Cat state, sub-Planck structure and weak measurement

Heisenberg-limited and weak measurements are the two intriguing notions, used in recent times for enhancing the sensitivity of measurements in quantum metrology. Using a quantum cat state, endowed with sub-Planck structure, we connect these two novel concepts. It is demonstrated that these two phenomena manifest in complementary regimes, depending upon the degree of overlap between the mesoscopic states constituting the cat state under consideration. In particular, we find that when sub-Planck structure manifests, the imaginary weak value is obscured and vice-versa.Comment: 7 pages, 7 figure

Energy Eigenvalues For Supersymmetric Potentials via Quantum Hamilton-Jacobi Formalism

Using quantum Hamilton-Jacobi formalism of Leacock and Padgett, we show how to obtain the exact eigenvalues for supersymmetric (SUSY) potentials.Comment: 15 pages Latex Compile twice to get cross references correct. 2 Figures not included. Requests for figures should be sent to [email protected]

Designing bound states in a band as a model for a quantum network

We provide a model of a one dimensional quantum network, in the framework of a lattice using Von Neumann and Wigner's idea of bound states in a continuum. The localized states acting as qubits are created by a controlled deformation of a periodic potential. These wave functions lie at the band edges and are defects in a lattice. We propose that these defect states, with atoms trapped in them, can be realized in an optical lattice and can act as a model for a quantum network.Comment: 8 pages, 10 figure