Quantifying entanglement in multipartite conditional states of open quantum systems by measurements of their photonic environment

A key lesson of the decoherence program is that information flowing out from an open system is stored in the quantum state of the surroundings. Simultaneously, quantum measurement theory shows that the evolution of any open system when its environment is measured is nonlinear and leads to pure states conditioned on the measurement record. Here we report the discovery of a fundamental relation between measurement and entanglement which is characteristic of this scenario. It takes the form of a scaling law between the amount of entanglement in the conditional state of the system and the probabilities of the experimental outcomes obtained from measuring the state of the environment. Using the scaling, we construct the distribution of entanglement over the ensemble of experimental outcomes for standard models with one open channel and provide rigorous results on finite-time disentanglement in systems coupled to non-Markovian baths. The scaling allows the direct experimental detection and quantification of entanglement in conditional states of a large class of open systems by quantum tomography of the bath.Comment: 12 pages (including supplementary information), 4 figure

Entanglement dynamics in open two-qubit systems via diffusive quantum trajectories

We use quantum diffusive trajectories to prove that the time evolution of two-qubit entanglement under spontaneous emission can be fully characterized by optimal continuous monitoring. We analytically determine this optimal unraveling and derive a deterministic evolution equation for the system's concurrence. Furthermore, we propose an experiment to monitor the entanglement dynamics in bipartite two-level systems and to determine the disentanglement time from a single trajectory.Comment: 4 pages, 2 figures, changed title, abstract and fig. 2, corrected typo

Semiclassical propagator of the Wigner function

Propagation of the Wigner function is studied on two levels of semiclassical propagation, one based on the van-Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a \emph{pair} of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.Comment: 4 pages, 3 figure

Quantom theory of amplifying random media

A quantum theory of lasing in random media is presented. The theory constitutes a generalization of the standard laser theory, accounting for lasing in resonators with spectrally overlapping modes due to large outcoupling losses, and incorporating in a natural fashion the statistical properties of chaotic modes when apply to lasers in random media or inside chaotic resonators. We study the photocount statistics of the radiation emitted from a chaotic laser resonator in the regime of single-mode lasing. The random spatial variations of the resonator eigenfunctions are incorporated in the theory, and showed to lead to strong mode-to-mode uctuations of the laser emission. The distribution of the mean photocount over an ensemble of modes changes qualitatively at the lasing transition, and displays up to three peaks above the lasing threshold. We then address the quantization of the electromagnetic field in weakly confining resonators using Feshbach's projection technique. We consider both inhomogeneous dielectric resonators with a scalar dielectric constant epsilon(r) and cavities defined by mirrors of arbitrary shape. The field is quantized in terms of a set of resonator and bath modes. We rigorously show that the field Hamiltonian reduces to the system-and-bath Hamiltonian of quantum optics. The field dynamics is investigated using the inputoutput theory of Gardiner and Collet. In the case of strong coupling to the external radiation field we find spectrally overlapping resonator modes. The mode dynamics is coupled due to the damping and noise in icted by the external radiation field. We derived Langevin equations and a master equation for the resonator modes. For linear optical systems, including gain/loss contributions, it is shown that the field dynamics is described by the system S matrix. For wave chaotic resonator the dynamics is determined by a non-Hermitian random matrix. After including an amplifying medium, we use the open-resonator dynamics to construct a quantum theory for lasing in random media. We investigate the emission spectrum of lasers in cavities with overlapping modes operating in the single-mode regime. The noise properties of such lasers are seen to differ from traditional lasers due to the presence of excess noise. Our theory not only accounts for the Petermann linewidth enhancement, but predicts deviations of the laser line from a Lorentzian shape. To conclude, the emission spectrum of random lasers is discussed