Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom

Published versio

Critical behavior in ultra-strong-coupled oscillators

We investigate the strong coupling regime of a linear $x$-$x$ coupled harmonic oscillator system, by performing a direct diagonalization of the hamiltonian. It is shown that the $x$-$x$ coupled hamiltonian can be equivalently described by a Mach-Zehnder-type interferometer with a quadratic unitary operation in each of its arms. We show a sharp transition of the unitary operation from an elliptical phase rotator to an elliptical squeezer as the coupling gets stronger, which leads to the continuous generation of entanglement, even for a significantly thermal state, in the ultra-strong coupled regime. It is also shown that this critical regime cannot be achieved by a classical Hookian coupling. Finally, the effect of a finite-temperature environment is analyzed, showing that entanglement can still be generated from a thermal state in the ultra-strong coupled regime, but is destroyed rapidly

Decoherence and asymptotic entanglement in open quantum dynamics

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations become comparable with quantum fluctuations. Then we solve the master equation for two independent harmonic oscillators interacting with an environment in the asymptotic long-time regime. We give a description of the continuous-variable asymptotic entanglement in terms of the covariance matrix of the quantum states of the considered system for an arbitrary Gaussian input state. Using the Peres-Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that the two non-interacting systems immersed in a common environment become asymptotically entangled for certain environments, so that in the long-time regime they manifest non-local quantum correlations.Comment: 17 pages, 2 figures; talk at the X International Conference on Squeezed States and Uncertainty Relations (ICSSUR), Bradford, UK (2007

Entanglement dynamics during decoherence

The evolution of the entanglement between oscillators that interact with the same environment displays highly non-trivial behavior in the long time regime. When the oscillators only interact through the environment, three dynamical phases were identified and a simple phase diagram characterizing them was presented. Here we generalize those results to the cases where the oscillators are directly coupled and we show how a degree of mixidness can affect the final entanglement. In both cases, entanglement dynamics is fully characterized by three phases (SD: sudden death, NSD: no-sudden death and SDR: sudden death and revivals) which cover a phase diagram that is a simple variant of the previously introduced one. We present results when the oscillators are coupled to the environment through their position and also for the case where the coupling is symmetric in position and momentum (as obtained in the RWA). As a bonus, in the last case we present a very simple derivation of an exact master equation valid for arbitrary temperatures of the environment.Comment: to appear in QIP special issue on Quantum Decoherence and Entanglemen

Entanglement generation in harmonic chains: tagging by squeezing

We address the problem of spring-like coupling between bosons in an open chain configuration where the counter-rotating terms are explicitly included. We show that fruitful insight can be gained by decomposing the time-evolution operator of this problem into a pattern of linear-optics elements. This allows us to provide a clear picture of the effects of the counter-rotating terms in the important problem of long-haul entanglement distribution. The analytic control over the variance matrix of the state of the bosonic register allows us to track the dynamics of the entanglement. This helps in designing a global addressing scheme, complemented by a proper initialization of the register, which quantitatively improves the entanglement between the extremal oscillators in the chain, thus providing a strategy for feasible long distance entanglement distribution.Comment: 8 pages, 8 figures, RevTeX