CEWQO17(St Andrews

Multi-mode entanglement of N harmonic oscillators coupled to a non-Markovian reservoir

Multi-mode entanglement is investigated in the system composed of $N$ coupled identical harmonic oscillators interacting with a common environment. We treat the problem very general by working with the Hamiltonian without the rotating-wave approximation and by considering the environment as a non-Markovian reservoir to the oscillators. We invoke an $N$-mode unitary transformation of the position and momentum operators and find that in the transformed basis the system is represented by a set of independent harmonic oscillators with only one of them coupled to the environment. Working in the Wigner representation of the density operator, we find that the covariance matrix has a block diagonal form that it can be expressed in terms of multiples of $3\times 3$ and $4\times 4$ matrices. This simple property allows to treat the problem to some extend analytically. We illustrate the advantage of working in the transformed basis on a simple example of three harmonic oscillators and find that the entanglement can persists for long times due to presence of constants of motion for the covariance matrix elements. We find that, in contrast to what one could expect, a strong damping of the oscillators leads to a better stationary entanglement than in the case of a weak damping.Comment: 21 pages, 4 figure

Characterization of bipartite states using a single homodyne detector

We suggest a scheme to reconstruct the covariance matrix of a two-mode state using a single homodyne detector plus a polarizing beam splitter and a polarization rotator. It can be used to fully characterize bipartite Gaussian states and to extract relevant informations on generic states.Comment: 7 pages, 1 figur

Markovian Master Equations: A Critical Study

We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact numerical simulations of the evolution of the global system, we precisely delimit their validity regimes and assess the robustness of the assumptions usually made in the process of deriving the reduced dynamics. The proposed method is sufficiently general to suggest that the conclusions made here are widely applicable to a large class of settings involving interacting chains subject to a weak interaction with an environment.Comment: 40 pages, 14 figures, final versio

Quantifying decoherence in continuous variable systems

We present a detailed report on the decoherence of quantum states of continuous variable systems under the action of a quantum optical master equation resulting from the interaction with general Gaussian uncorrelated environments. The rate of decoherence is quantified by relating it to the decay rates of various, complementary measures of the quantum nature of a state, such as the purity, some nonclassicality indicators in phase space and, for two-mode states, entanglement measures and total correlations between the modes. Different sets of physically relevant initial configurations are considered, including one- and two-mode Gaussian states, number states, and coherent superpositions. Our analysis shows that, generally, the use of initially squeezed configurations does not help to preserve the coherence of Gaussian states, whereas it can be effective in protecting coherent superpositions of both number states and Gaussian wave packets.Comment: Review article; 36 pages, 19 figures; typos corrected, references adde