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Accueil > EN > Research Areas > Complex Systems Dynamics > Optical Systems > Quantum Optics and Quantum Information

Multimode quantum optics and multipartite entanglement

par Giuseppe PATERA, Mikhail KOLOBOV - publié le

Activités de Recherche :

Multimode quantum optics, in general, studies the properties of quantum noise and quantum correlations in optical systems characterized by a large number of modes. An optical image is an example of multimode optical field since it can be decomposed over a basis of transverse modes (i.e. Hermite-Gauss, Laguerre-Gauss modes).

Mainly interested to optical systems with a large number of photons, also known as Continuous Variable (CV) regime, our work is focused on

  • the study of compact and scalable sources and their dynamical properties for the generation of multimode CV quantum optical states :
    in multimode quantum states, quantum correlations are shared and distributed among the parties, according to the source, in order to exploit the generated states for quantum tasks like teleportation, quantum key distribution or one-way quantum computation. Typical states of interest are for example Green-Horne-Zeilinger states, Werner states, cluster states.
    We are actually concerned with the Synchronously Pumped Optical Parametric Oscillator (SPOPO) generating temporal multimode quantum states and Optical Parametric Amplifiers (OPA) pumped with multiple pumps and generating spatial multimode quantum states. In both the systems the multimode quantum regime is obtained due to the interplay between a multimode pumping field (in the SPOPO a mode-locked field, in the OPA a spatially multiple pump field) and the parametric down-conversion inside a quadratic non-linear medium.
  • the study of fundamental properties and characterization of CV quantum states :
    Typical sources exploiting second order non-linearities generates quantum states whose statistical distribution of noise fluctuations can be completely described by a Gaussian characteristic function. In this case all the information is contained in the covariance matrix.
    We study the symplectic invariants associated to a given state in order to characterize the amount of multipartite entanglement ; in particular we are interested to the structure of multipartite correlations generated in systems such as multimode OPOs and OPAs. For those systems we proved that the scaling properties of entanglement as a function of the number N of parties considered are different and depends of the structure of the intermode coupling matrix (also known as the adjacency matrix).
    We developped a generalized theory of the symplectic characterization of multimode entanglement by considering the spatial and temporal degrees of freedom of the modes involved in the entangling process. It is possible, in fact, to define in a more general way a correlation matrix, which is the generalization of the covariance matrix, by keeping into account the space and time variables. Also, for systems that are homogeneous in space and stationary in time, it is possible to define a spectral density component of correlation function in the Fourier domain depending on one space-time frequency. As a consequence every symplectic invariant can be completely generalized to the space and time degrees of freedom and the multimode entanglement results to be dependent on these variables too. Accordingly defined a temporal and a spatial dimensions that characterize the structure of multipartite entanglement. In particular we shown that such dimensions depends on the number N of modes participating to multimode entanglement.